Daily Papers

Prompt learning has become the most effective paradigm for adapting large pre-trained vision-language models (VLMs) to downstream tasks. Recently, unsupervised prompt tuning methods, such as UPL and POUF, directly leverage pseudo-labels as supervisory information to fine-tune additional adaptation modules on unlabeled data. However, inaccurate pseudo labels easily misguide the tuning process and result in poor representation capabilities. In light of this, we propose Training-Free Unsupervised Prompts (TFUP), which maximally preserves the inherent representation capabilities and enhances them with a residual connection to similarity-based prediction probabilities in a training-free and labeling-free manner. Specifically, we integrate both instance confidence and prototype scores to select representative samples, which are used to customize a reliable Feature Cache Model (FCM) for training-free inference. Then, we design a Multi-level Similarity Measure (MSM) that considers both feature-level and semantic-level similarities to calculate the distance between each test image and the cached sample as the weight of the corresponding cached label to generate similarity-based prediction probabilities. In this way, TFUP achieves surprising performance, even surpassing the training-base method on multiple classification datasets. Based on our TFUP, we propose a training-based approach (TFUP-T) to further boost the adaptation performance. In addition to the standard cross-entropy loss, TFUP-T adopts an additional marginal distribution entropy loss to constrain the model from a global perspective. Our TFUP-T achieves new state-of-the-art classification performance compared to unsupervised and few-shot adaptation approaches on multiple benchmarks. In particular, TFUP-T improves the classification accuracy of POUF by 3.3% on the most challenging Domain-Net dataset.

Cell instance segmentation (CIS) is crucial for identifying individual cell morphologies in histopathological images, providing valuable insights for biological and medical research. While unsupervised CIS (UCIS) models aim to reduce the heavy reliance on labor-intensive image annotations, they fail to accurately capture cell boundaries, causing missed detections and poor performance. Recognizing the absence of error-free instances as a key limitation, we present COIN (COnfidence score-guided INstance distillation), a novel annotation-free framework with three key steps: (1) Increasing the sensitivity for the presence of error-free instances via unsupervised semantic segmentation with optimal transport, leveraging its ability to discriminate spatially minor instances, (2) Instance-level confidence scoring to measure the consistency between model prediction and refined mask and identify highly confident instances, offering an alternative to ground truth annotations, and (3) Progressive expansion of confidence with recursive self-distillation. Extensive experiments across six datasets show COIN outperforming existing UCIS methods, even surpassing semi- and weakly-supervised approaches across all metrics on the MoNuSeg and TNBC datasets. The code is available at https://github.com/shjo-april/COIN.

Vision-language models (VLMs) benefit from multiple vision encoders, but naively stacking them yields diminishing returns while multiplying inference costs. We propose SCOPE, a Mixture-of-Encoders (MoEnc) framework that dynamically selects one specialized encoder per image-text pair via instance-level routing, unlike token-level routing in traditional MoE. SCOPE maintains a shared encoder and a pool of routed encoders. A lightweight router uses cross-attention between text prompts and shared visual features to select the optimal encoder from the routed encoders. To train this router, we introduce dual entropy regularization with auxiliary losses to balance dataset-level load distribution with instance-level routing confidence. Remarkably, SCOPE with one shared plus one routed encoder outperforms models using all four extra encoders simultaneously, while reducing compute by 24-49\%. This demonstrates that intelligent encoder selection beats brute-force aggregation, challenging the prevailing paradigm in multi-encoder VLMs.

This paper presents a new methodology to alleviate the fundamental trade-off between accuracy and latency in spiking neural networks (SNNs). The approach involves decoding confidence information over time from the SNN outputs and using it to develop a decision-making agent that can dynamically determine when to terminate each inference. The proposed method, Dynamic Confidence, provides several significant benefits to SNNs. 1. It can effectively optimize latency dynamically at runtime, setting it apart from many existing low-latency SNN algorithms. Our experiments on CIFAR-10 and ImageNet datasets have demonstrated an average 40% speedup across eight different settings after applying Dynamic Confidence. 2. The decision-making agent in Dynamic Confidence is straightforward to construct and highly robust in parameter space, making it extremely easy to implement. 3. The proposed method enables visualizing the potential of any given SNN, which sets a target for current SNNs to approach. For instance, if an SNN can terminate at the most appropriate time point for each input sample, a ResNet-50 SNN can achieve an accuracy as high as 82.47% on ImageNet within just 4.71 time steps on average. Unlocking the potential of SNNs needs a highly-reliable decision-making agent to be constructed and fed with a high-quality estimation of ground truth. In this regard, Dynamic Confidence represents a meaningful step toward realizing the potential of SNNs.

Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confidence. However, this can fail to represent uncertainty arising when the input is ambiguous, e.g., due to occlusion or blurriness. This work addresses this issue and explicitly models the uncertainty by hedging the location of each input in the embedding space. We introduce the hedged instance embedding (HIB) in which embeddings are modeled as random variables and the model is trained under the variational information bottleneck principle. Empirical results on our new N-digit MNIST dataset show that our method leads to the desired behavior of hedging its bets across the embedding space upon encountering ambiguous inputs. This results in improved performance for image matching and classification tasks, more structure in the learned embedding space, and an ability to compute a per-exemplar uncertainty measure that is correlated with downstream performance.

Large language models (LLMs) excel at zero-shot inference but continue to struggle with complex, multi-step reasoning. Recent methods that augment LLMs with intermediate reasoning steps such as Chain of Thought (CoT) and Program of Thought (PoT) improve performance but often produce undesirable solutions, especially in algorithmic domains. We introduce Per-Instance Program Synthesis (PIPS), a method that generates and refines programs at the instance-level using structural feedback without relying on task-specific guidance or explicit test cases. To further improve performance, PIPS incorporates a confidence metric that dynamically chooses between direct inference and program synthesis on a per-instance basis. Experiments across three frontier LLMs and 30 benchmarks including all tasks of Big Bench Extra Hard (BBEH), visual question answering tasks, relational reasoning tasks, and mathematical reasoning tasks show that PIPS improves the absolute harmonic mean accuracy by up to 8.6% and 9.4% compared to PoT and CoT respectively, and reduces undesirable program generations by 65.1% on the algorithmic tasks compared to PoT with Gemini-2.0-Flash.

Rip currents are strong, localized and narrow currents of water that flow outwards into the sea, causing numerous beach-related injuries and fatalities worldwide. Accurate identification of rip currents remains challenging due to their amorphous nature and the lack of annotated data, which often requires expert knowledge. To address these issues, we present RipVIS, a large-scale video instance segmentation benchmark explicitly designed for rip current segmentation. RipVIS is an order of magnitude larger than previous datasets, featuring 184 videos (212,328 frames), of which 150 videos (163,528 frames) are with rip currents, collected from various sources, including drones, mobile phones, and fixed beach cameras. Our dataset encompasses diverse visual contexts, such as wave-breaking patterns, sediment flows, and water color variations, across multiple global locations, including USA, Mexico, Costa Rica, Portugal, Italy, Greece, Romania, Sri Lanka, Australia and New Zealand. Most videos are annotated at 5 FPS to ensure accuracy in dynamic scenarios, supplemented by an additional 34 videos (48,800 frames) without rip currents. We conduct comprehensive experiments with Mask R-CNN, Cascade Mask R-CNN, SparseInst and YOLO11, fine-tuning these models for the task of rip current segmentation. Results are reported in terms of multiple metrics, with a particular focus on the F_2 score to prioritize recall and reduce false negatives. To enhance segmentation performance, we introduce a novel post-processing step based on Temporal Confidence Aggregation (TCA). RipVIS aims to set a new standard for rip current segmentation, contributing towards safer beach environments. We offer a benchmark website to share data, models, and results with the research community, encouraging ongoing collaboration and future contributions, at https://ripvis.ai.

Traditionally, algorithms that learn to segment object instances in 2D images have heavily relied on large amounts of human-annotated data. Only recently, novel approaches have emerged tackling this problem in an unsupervised fashion. Generally, these approaches first generate pseudo-masks and then train a class-agnostic detector. While such methods deliver the current state of the art, they often fail to correctly separate instances overlapping in 2D image space since only semantics are considered. To tackle this issue, we instead propose to cut the semantic masks in 3D to obtain the final 2D instances by utilizing a point cloud representation of the scene. Furthermore, we derive a Spatial Importance function, which we use to resharpen the semantics along the 3D borders of instances. Nevertheless, these pseudo-masks are still subject to mask ambiguity. To address this issue, we further propose to augment the training of a class-agnostic detector with three Spatial Confidence components aiming to isolate a clean learning signal. With these contributions, our approach outperforms competing methods across multiple standard benchmarks for unsupervised instance segmentation and object detection.

Survival prediction using whole slide images (WSIs) can be formulated as a multiple instance learning (MIL) problem. However, existing MIL methods often fail to explicitly capture pathological heterogeneity within WSIs, both globally -- through long-tailed morphological distributions, and locally through -- tile-level prediction uncertainty. Optimal transport (OT) provides a principled way of modeling such heterogeneity by incorporating marginal distribution constraints. Building on this insight, we propose OTSurv, a novel MIL framework from an optimal transport perspective. Specifically, OTSurv formulates survival predictions as a heterogeneity-aware OT problem with two constraints: (1) global long-tail constraint that models prior morphological distributions to avert both mode collapse and excessive uniformity by regulating transport mass allocation, and (2) local uncertainty-aware constraint that prioritizes high-confidence patches while suppressing noise by progressively raising the total transport mass. We then recast the initial OT problem, augmented by these constraints, into an unbalanced OT formulation that can be solved with an efficient, hardware-friendly matrix scaling algorithm. Empirically, OTSurv sets new state-of-the-art results across six popular benchmarks, achieving an absolute 3.6% improvement in average C-index. In addition, OTSurv achieves statistical significance in log-rank tests and offers high interpretability, making it a powerful tool for survival prediction in digital pathology. Our codes are available at https://github.com/Y-Research-SBU/OTSurv.

Classifier-Free Guidance (CFG) significantly enhances controllability in generative models by interpolating conditional and unconditional predictions. However, standard CFG often employs a static unconditional input, which can be suboptimal for iterative generation processes where model uncertainty varies dynamically. We introduce Adaptive Classifier-Free Guidance (A-CFG), a novel method that tailors the unconditional input by leveraging the model's instantaneous predictive confidence. At each step of an iterative (masked) diffusion language model, A-CFG identifies tokens in the currently generated sequence for which the model exhibits low confidence. These tokens are temporarily re-masked to create a dynamic, localized unconditional input. This focuses CFG's corrective influence precisely on areas of ambiguity, leading to more effective guidance. We integrate A-CFG into a state-of-the-art masked diffusion language model and demonstrate its efficacy. Experiments on diverse language generation benchmarks show that A-CFG yields substantial improvements over standard CFG, achieving, for instance, a 3.9 point gain on GPQA. Our work highlights the benefit of dynamically adapting guidance mechanisms to model uncertainty in iterative generation.

Large language models (LLMs) have shown impressive performance in various reasoning benchmarks with the emergence of Chain-of-Thought (CoT) and its derivative methods, particularly in tasks involving multi-choice questions (MCQs). However, current works all process data uniformly without considering the problem-solving difficulty, which means an excessive focus on simple questions while insufficient to intricate ones. To address this challenge, we inspired by humans using heuristic strategies to categorize tasks and handle them individually, propose to apply the Divide and Conquer to LLMs reasoning. First, we divide questions into different subsets based on the statistical confidence score (CS), then fix nearly resolved sets and conquer demanding nuanced process ones with elaborately designed methods, including Prior Knowledge based Reasoning (PKR) and Filter Choices based Reasoning (FCR), as well as their integration variants. Our experiments demonstrate that this proposed strategy significantly boosts the models' reasoning abilities across nine datasets involving arithmetic, commonsense, and logic tasks. For instance, compared to baseline, we make a striking improvement on low confidence subsets of 8.72\% for AQuA, 15.07\% for ARC Challenge and 7.71\% for RiddleSense. In addition, through extensive analysis on length of rationale and number of options, we verify that longer reasoning paths in PKR could prevent models from referring infer-harmful shortcuts, and also find that removing irrelevant choices in FCR would substantially avoid models' confusion. The code is at https://github.com/AiMijie/Divide-and-Conquer

The alignment of Large Language Models (LLMs) is crucial for ensuring their safety and reliability in practical applications. Direct Preference Optimization (DPO) has emerged as an efficient method that directly optimizes models using preference pairs, significantly reducing resource demands. However, the effectiveness of DPO heavily depends on the data quality, which is frequently compromised by noise. In this work, we propose gamma-PO, a dynamic target margin preference optimization algorithm that adjust reward margins at the pairwise level. By introducing instance-specific margin calibration, gamma-PO strategically prioritizes high-confidence pairs (those demonstrating higher reward margins) while suppressing potential noise from ambiguous pairs. Moreover, gamma-PO is a plug-and-play method, compatible with variants of DPO that rely on reward margin between preference pairs. Across benchmarks such as AlpacaEval2 and Arena-Hard, gamma-PO achieves an average 4.4\% improvement over other baselines, setting new benchmarks for state-of-the-art performance. Additionally, gamma-PO requires minimal code changes and has a negligible impact on training efficiency, making it a robust solution for enhancing LLMs alignment. Our codes are available at https://github.com/sunjie279/gammaPO{https://github.com/sunjie279/gammaPO}.

Text classification tasks often encounter few shot scenarios with limited labeled data, and addressing data scarcity is crucial. Data augmentation with mixup has shown to be effective on various text classification tasks. However, most of the mixup methods do not consider the varying degree of learning difficulty in different stages of training and generate new samples with one hot labels, resulting in the model over confidence. In this paper, we propose a self evolution learning (SE) based mixup approach for data augmentation in text classification, which can generate more adaptive and model friendly pesudo samples for the model training. SE focuses on the variation of the model's learning ability. To alleviate the model confidence, we introduce a novel instance specific label smoothing approach, which linearly interpolates the model's output and one hot labels of the original samples to generate new soft for label mixing up. Through experimental analysis, in addition to improving classification accuracy, we demonstrate that SE also enhances the model's generalize ability.

Process reward models (PRMs) play a central role in guiding inference-time scaling algorithms for large language models (LLMs). However, we observe that even state-of-the-art PRMs can be poorly calibrated and often overestimate success probabilities. To address this, we present a calibration approach, performed via quantile regression, that adjusts PRM outputs to better align with true success probabilities. Leveraging these calibrated success estimates and their associated confidence bounds, we introduce an instance-adaptive scaling (IAS) framework that dynamically adjusts the inference budget based on the estimated likelihood that a partial reasoning trajectory will yield a correct final answer. Unlike conventional methods that allocate a fixed number of reasoning trajectories per query, this approach successfully adapts to each instance and reasoning step when using our calibrated PRMs. Experiments on mathematical reasoning benchmarks show that (i) our PRM calibration method successfully achieves small calibration error, outperforming the baseline methods, (ii) calibration is crucial for enabling effective adaptive scaling, and (iii) the proposed IAS strategy reduces inference costs while maintaining final answer accuracy, utilizing less compute on more confident problems as desired.

Learning from label proportions (LLP) is a promising weakly supervised learning problem. In LLP, a set of instances (bag) has label proportions, but no instance-level labels are given. LLP aims to train an instance-level classifier by using the label proportions of the bag. In this paper, we propose a bag-level data augmentation method for LLP called MixBag, based on the key observation from our preliminary experiments; that the instance-level classification accuracy improves as the number of labeled bags increases even though the total number of instances is fixed. We also propose a confidence interval loss designed based on statistical theory to use the augmented bags effectively. To the best of our knowledge, this is the first attempt to propose bag-level data augmentation for LLP. The advantage of MixBag is that it can be applied to instance-level data augmentation techniques and any LLP method that uses the proportion loss. Experimental results demonstrate this advantage and the effectiveness of our method.

Contrastive learning (CL) continuously achieves significant breakthroughs across multiple domains. However, the most common InfoNCE-based methods suffer from some dilemmas, such as uniformity-tolerance dilemma (UTD) and gradient reduction, both of which are related to a P_{ij} term. It has been identified that UTD can lead to unexpected performance degradation. We argue that the fixity of temperature is to blame for UTD. To tackle this challenge, we enrich the CL loss family by presenting a Model-Aware Contrastive Learning (MACL) strategy, whose temperature is adaptive to the magnitude of alignment that reflects the basic confidence of the instance discrimination task, then enables CL loss to adjust the penalty strength for hard negatives adaptively. Regarding another dilemma, the gradient reduction issue, we derive the limits of an involved gradient scaling factor, which allows us to explain from a unified perspective why some recent approaches are effective with fewer negative samples, and summarily present a gradient reweighting to escape this dilemma. Extensive remarkable empirical results in vision, sentence, and graph modality validate our approach's general improvement for representation learning and downstream tasks.

As large language models (LLMs) are increasingly deployed in user-facing applications, building trust and maintaining safety by accurately quantifying a model's confidence in its prediction becomes even more important. However, finding effective ways to calibrate LLMs - especially when the only interface to the models is their generated text - remains a challenge. We propose APRICOT (auxiliary prediction of confidence targets): A method to set confidence targets and train an additional model that predicts an LLM's confidence based on its textual input and output alone. This approach has several advantages: It is conceptually simple, does not require access to the target model beyond its output, does not interfere with the language generation, and has a multitude of potential usages, for instance by verbalizing the predicted confidence or adjusting the given answer based on the confidence. We show how our approach performs competitively in terms of calibration error for white-box and black-box LLMs on closed-book question-answering to detect incorrect LLM answers.

There is a growing literature on reasoning by large language models (LLMs), but the discussion on the uncertainty in their responses is still lacking. Our aim is to assess the extent of confidence that LLMs have in their answers and how it correlates with accuracy. Confidence is measured (i) qualitatively in terms of persistence in keeping their answer when prompted to reconsider, and (ii) quantitatively in terms of self-reported confidence score. We investigate the performance of three LLMs -- GPT4o, GPT4-turbo and Mistral -- on two benchmark sets of questions on causal judgement and formal fallacies and a set of probability and statistical puzzles and paradoxes. Although the LLMs show significantly better performance than random guessing, there is a wide variability in their tendency to change their initial answers. There is a positive correlation between qualitative confidence and accuracy, but the overall accuracy for the second answer is often worse than for the first answer. There is a strong tendency to overstate the self-reported confidence score. Confidence is only partially explained by the underlying token-level probability. The material effects of prompting on qualitative confidence and the strong tendency for overconfidence indicate that current LLMs do not have any internally coherent sense of confidence.

Recent advances in handling long sequences have facilitated the exploration of long-context in-context learning (ICL). While much of the existing research emphasizes performance improvements driven by additional in-context examples, the influence on the trustworthiness of generated responses remains underexplored. This paper addresses this gap by investigating how increased examples influence predictive uncertainty, an essential aspect in trustworthiness. We begin by systematically quantifying the uncertainty of ICL with varying shot counts, analyzing the impact of example quantity. Through uncertainty decomposition, we introduce a novel perspective on performance enhancement, with a focus on epistemic uncertainty (EU). Our results reveal that additional examples reduce total uncertainty in both simple and complex tasks by injecting task-specific knowledge, thereby diminishing EU and enhancing performance. For complex tasks, these advantages emerge only after addressing the increased noise and uncertainty associated with longer inputs. Finally, we explore the evolution of internal confidence across layers, unveiling the mechanisms driving the reduction in uncertainty.

Large Language Models (LLMs) have acquired ubiquitous attention for their performances across diverse domains. Our study here searches through LLMs' cognitive abilities and confidence dynamics. We dive deep into understanding the alignment between their self-assessed confidence and actual performance. We exploit these models with diverse sets of questionnaires and real-world scenarios and extract how LLMs exhibit confidence in their responses. Our findings reveal intriguing instances where models demonstrate high confidence even when they answer incorrectly. This is reminiscent of the Dunning-Kruger effect observed in human psychology. In contrast, there are cases where models exhibit low confidence with correct answers revealing potential underestimation biases. Our results underscore the need for a deeper understanding of their cognitive processes. By examining the nuances of LLMs' self-assessment mechanism, this investigation provides noteworthy revelations that serve to advance the functionalities and broaden the potential applications of these formidable language models.

Real-world machine learning deployments are characterized by mismatches between the source (training) and target (test) distributions that may cause performance drops. In this work, we investigate methods for predicting the target domain accuracy using only labeled source data and unlabeled target data. We propose Average Thresholded Confidence (ATC), a practical method that learns a threshold on the model's confidence, predicting accuracy as the fraction of unlabeled examples for which model confidence exceeds that threshold. ATC outperforms previous methods across several model architectures, types of distribution shifts (e.g., due to synthetic corruptions, dataset reproduction, or novel subpopulations), and datasets (Wilds, ImageNet, Breeds, CIFAR, and MNIST). In our experiments, ATC estimates target performance 2-4times more accurately than prior methods. We also explore the theoretical foundations of the problem, proving that, in general, identifying the accuracy is just as hard as identifying the optimal predictor and thus, the efficacy of any method rests upon (perhaps unstated) assumptions on the nature of the shift. Finally, analyzing our method on some toy distributions, we provide insights concerning when it works. Code is available at https://github.com/saurabhgarg1996/ATC_code/.

Language models (LMs) should provide reliable confidence estimates to help users detect mistakes in their outputs and defer to human experts when necessary. Asking a language model to assess its confidence ("Score your confidence from 0-1.") is a natural way of evaluating its uncertainty. However, models struggle to provide absolute assessments of confidence (i.e. judging confidence in answering a question independent of other questions) and the coarse-grained scores they produce are not useful for evaluating the correctness of their answers. We propose relative confidence estimation, where we match up questions against each other and ask the model to make relative judgments of confidence ("Which question are you more confident in answering correctly?"). Treating each question as a "player" in a series of matchups against other questions and the model's preferences as match outcomes, we can use rank aggregation methods like Elo rating and Bradley-Terry to translate the model's confidence preferences into confidence scores. We evaluate relative confidence estimation against absolute confidence estimation and self-consistency confidence methods on five state-of-the-art LMs -- GPT-4, GPT-4o, Gemini 1.5 Pro, Claude 3.5 Sonnet, and Llama 3.1 405B -- across 14 challenging STEM, social science, and commonsense reasoning question answering tasks. Our results demonstrate that relative confidence estimation consistently provides more reliable confidence scores than absolute confidence estimation, with average gains of 3.5% in selective classification AUC over direct absolute confidence estimation methods and 1.7% over self-consistency approaches across all models and datasets.

Empowering large language models to accurately express confidence in their answers is essential for trustworthy decision-making. Previous confidence elicitation methods, which primarily rely on white-box access to internal model information or model fine-tuning, have become less suitable for LLMs, especially closed-source commercial APIs. This leads to a growing need to explore the untapped area of black-box approaches for LLM uncertainty estimation. To better break down the problem, we define a systematic framework with three components: prompting strategies for eliciting verbalized confidence, sampling methods for generating multiple responses, and aggregation techniques for computing consistency. We then benchmark these methods on two key tasks-confidence calibration and failure prediction-across five types of datasets (e.g., commonsense and arithmetic reasoning) and five widely-used LLMs including GPT-4 and LLaMA 2 Chat. Our analysis uncovers several key insights: 1) LLMs, when verbalizing their confidence, tend to be overconfident, potentially imitating human patterns of expressing confidence. 2) As model capability scales up, both calibration and failure prediction performance improve. 3) Employing our proposed strategies, such as human-inspired prompts, consistency among multiple responses, and better aggregation strategies can help mitigate this overconfidence from various perspectives. 4) Comparisons with white-box methods indicate that while white-box methods perform better, the gap is narrow, e.g., 0.522 to 0.605 in AUROC. Despite these advancements, none of these techniques consistently outperform others, and all investigated methods struggle in challenging tasks, such as those requiring professional knowledge, indicating significant scope for improvement. We believe this study can serve as a strong baseline and provide insights for eliciting confidence in black-box LLMs.

We show that a GPT-3 model can learn to express uncertainty about its own answers in natural language -- without use of model logits. When given a question, the model generates both an answer and a level of confidence (e.g. "90% confidence" or "high confidence"). These levels map to probabilities that are well calibrated. The model also remains moderately calibrated under distribution shift, and is sensitive to uncertainty in its own answers, rather than imitating human examples. To our knowledge, this is the first time a model has been shown to express calibrated uncertainty about its own answers in natural language. For testing calibration, we introduce the CalibratedMath suite of tasks. We compare the calibration of uncertainty expressed in words ("verbalized probability") to uncertainty extracted from model logits. Both kinds of uncertainty are capable of generalizing calibration under distribution shift. We also provide evidence that GPT-3's ability to generalize calibration depends on pre-trained latent representations that correlate with epistemic uncertainty over its answers.

Large language models (LLMs) have demonstrated impressive performance on several tasks and are increasingly deployed in real-world applications. However, especially in high-stakes settings, it becomes vital to know when the output of an LLM may be unreliable. Depending on whether an answer is trustworthy, a system can then choose to route the question to another expert, or otherwise fall back on a safe default behavior. In this work, we study the extent to which LLMs can reliably indicate confidence in their answers, and how this notion of confidence can translate into downstream accuracy gains. We propose Self-REF, a lightweight training strategy to teach LLMs to express confidence in whether their answers are correct in a reliable manner. Self-REF introduces confidence tokens into the LLM, from which a confidence score can be extracted. Compared to conventional approaches such as verbalizing confidence and examining token probabilities, we demonstrate empirically that confidence tokens show significant improvements in downstream routing and rejection learning tasks.

Increasing test-time computation is a straightforward approach to enhancing the quality of responses in Large Language Models (LLMs). While Best-of-N sampling and Self-Consistency with majority voting are simple and effective, they require a fixed number of sampling responses for each query, regardless of its complexity. This could result in wasted computation for simpler questions and insufficient exploration for more challenging ones. In this work, we argue that model confidence of responses can be used for improving the efficiency of test-time scaling. Unfortunately, LLMs are known to be overconfident and provide unreliable confidence estimation. To address this limitation, we introduce Self-Calibration by distilling Self-Consistency-derived confidence into the model itself. This enables reliable confidence estimation at test time with one forward pass. We then design confidence-based efficient test-time scaling methods to handle queries of various difficulty, such as Early-Stopping for Best-of-N and Self-Consistency with calibrated confidence. Experiments on three LLMs across six datasets demonstrate the effectiveness of our approach. Specifically, applying confidence-based Early Stopping to Best-of-N improves MathQA accuracy from 81.0 to 83.6 with a sample budget of 16 responses, indicating the efficacy of confidence-based sampling strategy at inference time.

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

Large reasoning models (LRMs) have recently demonstrated impressive capabilities in complex reasoning tasks by leveraging increased test-time computation and exhibiting behaviors reminiscent of human-like self-reflection. While LRMs show a clear capacity for valuable self-reflection, how this ability interacts with other model behaviors remains underexplored. We investigate this connection by analyzing verbalized confidence, how models articulate their certainty, as a lens into the nature of self-reflection in LRMs. We find that supervised fine-tuning on reasoning traces (i.e., distillation) and reinforcement learning can improve verbalized calibration in reasoning-intensive settings in a progressive, laddered fashion. However, our results also indicate that reasoning models may possess a diminished awareness of their own knowledge boundaries, as evidenced by significantly lower "I don't know" response rates on factuality benchmarks. Moreover, we examine the relationship between verbalized confidence and reasoning chains, finding that models tend to express higher confidence when providing shorter or less elaborate reasoning. Our findings highlight how reasoning-oriented training can enhance performance in reasoning-centric tasks while potentially incurring a "reasoning tax," a cost reflected in the model's reduced ability to accurately recognize the limits of its own knowledge in small-scale models. More broadly, our work showcases how this erosion of knowledge boundaries can compromise model faithfulness, as models grow more confident without a commensurate understanding of when they should abstain.

Estimating uncertainty or confidence in the responses of a model can be significant in evaluating trust not only in the responses, but also in the model as a whole. In this paper, we explore the problem of estimating confidence for responses of large language models (LLMs) with simply black-box or query access to them. We propose a simple and extensible framework where, we engineer novel features and train a (interpretable) model (viz. logistic regression) on these features to estimate the confidence. We empirically demonstrate that our simple framework is effective in estimating confidence of flan-ul2, llama-13b and mistral-7b with it consistently outperforming existing black-box confidence estimation approaches on benchmark datasets such as TriviaQA, SQuAD, CoQA and Natural Questions by even over 10% (on AUROC) in some cases. Additionally, our interpretable approach provides insight into features that are predictive of confidence, leading to the interesting and useful discovery that our confidence models built for one LLM generalize zero-shot across others on a given dataset.

For large language models (LLMs) to be trusted by humans they need to be well-calibrated in the sense that they can accurately assess and communicate how likely it is that their predictions are correct. Recent work has focused on the quality of internal LLM confidence assessments, but the question remains of how well LLMs can communicate this internal model confidence to human users. This paper explores the disparity between external human confidence in an LLM's responses and the internal confidence of the model. Through experiments involving multiple-choice questions, we systematically examine human users' ability to discern the reliability of LLM outputs. Our study focuses on two key areas: (1) assessing users' perception of true LLM confidence and (2) investigating the impact of tailored explanations on this perception. The research highlights that default explanations from LLMs often lead to user overestimation of both the model's confidence and its' accuracy. By modifying the explanations to more accurately reflect the LLM's internal confidence, we observe a significant shift in user perception, aligning it more closely with the model's actual confidence levels. This adjustment in explanatory approach demonstrates potential for enhancing user trust and accuracy in assessing LLM outputs. The findings underscore the importance of transparent communication of confidence levels in LLMs, particularly in high-stakes applications where understanding the reliability of AI-generated information is essential.

Large language models (LLMs) often generate inaccurate or fabricated information and generally fail to indicate their confidence, which limits their broader applications. Previous work elicits confidence from LLMs by direct or self-consistency prompting, or constructing specific datasets for supervised finetuning. The prompting-based approaches have inferior performance, and the training-based approaches are limited to binary or inaccurate group-level confidence estimates. In this work, we present the advanced SaySelf, a training framework that teaches LLMs to express more accurate fine-grained confidence estimates. In addition, beyond the confidence scores, SaySelf initiates the process of directing LLMs to produce self-reflective rationales that clearly identify gaps in their parametric knowledge and explain their uncertainty. This is achieved by using an LLM to automatically summarize the uncertainties in specific knowledge via natural language. The summarization is based on the analysis of the inconsistency in multiple sampled reasoning chains, and the resulting data is utilized for supervised fine-tuning. Moreover, we utilize reinforcement learning with a meticulously crafted reward function to calibrate the confidence estimates, motivating LLMs to deliver accurate, high-confidence predictions and to penalize overconfidence in erroneous outputs. Experimental results in both in-distribution and out-of-distribution datasets demonstrate the effectiveness of SaySelf in reducing the confidence calibration error and maintaining the task performance. We show that the generated self-reflective rationales are reasonable and can further contribute to the calibration. The code is made public at https://github.com/xu1868/SaySelf.

Language models are increasingly used in Brazil, but most evaluation remains English-centric. This paper presents Alvorada-Bench, a 4,515-question, text-only benchmark drawn from five Brazilian university entrance examinations. Evaluating twenty models under zero-shot, role-playing, and chain-of-thought prompting, producing 270,900 responses with structured self-reports of confidence, perceived difficulty, and Bloom level. The top models exceed 94% accuracy overall, but accuracy declines on Mathematics and on the engineering oriented IME and ITA exams, indicating persistent weaknesses in multi-step reasoning. Confidence is well calibrated and correlates with perceived difficulty, revealing that models can accurately assess their own certainty capabilities. A cost accuracy analysis shows that high accuracy is achievable at under $2 per 1K tokens. On ENEM 2024 the top model (O3) achieved perfect scores in Languages subject questions while even the weakest system (GPT-4.1 Nano) only underperforms humans in Mathematics. Through exams that distill decades of Brazilian educational priorities and assess millions of students yearly, Alvorada-Bench establishes whether language models can navigate the intersection of language, culture, and reasoning that defines academic readiness in Brazil.

Retrieval Augmented Generation (RAG) complements the knowledge of Large Language Models (LLMs) by leveraging external information to enhance response accuracy for queries. This approach is widely applied in several fields by taking its advantage of injecting the most up-to-date information, and researchers are focusing on understanding and improving this aspect to unlock the full potential of RAG in such high-stakes applications. However, despite the potential of RAG to address these needs, the mechanisms behind the confidence levels of its outputs remain underexplored, although the confidence of information is very critical in some domains, such as finance, healthcare, and medicine. Our study focuses the impact of RAG on confidence within the medical domain under various configurations and models. We evaluate confidence by treating the model's predicted probability as its output and calculating Expected Calibration Error (ECE) and Adaptive Calibration Error (ACE) scores based on the probabilities and accuracy. In addition, we analyze whether the order of retrieved documents within prompts calibrates the confidence. Our findings reveal large variation in confidence and accuracy depending on the model, settings, and the format of input prompts. These results underscore the necessity of optimizing configurations based on the specific model and conditions.

To maintain user trust, large language models (LLMs) should signal low confidence on examples where they are incorrect, instead of misleading the user. The standard approach of estimating confidence is to use the softmax probabilities of these models, but as of November 2023, state-of-the-art LLMs such as GPT-4 and Claude-v1.3 do not provide access to these probabilities. We first study eliciting confidence linguistically -- asking an LLM for its confidence in its answer -- which performs reasonably (80.5% AUC on GPT-4 averaged across 12 question-answering datasets -- 7% above a random baseline) but leaves room for improvement. We then explore using a surrogate confidence model -- using a model where we do have probabilities to evaluate the original model's confidence in a given question. Surprisingly, even though these probabilities come from a different and often weaker model, this method leads to higher AUC than linguistic confidences on 9 out of 12 datasets. Our best method composing linguistic confidences and surrogate model probabilities gives state-of-the-art confidence estimates on all 12 datasets (84.6% average AUC on GPT-4).

Tool-using agents that act in the world need to be both useful and safe. Well-calibrated model confidences can be used to weigh the risk versus reward of potential actions, but prior work shows that many models are poorly calibrated. Inspired by interpretability literature exploring the internals of models, we propose a novel class of model-internal confidence estimators (MICE) to better assess confidence when calling tools. MICE first decodes from each intermediate layer of the language model using logitLens and then computes similarity scores between each layer's generation and the final output. These features are fed into a learned probabilistic classifier to assess confidence in the decoded output. On the simulated trial and error (STE) tool-calling dataset using Llama3 models, we find that MICE beats or matches the baselines on smoothed expected calibration error. Using MICE confidences to determine whether to call a tool significantly improves over strong baselines on a new metric, expected tool-calling utility. Further experiments show that MICE is sample-efficient, can generalize zero-shot to unseen APIs, and results in higher tool-calling utility in scenarios with varying risk levels. Our code is open source, available at https://github.com/microsoft/mice_for_cats.

Can LLMs accurately adjust their confidence when facing opposition? Building on previous studies measuring calibration on static fact-based question-answering tasks, we evaluate Large Language Models (LLMs) in a dynamic, adversarial debate setting, uniquely combining two realistic factors: (a) a multi-turn format requiring models to update beliefs as new information emerges, and (b) a zero-sum structure to control for task-related uncertainty, since mutual high-confidence claims imply systematic overconfidence. We organized 60 three-round policy debates among ten state-of-the-art LLMs, with models privately rating their confidence (0-100) in winning after each round. We observed five concerning patterns: (1) Systematic overconfidence: models began debates with average initial confidence of 72.9% vs. a rational 50% baseline. (2) Confidence escalation: rather than reducing confidence as debates progressed, debaters increased their win probabilities, averaging 83% by the final round. (3) Mutual overestimation: in 61.7% of debates, both sides simultaneously claimed >=75% probability of victory, a logical impossibility. (4) Persistent self-debate bias: models debating identical copies increased confidence from 64.1% to 75.2%; even when explicitly informed their chance of winning was exactly 50%, confidence still rose (from 50.0% to 57.1%). (5) Misaligned private reasoning: models' private scratchpad thoughts sometimes differed from their public confidence ratings, raising concerns about faithfulness of chain-of-thought reasoning. These results suggest LLMs lack the ability to accurately self-assess or update their beliefs in dynamic, multi-turn tasks; a major concern as LLMs are now increasingly deployed without careful review in assistant and agentic roles. Code for our experiments is available at https://github.com/pradyuprasad/llms_overconfidence

We investigate the extent to which offline demonstration data can improve online learning. It is natural to expect some improvement, but the question is how, and by how much? We show that the degree of improvement must depend on the quality of the demonstration data. To generate portable insights, we focus on Thompson sampling (TS) applied to a multi-armed bandit as a prototypical online learning algorithm and model. The demonstration data is generated by an expert with a given competence level, a notion we introduce. We propose an informed TS algorithm that utilizes the demonstration data in a coherent way through Bayes' rule and derive a prior-dependent Bayesian regret bound. This offers insight into how pretraining can greatly improve online performance and how the degree of improvement increases with the expert's competence level. We also develop a practical, approximate informed TS algorithm through Bayesian bootstrapping and show substantial empirical regret reduction through experiments.

The increasing complexity of foundational models underscores the necessity for explainability, particularly for fine-tuning, the most widely used training method for adapting models to downstream tasks. Instance attribution, one type of explanation, attributes the model prediction to each training example by an instance score. However, the robustness of instance scores, specifically towards dataset resampling, has been overlooked. To bridge this gap, we propose a notion of robustness on the sign of the instance score. We theoretically and empirically demonstrate that the popular leave-one-out-based methods lack robustness, while the Shapley value behaves significantly better, but at a higher computational cost. Accordingly, we introduce an efficient fine-tuning-free approximation of the Shapley value (FreeShap) for instance attribution based on the neural tangent kernel. We empirically demonstrate that FreeShap outperforms other methods for instance attribution and other data-centric applications such as data removal, data selection, and wrong label detection, and further generalize our scale to large language models (LLMs). Our code is available at https://github.com/JTWang2000/FreeShap.

Major cloud providers have employed advanced AI-based solutions like large language models to aid humans in identifying the root causes of cloud incidents. Despite the growing prevalence of AI-driven assistants in the root cause analysis process, their effectiveness in assisting on-call engineers is constrained by low accuracy due to the intrinsic difficulty of the task, a propensity for LLM-based approaches to hallucinate, and difficulties in distinguishing these well-disguised hallucinations. To address this challenge, we propose to perform confidence estimation for the predictions to help on-call engineers make decisions on whether to adopt the model prediction. Considering the black-box nature of many LLM-based root cause predictors, fine-tuning or temperature-scaling-based approaches are inapplicable. We therefore design an innovative confidence estimation framework based on prompting retrieval-augmented large language models (LLMs) that demand a minimal amount of information from the root cause predictor. This approach consists of two scoring phases: the LLM-based confidence estimator first evaluates its confidence in making judgments in the face of the current incident that reflects its ``grounded-ness" level in reference data, then rates the root cause prediction based on historical references. An optimization step combines these two scores for a final confidence assignment. We show that our method is able to produce calibrated confidence estimates for predicted root causes, validate the usefulness of retrieved historical data and the prompting strategy as well as the generalizability across different root cause prediction models. Our study takes an important move towards reliably and effectively embedding LLMs into cloud incident management systems.

Large language models (LLMs) have demonstrated impressive capabilities across various tasks, but their performance is highly sensitive to the prompts utilized. This variability poses challenges for accurate assessment and user satisfaction. Current research frequently overlooks instance-level prompt variations and their implications on subjective evaluations. To address these shortcomings, we introduce ProSA, a framework designed to evaluate and comprehend prompt sensitivity in LLMs. ProSA incorporates a novel sensitivity metric, PromptSensiScore, and leverages decoding confidence to elucidate underlying mechanisms. Our extensive study, spanning multiple tasks, uncovers that prompt sensitivity fluctuates across datasets and models, with larger models exhibiting enhanced robustness. We observe that few-shot examples can alleviate this sensitivity issue, and subjective evaluations are also susceptible to prompt sensitivities, particularly in complex, reasoning-oriented tasks. Furthermore, our findings indicate that higher model confidence correlates with increased prompt robustness. We believe this work will serve as a helpful tool in studying prompt sensitivity of LLMs. The project is released at: https://github.com/open-compass/ProSA .

Scaling the test-time compute of large language models has demonstrated impressive performance on reasoning benchmarks. However, existing evaluations of test-time scaling make the strong assumption that a reasoning system should always give an answer to any question provided. This overlooks concerns about whether a model is confident in its answer, and whether it is appropriate to always provide a response. To address these concerns, we extract confidence scores during reasoning for thresholding model responses. We find that increasing compute budget at inference time not only helps models answer more questions correctly, but also increases confidence in correct responses. We then extend the current paradigm of zero-risk responses during evaluation by considering settings with non-zero levels of response risk, and suggest a recipe for reporting evaluations under these settings.

In continual learning, many classifiers use softmax function to learn confidence. However, numerous studies have pointed out its inability to accurately determine confidence distributions for outliers, often referred to as epistemic uncertainty. This inherent limitation also curtails the accurate decisions for selecting what to forget and keep in previously trained confidence distributions over continual learning process. To address the issue, we revisit the effects of masking softmax function. While this method is both simple and prevalent in literature, its implication for retaining confidence distribution during continual learning, also known as stability, has been under-investigated. In this paper, we revisit the impact of softmax masking, and introduce a methodology to utilize its confidence preservation effects. In class- and task-incremental learning benchmarks with and without memory replay, our approach significantly increases stability while maintaining sufficiently large plasticity. In the end, our methodology shows better overall performance than state-of-the-art methods, particularly in the use with zero or small memory. This lays a simple and effective foundation of strongly stable replay-based continual learning.

The recent success of Large Language Models (LLMs) has catalyzed an increasing interest in their self-correction capabilities. This paper presents a comprehensive investigation into the intrinsic self-correction of LLMs, attempting to address the ongoing debate about its feasibility. Our research has identified an important latent factor - the "confidence" of LLMs - during the self-correction process. Overlooking this factor may cause the models to over-criticize themselves, resulting in unreliable conclusions regarding the efficacy of self-correction. We have experimentally observed that LLMs possess the capability to understand the "confidence" in their own responses. It motivates us to develop an "If-or-Else" (IoE) prompting framework, designed to guide LLMs in assessing their own "confidence", facilitating intrinsic self-corrections. We conduct extensive experiments and demonstrate that our IoE-based Prompt can achieve a consistent improvement regarding the accuracy of self-corrected responses over the initial answers. Our study not only sheds light on the underlying factors affecting self-correction in LLMs, but also introduces a practical framework that utilizes the IoE prompting principle to efficiently improve self-correction capabilities with "confidence". The code is available at https://github.com/MBZUAI-CLeaR/IoE-Prompting.git.

Generating accurate and calibrated confidence estimates is critical for deploying LLMs in high-stakes or user-facing applications, and remains an open challenge. Prior research has often framed confidence as a problem of eliciting a model's "self-knowledge", i.e., the ability of an LLM to judge whether its own answers are correct; this approach implicitly assumes that there is some privileged information about the answer's correctness that is accessible to the model itself. However, our experiments reveal that an LLM attempting to predict the correctness of its own outputs generally performs no better than an unrelated LLM. Moreover, we hypothesize that a key factor in building a "Correctness Model" (CM) is exposure to a target model's historical predictions. We propose multiple methods to inject this historical correctness information, creating a Generalized Correctness Model (GCM). We first show that GCMs can be trained on the correctness data from many LLMs and learn patterns for correctness prediction applicable across datasets and models. We then use CMs as a lens for studying the source of correctness prediction ability and its generalization, systematically controlling their training data and finding that answer phrasing is a strong predictor for correctness. We further explore alternative methods of injecting history without training an LLM, finding that including history as in-context examples can help improve correctness prediction, and post-hoc calibration can provide complementary reductions in calibration error. We evaluate GCMs based on Qwen3-8B across 5 model families and the MMLU and TriviaQA datasets, as well as on a downstream selective prediction task, finding that reliable LLM confidence estimation is a generalizable and model-agnostic skill learned by systematically encoding correctness history rather than a model-specific skill reliant on self-introspection.

Recent work in open-domain question answering (ODQA) has shown that adversarial poisoning of the input contexts can cause large drops in accuracy for production systems. However, little to no work has proposed methods to defend against these attacks. To do so, we introduce a new method that uses query augmentation to search for a diverse set of retrieved passages that could answer the original question. We integrate these new passages into the model through the design of a novel confidence method, comparing the predicted answer to its appearance in the retrieved contexts (what we call Confidence from Answer Redundancy, e.g. CAR). Together these methods allow for a simple but effective way to defend against poisoning attacks and provide gains of 5-20% exact match across varying levels of data poisoning.

Self-training is a well-known approach for semi-supervised learning. It consists of iteratively assigning pseudo-labels to unlabeled data for which the model is confident and treating them as labeled examples. For neural networks, softmax prediction probabilities are often used as a confidence measure, although they are known to be overconfident, even for wrong predictions. This phenomenon is particularly intensified in the presence of sample selection bias, i.e., when data labeling is subject to some constraint. To address this issue, we propose a novel confidence measure, called T-similarity, built upon the prediction diversity of an ensemble of linear classifiers. We provide the theoretical analysis of our approach by studying stationary points and describing the relationship between the diversity of the individual members and their performance. We empirically demonstrate the benefit of our confidence measure for three different pseudo-labeling policies on classification datasets of various data modalities. The code is available at https://github.com/ambroiseodt/tsim.

Multi-agent debates have been introduced to improve the accuracy of Large Language Models (LLMs) by having multiple agents discuss solutions to a problem over several rounds of debate. However, models often generate incorrect yet confident-sounding responses, which can mislead others. This issue arises partly because agents do not consider how confident their peers are. To address this, we propose DebUnc, a debate framework that uses uncertainty metrics to assess agent confidence. Confidence is then conveyed through a modified attention mechanism that adjusts token weights, or through textual prompts. Evaluations across benchmarks show that attention-based methods are particularly effective and that performance continues to improve as uncertainty estimation becomes more reliable. The code is available at https://github.com/lukeyoffe/debunc.

A critical component in the trustworthiness of LLMs is reliable uncertainty communication, yet LLMs often use assertive language when conveying false claims, leading to over-reliance and eroded trust. We present the first systematic study of faithful confidence calibration of LLMs, benchmarking models' ability to use linguistic expressions of uncertainty that faithfully reflect their intrinsic uncertainty, across a comprehensive array of models, datasets, and prompting strategies. Our results demonstrate that LLMs largely fail at this task, and that existing interventions are insufficient: standard prompt approaches provide only marginal gains, and existing, factuality-based calibration techniques can even harm faithful calibration. To address this critical gap, we introduce MetaFaith, a novel prompt-based calibration approach inspired by human metacognition. We show that MetaFaith robustly improves faithful calibration across diverse models and task domains, enabling up to 61% improvement in faithfulness and achieving an 83% win rate over original generations as judged by humans.

Collecting high-quality training examples for language model fine-tuning is expensive, with practical budgets limiting the amount of data that can be procured. We investigate whether example difficulty affects GRPO training effectiveness by comparing selection strategies (easy, medium, hard, random) across multiple models and reasoning tasks. Training on the hardest 10\% of examples (those where the base model fails most often) yields dramatic performance gains up to 47\%, while easy examples produce minimal improvements of 3-15\%. This occurs because GRPO requires outcome variance to generate learning signals; hard examples maintain mixed success/failure outcomes throughout training while easy examples quickly converge to consistent success, eliminating learning opportunities. Moreover, models trained on hard examples show superior out-of-distribution generalization, with only hard-trained models achieving meaningful gains on the AIME2025 benchmark. Our findings provide clear guidance: when budget-constrained, prioritize collecting and annotating examples where your base model struggles, as these drive nearly all learning value in GRPO fine-tuning

Machine learning models are widely used, but can also often be wrong. Users would benefit from a reliable indication of whether a given output from a given model should be trusted, so a rational decision can be made whether to use the output or not. For example, outputs can be associated with a confidence measure; if this confidence measure is strongly associated with likelihood of correctness, then the model is said to be well-calibrated. A well-calibrated confidence measure can serve as a basis for rational, graduated decision-making on how much review and care is needed when using generated code. Calibration has so far been studied in mostly non-generative (e.g. classification) settings, especially in software engineering. However, generated code can quite often be wrong: Given generated code, developers must decide whether to use directly, use after varying intensity of careful review, or discard model-generated code. Thus, calibration is vital in generative settings. We make several contributions. We develop a framework for evaluating the calibration of code-generating models. We consider several tasks, correctness criteria, datasets, and approaches, and find that, by and large, generative code models we test are not well-calibrated out of the box. We then show how calibration can be improved using standard methods, such as Platt scaling. Since Platt scaling relies on the prior availability of correctness data, we evaluate the applicability and generalizability of Platt scaling in software engineering, discuss settings where it has good potential for practical use, and settings where it does not. Our contributions will lead to better-calibrated decision-making in the current use of code generated by language models, and offers a framework for future research to further improve calibration methods for generative models in software engineering.

Multimodal machine learning has achieved remarkable progress in a wide range of scenarios. However, the reliability of multimodal learning remains largely unexplored. In this paper, through extensive empirical studies, we identify current multimodal classification methods suffer from unreliable predictive confidence that tend to rely on partial modalities when estimating confidence. Specifically, we find that the confidence estimated by current models could even increase when some modalities are corrupted. To address the issue, we introduce an intuitive principle for multimodal learning, i.e., the confidence should not increase when one modality is removed. Accordingly, we propose a novel regularization technique, i.e., Calibrating Multimodal Learning (CML) regularization, to calibrate the predictive confidence of previous methods. This technique could be flexibly equipped by existing models and improve the performance in terms of confidence calibration, classification accuracy, and model robustness.

When answering questions, LLMs can convey not only an answer, but a level of confidence about the answer being correct. This includes explicit confidence markers (e.g. giving a numeric score) as well as implicit markers, like an authoritative tone or elaborating with additional knowledge. For LLMs to be trustworthy knowledge sources, the confidence they convey should match their actual expertise; however, most current models tend towards overconfidence. To calibrate both implicit and explicit confidence markers, we introduce a pragmatic, listener-aware finetuning method (LACIE) that models the listener, considering not only whether an answer is right, but whether it will be accepted by a listener. We cast calibration as preference optimization, creating data via a two-agent game, where a speaker model's outputs are judged by a simulated listener. We then finetune three LLMs (Mistral-7B, Llama3-8B, Llama3-70B) with LACIE, and show that the resulting models are better calibrated w.r.t. a simulated listener. Crucially, these trends transfer to human listeners, helping them correctly predict model correctness: we conduct a human evaluation where annotators accept or reject an LLM's answers, finding that training with LACIE results in 47% fewer incorrect answers being accepted while maintaining the same level of acceptance for correct answers. Furthermore, LACIE generalizes to another dataset, resulting in a large increase in truthfulness on TruthfulQA when trained on TriviaQA. Our analysis indicates that LACIE leads to a better confidence separation between correct and incorrect examples. Qualitatively, we find that a LACIE-trained model hedges more and implicitly signals certainty when it is correct by using an authoritative tone or including details. Finally, LACIE finetuning leads to an emergent increase in model abstention (e.g. saying "I don't know") for answers that are likely wrong.

Large Reasoning Models (LRMs) perform strongly in complex reasoning tasks via Chain-of-Thought (CoT) prompting, but often suffer from verbose outputs caused by redundant content, increasing computational overhead, and degrading user experience. Existing compression methods either operate post-hoc pruning, risking disruption to reasoning coherence, or rely on sampling-based selection, which fails to intervene effectively during generation. In this work, we introduce a confidence-guided perspective to explain the emergence of redundant reflection in LRMs, identifying two key patterns: Confidence Deficit, where the model reconsiders correct steps due to low internal confidence, and Termination Delay, where reasoning continues even after reaching a confident answer. Based on this analysis, we propose ConCISE (Confidence-guided Compression In Step-by-step Efficient Reasoning), a framework that simplifies reasoning chains by reinforcing the model's confidence during inference, thus preventing the generation of redundant reflection steps. It integrates Confidence Injection to stabilize intermediate steps and Early Stopping to terminate reasoning when confidence is sufficient. Extensive experiments demonstrate that fine-tuning LRMs on ConCISE-generated data yields significantly shorter outputs, reducing length by up to approximately 50% under SimPO, while maintaining high task accuracy. ConCISE consistently outperforms existing baselines across multiple reasoning benchmarks.

This study investigates GPT-4's assessment of its performance in healthcare applications. A simple prompting technique was used to prompt the LLM with questions taken from the United States Medical Licensing Examination (USMLE) questionnaire and it was tasked to evaluate its confidence score before posing the question and after asking the question. The questionnaire was categorized into two groups-questions with feedback (WF) and questions with no feedback(NF) post-question. The model was asked to provide absolute and relative confidence scores before and after each question. The experimental findings were analyzed using statistical tools to study the variability of confidence in WF and NF groups. Additionally, a sequential analysis was conducted to observe the performance variation for the WF and NF groups. Results indicate that feedback influences relative confidence but doesn't consistently increase or decrease it. Understanding the performance of LLM is paramount in exploring its utility in sensitive areas like healthcare. This study contributes to the ongoing discourse on the reliability of AI, particularly of LLMs like GPT-4, within healthcare, offering insights into how feedback mechanisms might be optimized to enhance AI-assisted medical education and decision support.

The hallucination of non-existent facts by LLMs is an important problem given its widespread adoption across various applications. Previous research addresses this problem by analyzing the internal parameterized knowledge boundaries to estimate confidence. However, these studies focus on the single-problem setting and have not explored the more challenging multi-problem setting, which requires accurately answering multiple questions simultaneously. We introduce a novel method for the multi-problem setting, Multiple Answers and Confidence Stepwise Tuning (MAC-Tuning), that separates the learning of answer prediction and confidence estimation during fine-tuning on instruction data. Extensive experiments demonstrate that our method outperforms baselines by up to 25\% in average precision.

Multiple Instance Learning (MIL) is a sub-domain of classification problems with positive and negative labels and a "bag" of inputs, where the label is positive if and only if a positive element is contained within the bag, and otherwise is negative. Training in this context requires associating the bag-wide label to instance-level information, and implicitly contains a causal assumption and asymmetry to the task (i.e., you can't swap the labels without changing the semantics). MIL problems occur in healthcare (one malignant cell indicates cancer), cyber security (one malicious executable makes an infected computer), and many other tasks. In this work, we examine five of the most prominent deep-MIL models and find that none of them respects the standard MIL assumption. They are able to learn anti-correlated instances, i.e., defaulting to "positive" labels until seeing a negative counter-example, which should not be possible for a correct MIL model. We suspect that enhancements and other works derived from these models will share the same issue. In any context in which these models are being used, this creates the potential for learning incorrect models, which creates risk of operational failure. We identify and demonstrate this problem via a proposed "algorithmic unit test", where we create synthetic datasets that can be solved by a MIL respecting model, and which clearly reveal learning that violates MIL assumptions. The five evaluated methods each fail one or more of these tests. This provides a model-agnostic way to identify violations of modeling assumptions, which we hope will be useful for future development and evaluation of MIL models.

Reward models can significantly enhance the reasoning capabilities of large language models (LLMs), but they typically require extensive curated data and costly training. To mitigate these challenges, training-free approaches such as LLM-as-a-Judge leverage the intrinsic reasoning abilities of LLMs to evaluate responses, achieving promising results. Recent works have also indicated that model confidence can serve effectively as a reward metric, distinguishing between chain-of-thought (CoT) and non-CoT paths. However, the concept of using confidence as a reward has not been comprehensively studied. In this work, we systematically investigate Confidence-as-a-Reward (CRew), a simple yet powerful training-free method that utilizes token-level confidence in the model's final answers as a proxy for reward, especially suitable for close-ended tasks. Through extensive experiments on mathematical reasoning tasks, we demonstrate that CRew outperforms existing training-free reward approaches on the MATH500 and RewardMATH benchmarks, and even surpasses most trained reward models. We further identify a strong correlation between CRew scores and the actual reasoning performance of the model. Additionally, we find that CRew can effectively filter high-quality training data. Building upon these insights, we propose CRew-DPO, a training strategy that constructs preference data from confidence scores combined with correctness signals. Finetuning with CRew-DPO further enhances the model's judging capabilities and consistently outperforms existing self-training methods.

Multimodal large language models (MLLMs) hold considerable promise for applications in healthcare. However, their deployment in safety-critical settings is hindered by two key limitations: (i) sensitivity to prompt design, and (ii) a tendency to generate incorrect responses with high confidence. As clinicians may rely on a model's stated confidence to gauge the reliability of its predictions, it is especially important that when a model expresses high confidence, it is also highly accurate. We introduce Prompt4Trust, the first reinforcement learning (RL) framework for prompt augmentation targeting confidence calibration in MLLMs. A lightweight LLM is trained to produce context-aware auxiliary prompts that guide a downstream task MLLM to generate responses in which the expressed confidence more accurately reflects predictive accuracy. Unlike conventional calibration techniques, Prompt4Trust specifically prioritizes aspects of calibration most critical for safe and trustworthy clinical decision-making. Beyond improvements driven by this clinically motivated calibration objective, our proposed method also improves task accuracy, achieving state-of-the-art medical visual question answering (VQA) performance on the PMC-VQA benchmark, which is composed of multiple-choice questions spanning diverse medical imaging modalities. Moreover, our framework trained with a small downstream task MLLM showed promising zero-shot generalization to larger MLLMs in our experiments, suggesting the potential for scalable calibration without the associated computational costs. This work demonstrates the potential of automated yet human-aligned prompt engineering for improving the the trustworthiness of MLLMs in safety critical settings. Our codebase can be found at https://github.com/xingbpshen/prompt4trust.

Confidence calibration -- the problem of predicting probability estimates representative of the true correctness likelihood -- is important for classification models in many applications. We discover that modern neural networks, unlike those from a decade ago, are poorly calibrated. Through extensive experiments, we observe that depth, width, weight decay, and Batch Normalization are important factors influencing calibration. We evaluate the performance of various post-processing calibration methods on state-of-the-art architectures with image and document classification datasets. Our analysis and experiments not only offer insights into neural network learning, but also provide a simple and straightforward recipe for practical settings: on most datasets, temperature scaling -- a single-parameter variant of Platt Scaling -- is surprisingly effective at calibrating predictions.

Large Language Models deployed as question answering tools require robust calibration to avoid overconfidence. We systematically evaluate how reasoning capabilities and budget affect confidence assessment accuracy, using the ClimateX dataset (Lacombe et al., 2023) and expanding it to human and planetary health. Our key finding challenges the "test-time scaling" paradigm: while recent reasoning LLMs achieve 48.7% accuracy in assessing expert confidence, increasing reasoning budgets consistently impairs rather than improves calibration. Extended reasoning leads to systematic overconfidence that worsens with longer thinking budgets, producing diminishing and negative returns beyond modest computational investments. Conversely, search-augmented generation dramatically outperforms pure reasoning, achieving 89.3% accuracy by retrieving relevant evidence. Our results suggest that information access, rather than reasoning depth or inference budget, may be the critical bottleneck for improved confidence calibration of knowledge-intensive tasks.

Test-time adaptation (TTA) methods, which generally rely on the model's predictions (e.g., entropy minimization) to adapt the source pretrained model to the unlabeled target domain, suffer from noisy signals originating from 1) incorrect or 2) open-set predictions. Long-term stable adaptation is hampered by such noisy signals, so training models without such error accumulation is crucial for practical TTA. To address these issues, including open-set TTA, we propose a simple yet effective sample selection method inspired by the following crucial empirical finding. While entropy minimization compels the model to increase the probability of its predicted label (i.e., confidence values), we found that noisy samples rather show decreased confidence values. To be more specific, entropy minimization attempts to raise the confidence values of an individual sample's prediction, but individual confidence values may rise or fall due to the influence of signals from numerous other predictions (i.e., wisdom of crowds). Due to this fact, noisy signals misaligned with such 'wisdom of crowds', generally found in the correct signals, fail to raise the individual confidence values of wrong samples, despite attempts to increase them. Based on such findings, we filter out the samples whose confidence values are lower in the adapted model than in the original model, as they are likely to be noisy. Our method is widely applicable to existing TTA methods and improves their long-term adaptation performance in both image classification (e.g., 49.4% reduced error rates with TENT) and semantic segmentation (e.g., 11.7% gain in mIoU with TENT).

Large Language Models (LLMs) are increasingly deployed in high-stakes domains such as science, law, and healthcare, where accurate expressions of uncertainty are essential for reliability and trust. However, current LLMs are often observed to generate incorrect answers with high confidence, a phenomenon known as "overconfidence". Recent efforts have focused on calibrating LLMs' verbalized confidence: i.e., their expressions of confidence in text form, such as "I am 80% confident that...". Existing approaches either rely on prompt engineering or fine-tuning with heuristically generated uncertainty estimates, both of which have limited effectiveness and generalizability. Motivated by the notion of proper scoring rules for calibration in classical machine learning models, we introduce ConfTuner, a simple and efficient fine-tuning method that introduces minimal overhead and does not require ground-truth confidence scores or proxy confidence estimates. ConfTuner relies on a new loss function, tokenized Brier score, which we theoretically prove to be a proper scoring rule, intuitively meaning that it "correctly incentivizes the model to report its true probability of being correct". ConfTuner improves calibration across diverse reasoning tasks and generalizes to black-box models such as GPT-4o. Our results further show that better-calibrated confidence enables downstream gains in self-correction and model cascade, advancing the development of trustworthy LLM systems. The code is available at https://github.com/liushiliushi/ConfTuner.

We consider the problem of ranking n experts based on their performances on d tasks. We make a monotonicity assumption stating that for each pair of experts, one outperforms the other on all tasks. We consider the sequential setting where in each round, the learner has access to noisy evaluations of actively chosen pair of expert-task, given the information available up to the actual round. Given a confidence parameter delta in (0, 1), we provide strategies allowing to recover the correct ranking of experts and develop a bound on the total number of queries made by our algorithm that hold with probability at least 1 -- delta. We show that our strategy is adaptive to the complexity of the problem (our bounds are instance dependent), and develop matching lower bounds up to a poly-logarithmic factor. Finally, we adapt our strategy to the relaxed problem of best expert identification and provide numerical simulation consistent with our theoretical results.

It is important for Large Language Models to be aware of the boundary of their knowledge, the mechanism of identifying known and unknown queries. This type of awareness can help models perform adaptive inference, such as invoking RAG, engaging in slow and deep thinking, or adopting the abstention mechanism, which is beneficial to the development of efficient and trustworthy AI. In this work, we propose a method to detect knowledge boundaries via Query-Level Uncertainty, which aims to determine if the model is able to address a given query without generating any tokens. To this end, we introduce a novel and training-free method called Internal Confidence, which leverages self-evaluations across layers and tokens. Empirical results on both factual QA and mathematical reasoning tasks demonstrate that our internal confidence can outperform several baselines. Furthermore, we showcase that our proposed method can be used for efficient RAG and model cascading, which is able to reduce inference costs while maintaining performance.

We present a comprehensive evaluation of proprietary and open-weights large language models using the first astronomy-specific benchmarking dataset. This dataset comprises 4,425 multiple-choice questions curated from the Annual Review of Astronomy and Astrophysics, covering a broad range of astrophysical topics. Our analysis examines model performance across various astronomical subfields and assesses response calibration, crucial for potential deployment in research environments. Claude-3.5-Sonnet outperforms competitors by up to 4.6 percentage points, achieving 85.0% accuracy. For proprietary models, we observed a universal reduction in cost every 3-to-12 months to achieve similar score in this particular astronomy benchmark. Open-source models have rapidly improved, with LLaMA-3-70b (80.6%) and Qwen-2-72b (77.7%) now competing with some of the best proprietary models. We identify performance variations across topics, with non-English-focused models generally struggling more in exoplanet-related fields, stellar astrophysics, and instrumentation related questions. These challenges likely stem from less abundant training data, limited historical context, and rapid recent developments in these areas. This pattern is observed across both open-weights and proprietary models, with regional dependencies evident, highlighting the impact of training data diversity on model performance in specialized scientific domains. Top-performing models demonstrate well-calibrated confidence, with correlations above 0.9 between confidence and correctness, though they tend to be slightly underconfident. The development for fast, low-cost inference of open-weights models presents new opportunities for affordable deployment in astronomy. The rapid progress observed suggests that LLM-driven research in astronomy may become feasible in the near future.

One of the most widely used methods to evaluate LLMs are Multiple Choice Question (MCQ) tests. MCQ benchmarks enable the testing of LLM knowledge on almost any topic at scale as the results can be processed automatically. To help the LLM answer, a few examples called few shots can be included in the prompt. Moreover, the LLM can be asked to answer the question directly with the selected option or to first provide the reasoning and then the selected answer, which is known as chain of thought. In addition to checking whether the selected answer is correct, the evaluation can look at the LLM-estimated probability of its response as an indication of the confidence of the LLM in the response. In this paper, we study how the LLM confidence in its answer depends on whether the model has been asked to answer directly or to provide the reasoning before answering. The results of the evaluation of questions on a wide range of topics in seven different models show that LLMs are more confident in their answers when they provide reasoning before the answer. This occurs regardless of whether the selected answer is correct. Our hypothesis is that this behavior is due to the reasoning that modifies the probability of the selected answer, as the LLM predicts the answer based on the input question and the reasoning that supports the selection made. Therefore, LLM estimated probabilities seem to have intrinsic limitations that should be understood in order to use them in evaluation procedures. Interestingly, the same behavior has been observed in humans, for whom explaining an answer increases confidence in its correctness.

Large Language Models (LLMs) have limited performance when solving arithmetic reasoning tasks and often provide incorrect answers. Unlike natural language understanding, math problems typically have a single correct answer, making the task of generating accurate solutions more challenging for LLMs. To the best of our knowledge, we are not aware of any LLMs that indicate their level of confidence in their responses which fuels a trust deficit in these models impeding their adoption. To address this deficiency, we propose `MathPrompter', a technique that improves performance of LLMs on arithmetic problems along with increased reliance in the predictions. MathPrompter uses the Zero-shot chain-of-thought prompting technique to generate multiple Algebraic expressions or Python functions to solve the same math problem in different ways and thereby raise the confidence level in the output results. This is in contrast to other prompt based CoT methods, where there is no check on the validity of the intermediate steps followed. Our technique improves over state-of-the-art on the MultiArith dataset (78.7%rightarrow92.5%) evaluated using 175B parameter GPT-based LLM.

Large datasets have become commonplace in NLP research. However, the increased emphasis on data quantity has made it challenging to assess the quality of data. We introduce Data Maps---a model-based tool to characterize and diagnose datasets. We leverage a largely ignored source of information: the behavior of the model on individual instances during training (training dynamics) for building data maps. This yields two intuitive measures for each example---the model's confidence in the true class, and the variability of this confidence across epochs---obtained in a single run of training. Experiments across four datasets show that these model-dependent measures reveal three distinct regions in the data map, each with pronounced characteristics. First, our data maps show the presence of "ambiguous" regions with respect to the model, which contribute the most towards out-of-distribution generalization. Second, the most populous regions in the data are "easy to learn" for the model, and play an important role in model optimization. Finally, data maps uncover a region with instances that the model finds "hard to learn"; these often correspond to labeling errors. Our results indicate that a shift in focus from quantity to quality of data could lead to robust models and improved out-of-distribution generalization.

Accurate confidence estimation is essential for trustworthy large language models (LLMs) systems, as it empowers the user to determine when to trust outputs and enables reliable deployment in safety-critical applications. Current confidence estimation methods for LLMs neglect the relevance between responses and contextual information, a crucial factor in output quality evaluation, particularly in scenarios where background knowledge is provided. To bridge this gap, we propose CRUX (Context-aware entropy Reduction and Unified consistency eXamination), the first framework that integrates context faithfulness and consistency for confidence estimation via two novel metrics. First, contextual entropy reduction represents data uncertainty with the information gain through contrastive sampling with and without context. Second, unified consistency examination captures potential model uncertainty through the global consistency of the generated answers with and without context. Experiments across three benchmark datasets (CoQA, SQuAD, QuAC) and two domain-specific datasets (BioASQ, EduQG) demonstrate CRUX's effectiveness, achieving the highest AUROC than existing baselines.

Large Language Models (LLMs) have shown remarkable capabilities in general natural language processing tasks but often fall short in complex reasoning tasks. Recent studies have explored human-like problem-solving strategies, such as self-correct, to push further the boundary of single-model reasoning ability. In this work, we let a single model "step outside the box" by engaging multiple models to correct each other. We introduce a multi-agent collaboration strategy that emulates the academic peer review process. Each agent independently constructs its own solution, provides reviews on the solutions of others, and assigns confidence levels to its reviews. Upon receiving peer reviews, agents revise their initial solutions. Extensive experiments on three different types of reasoning tasks show that our collaboration approach delivers superior accuracy across all ten datasets compared to existing methods. Further study underscores the effectiveness of integrating confidence in reviews, demonstrates the superiority of feedback exchange over mere solution sharing, and highlights the role of capability and diversity in fostering successful collaboration.

Recently, large language models (LLMs), especially those that are pretrained on code, have demonstrated strong capabilities in generating programs from natural language inputs in a few-shot or even zero-shot manner. Despite promising results, there is a notable lack of a comprehensive evaluation of these models language-to-code generation capabilities. Existing studies often focus on specific tasks, model architectures, or learning paradigms, leading to a fragmented understanding of the overall landscape. In this work, we present L2CEval, a systematic evaluation of the language-to-code generation capabilities of LLMs on 7 tasks across the domain spectrum of semantic parsing, math reasoning and Python programming, analyzing the factors that potentially affect their performance, such as model size, pretraining data, instruction tuning, and different prompting methods. In addition to assessing model performance, we measure confidence calibration for the models and conduct human evaluations of the output programs. This enables us to identify and analyze the typical failure modes across various tasks and models. L2CEval offers a comprehensive understanding of the capabilities and limitations of LLMs in language-to-code generation. We also release the evaluation framework and all model outputs, hoping to lay the groundwork for further future research in this domain.

Analogical reasoning is a unique ability of humans to address unfamiliar challenges by transferring strategies from relevant past experiences. One key finding in psychology is that compared with irrelevant past experiences, recalling relevant ones can help humans better handle new tasks. Coincidentally, the NLP community has also recently found that self-generating relevant examples in the context can help large language models (LLMs) better solve a given problem than hand-crafted prompts. However, it is yet not clear whether relevance is the key factor eliciting such capability, i.e., can LLMs benefit more from self-generated relevant examples than irrelevant ones? In this work, we systematically explore whether LLMs can truly perform analogical reasoning on a diverse set of reasoning tasks. With extensive experiments and analysis, we show that self-generated random examples can surprisingly achieve comparable or even better performance, e.g., 4% performance boost on GSM8K with random biological examples. We find that the accuracy of self-generated examples is the key factor and subsequently design two improved methods with significantly reduced inference costs. Overall, we aim to advance a deeper understanding of LLM analogical reasoning and hope this work stimulates further research in the design of self-generated contexts.

Model evolution and constant availability of data are two common phenomena in large-scale real-world machine learning applications, e.g. ads and recommendation systems. To adapt, the real-world system typically retrain with all available data and online learn with recently available data to update the models periodically with the goal of better serving performance. In this paper, we propose a novel framework, named Confidence Ranking, which designs the optimization objective as a ranking function with two different models. Our confidence ranking loss allows direct optimization of the logits output for different convex surrogate functions of metrics, e.g. AUC and Accuracy depending on the target task and dataset. Armed with our proposed methods, our experiments show that the introduction of confidence ranking loss can outperform all baselines on the CTR prediction tasks of public and industrial datasets. This framework has been deployed in the advertisement system of JD.com to serve the main traffic in the fine-rank stage.

A trustworthy real-world prediction system should produce well-calibrated confidence scores; that is, its confidence in an answer should be indicative of the likelihood that the answer is correct, enabling deferral to an expert in cases of low-confidence predictions. Recent studies have shown that unsupervised pre-training produces large language models (LMs) whose conditional probabilities are remarkably well-calibrated. However, the most widely-used LMs are fine-tuned with reinforcement learning from human feedback (RLHF-LMs), and some studies have suggested that RLHF-LMs produce conditional probabilities that are very poorly calibrated. In light of this perceived weakness, we conduct a broad evaluation of methods for extracting confidence scores from RLHF-LMs. For RLHF-LMs such as ChatGPT, GPT-4, and Claude, we find that verbalized confidences emitted as output tokens are typically better-calibrated than the model's conditional probabilities on the TriviaQA, SciQ, and TruthfulQA benchmarks, often reducing the expected calibration error by a relative 50%.

Out-of-distribution (OOD) detection aims to identify OOD inputs from unknown classes, which is important for the reliable deployment of machine learning models in the open world. Various scoring functions are proposed to distinguish it from in-distribution (ID) data. However, existing methods generally focus on excavating the discriminative information from a single input, which implicitly limits its representation dimension. In this work, we introduce a novel perspective, i.e., employing different common corruptions on the input space, to expand that. We reveal an interesting phenomenon termed confidence mutation, where the confidence of OOD data can decrease significantly under the corruptions, while the ID data shows a higher confidence expectation considering the resistance of semantic features. Based on that, we formalize a new scoring method, namely, Confidence aVerage (CoVer), which can capture the dynamic differences by simply averaging the scores obtained from different corrupted inputs and the original ones, making the OOD and ID distributions more separable in detection tasks. Extensive experiments and analyses have been conducted to understand and verify the effectiveness of CoVer. The code is publicly available at: https://github.com/tmlr-group/CoVer.

Conducting contamination-free evaluation of mathematical capabilities can be difficult for two reasons: models may memorize a test set once it is made public, and current mathematical benchmarks are prone to overfitting due to having limited diversity of symbols and rules, coupled with closed-ended answers. This paper proposes a method to leverage these shortcomings as useful features to a construct dynamic, counterfactual benchmark, which can be used to both reveal overfitting and measure true reasoning. We demonstrate this via MatheMagic, which generates math test instances with the interpretations of numbers and operators altered, yet has automatically verifiable answers. Test instances are randomly seeded and constructed at test time to evaluate a model's induction or deduction capability, offering stability, extensibility, comparability, and robustness to overfitting. Our experiments find that models solve deduction more easily than induction, but they revert to standard math. Further analysis reveals that math-adapted models fail to exhibit a general "skill" of reasoning, and fine-tuning on induction tasks generalizes poorly.

In natural language processing, a recently popular line of work explores how to best report the experimental results of neural networks. One exemplar publication, titled "Show Your Work: Improved Reporting of Experimental Results," advocates for reporting the expected validation effectiveness of the best-tuned model, with respect to the computational budget. In the present work, we critically examine this paper. As far as statistical generalizability is concerned, we find unspoken pitfalls and caveats with this approach. We analytically show that their estimator is biased and uses error-prone assumptions. We find that the estimator favors negative errors and yields poor bootstrapped confidence intervals. We derive an unbiased alternative and bolster our claims with empirical evidence from statistical simulation. Our codebase is at http://github.com/castorini/meanmax.

We investigate the problem of determining the predictive confidence (or, conversely, uncertainty) of a neural classifier through the lens of low-resource languages. By training models on sub-sampled datasets in three different languages, we assess the quality of estimates from a wide array of approaches and their dependence on the amount of available data. We find that while approaches based on pre-trained models and ensembles achieve the best results overall, the quality of uncertainty estimates can surprisingly suffer with more data. We also perform a qualitative analysis of uncertainties on sequences, discovering that a model's total uncertainty seems to be influenced to a large degree by its data uncertainty, not model uncertainty. All model implementations are open-sourced in a software package.

We investigate large language model performance across five orders of magnitude of compute scaling in eleven recent model architectures. We show that average benchmark performance, aggregating over many individual tasks and evaluations as in the commonly-used BIG-Bench dataset, is decently predictable as a function of training compute scale. Specifically, when extrapolating BIG-Bench Hard performance across one order of magnitude in compute, we observe average absolute errors of 6 percentage points (pp). By contrast, extrapolation for individual BIG-Bench tasks across an order of magnitude in compute yields higher average errors of 18pp. Nonetheless, individual task performance remains significantly more predictable than chance. Overall, our work suggests compute scaling provides a promising basis to forecast AI capabilities in diverse benchmarks, though predicting performance in specific tasks poses challenges.

Reliable application of machine learning is of primary importance to the practical deployment of deep learning methods. A fundamental challenge is that models are often unreliable due to overconfidence. In this paper, we estimate a model's reliability by measuring the agreement between its latent space, and the latent space of a foundation model. However, it is challenging to measure the agreement between two different latent spaces due to their incoherence, \eg, arbitrary rotations and different dimensionality. To overcome this incoherence issue, we design a neighborhood agreement measure between latent spaces and find that this agreement is surprisingly well-correlated with the reliability of a model's predictions. Further, we show that fusing neighborhood agreement into a model's predictive confidence in a post-hoc way significantly improves its reliability. Theoretical analysis and extensive experiments on failure detection across various datasets verify the effectiveness of our method on both in-distribution and out-of-distribution settings.

Algorithms such as Differentially Private SGD enable training machine learning models with formal privacy guarantees. However, there is a discrepancy between the protection that such algorithms guarantee in theory and the protection they afford in practice. An emerging strand of work empirically estimates the protection afforded by differentially private training as a confidence interval for the privacy budget varepsilon spent on training a model. Existing approaches derive confidence intervals for varepsilon from confidence intervals for the false positive and false negative rates of membership inference attacks. Unfortunately, obtaining narrow high-confidence intervals for epsilon using this method requires an impractically large sample size and training as many models as samples. We propose a novel Bayesian method that greatly reduces sample size, and adapt and validate a heuristic to draw more than one sample per trained model. Our Bayesian method exploits the hypothesis testing interpretation of differential privacy to obtain a posterior for varepsilon (not just a confidence interval) from the joint posterior of the false positive and false negative rates of membership inference attacks. For the same sample size and confidence, we derive confidence intervals for varepsilon around 40% narrower than prior work. The heuristic, which we adapt from label-only DP, can be used to further reduce the number of trained models needed to get enough samples by up to 2 orders of magnitude.

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

Recent advances in large language models (LLMs) have fueled the vision of automated scientific discovery, often called AI Co-Scientists. To date, prior work casts these systems as generative co-authors responsible for crafting hypotheses, synthesizing code, or drafting manuscripts. In this work, we explore a complementary application: using LLMs as verifiers to automate the academic verification of scientific manuscripts. To that end, we introduce SPOT, a dataset of 83 published papers paired with 91 errors significant enough to prompt errata or retraction, cross-validated with actual authors and human annotators. Evaluating state-of-the-art LLMs on SPOT, we find that none surpasses 21.1\% recall or 6.1\% precision (o3 achieves the best scores, with all others near zero). Furthermore, confidence estimates are uniformly low, and across eight independent runs, models rarely rediscover the same errors, undermining their reliability. Finally, qualitative analysis with domain experts reveals that even the strongest models make mistakes resembling student-level misconceptions derived from misunderstandings. These findings highlight the substantial gap between current LLM capabilities and the requirements for dependable AI-assisted academic verification.

Orca 1 learns from rich signals, such as explanation traces, allowing it to outperform conventional instruction-tuned models on benchmarks like BigBench Hard and AGIEval. In Orca 2, we continue exploring how improved training signals can enhance smaller LMs' reasoning abilities. Research on training small LMs has often relied on imitation learning to replicate the output of more capable models. We contend that excessive emphasis on imitation may restrict the potential of smaller models. We seek to teach small LMs to employ different solution strategies for different tasks, potentially different from the one used by the larger model. For example, while larger models might provide a direct answer to a complex task, smaller models may not have the same capacity. In Orca 2, we teach the model various reasoning techniques (step-by-step, recall then generate, recall-reason-generate, direct answer, etc.). More crucially, we aim to help the model learn to determine the most effective solution strategy for each task. We evaluate Orca 2 using a comprehensive set of 15 diverse benchmarks (corresponding to approximately 100 tasks and over 36,000 unique prompts). Orca 2 significantly surpasses models of similar size and attains performance levels similar or better to those of models 5-10x larger, as assessed on complex tasks that test advanced reasoning abilities in zero-shot settings. We open-source Orca 2 to encourage further research on the development, evaluation, and alignment of smaller LMs.

Hallucinations in multimodal large language models (MLLMs) -- where the model generates content inconsistent with the input image -- pose significant risks in real-world applications, from misinformation in visual question answering to unsafe errors in decision-making. Existing benchmarks primarily test recognition accuracy, i.e., evaluating whether models can select the correct answer among distractors. This overlooks an equally critical capability for trustworthy AI: recognizing when none of the provided options are correct, a behavior reflecting epistemic humility. We present HumbleBench, a new hallucination benchmark designed to evaluate MLLMs' ability to reject plausible but incorrect answers across three hallucination types: object, relation, and attribute. Built from a panoptic scene graph dataset, we leverage fine-grained scene graph annotations to extract ground-truth entities and relations, and prompt GPT-4-Turbo to generate multiple-choice questions, followed by a rigorous manual filtering process. Each question includes a "None of the above" option, requiring models not only to recognize correct visual information but also to identify when no provided answer is valid. We evaluate a variety of state-of-the-art MLLMs -- including both general-purpose and specialized reasoning models -- on HumbleBench and share valuable findings and insights with the community. By incorporating explicit false-option rejection, HumbleBench fills a key gap in current evaluation suites, providing a more realistic measure of MLLM reliability in safety-critical settings. Our code and dataset are released publicly and can be accessed at https://github.com/maifoundations/HumbleBench.

LLM-as-a-Judge (LLMaaJ) now underpins scalable evaluation, yet we lack a decisive test of a judge's qualification: can it recover a conversation's latent objective and know when that inference is trustworthy? LLMs degrade under irrelevant or long context; multi-turn jailbreaks further hide goals across turns. We introduce ObjexMT, a benchmark for objective extraction and metacognition. Given a multi-turn transcript, a model must return a one-sentence base objective and a self-reported confidence. Accuracy is computed via LLM-judge semantic similarity to gold objectives, converted to binary correctness by a single human-aligned threshold calibrated once on N = 100 items (tau^*=0.61). Metacognition is evaluated with ECE, Brier, Wrong-at-High-Conf, and risk-coverage. Across gpt-4.1, claude-sonnet-4, and Qwen3-235B-A22B-FP8 on SafeMTData_Attack600, SafeMTData_1K, MHJ, and CoSafe, claude-sonnet-4 attains the best objective-extraction accuracy (0.515) and calibration (ECE 0.296; Brier 0.324); gpt-4.1 and Qwen3-235B-A22B-FP8 tie at 0.441 but are overconfident (mean confidence approx0.88 vs. accuracy approx0.44; Wrong-at-0.90 approx48-52%). Performance varies by dataset (approx0.167-0.865). ObjexMT thus supplies an actionable test for LLM judges: when objectives are not explicit, judges often misinfer them with high confidence. We recommend exposing objectives when feasible and gating decisions by confidence otherwise. Code and data at https://github.com/hyunjun1121/ObjexMT_dataset.

We study whether language models can evaluate the validity of their own claims and predict which questions they will be able to answer correctly. We first show that larger models are well-calibrated on diverse multiple choice and true/false questions when they are provided in the right format. Thus we can approach self-evaluation on open-ended sampling tasks by asking models to first propose answers, and then to evaluate the probability "P(True)" that their answers are correct. We find encouraging performance, calibration, and scaling for P(True) on a diverse array of tasks. Performance at self-evaluation further improves when we allow models to consider many of their own samples before predicting the validity of one specific possibility. Next, we investigate whether models can be trained to predict "P(IK)", the probability that "I know" the answer to a question, without reference to any particular proposed answer. Models perform well at predicting P(IK) and partially generalize across tasks, though they struggle with calibration of P(IK) on new tasks. The predicted P(IK) probabilities also increase appropriately in the presence of relevant source materials in the context, and in the presence of hints towards the solution of mathematical word problems. We hope these observations lay the groundwork for training more honest models, and for investigating how honesty generalizes to cases where models are trained on objectives other than the imitation of human writing.

Expressing confidence is challenging for embodied agents navigating dynamic multimodal environments, where uncertainty arises from both perception and decision-making processes. We present the first work investigating embodied confidence elicitation in open-ended multimodal environments. We introduce Elicitation Policies, which structure confidence assessment across inductive, deductive, and abductive reasoning, along with Execution Policies, which enhance confidence calibration through scenario reinterpretation, action sampling, and hypothetical reasoning. Evaluating agents in calibration and failure prediction tasks within the Minecraft environment, we show that structured reasoning approaches, such as Chain-of-Thoughts, improve confidence calibration. However, our findings also reveal persistent challenges in distinguishing uncertainty, particularly under abductive settings, underscoring the need for more sophisticated embodied confidence elicitation methods.

Retrieval-augmented generation (RAG) has emerged as a popular solution to mitigate the hallucination issues of large language models. However, existing studies on RAG seldom address the issue of predictive uncertainty, i.e., how likely it is that a RAG model's prediction is incorrect, resulting in uncontrollable risks in real-world applications. In this work, we emphasize the importance of risk control, ensuring that RAG models proactively refuse to answer questions with low confidence. Our research identifies two critical latent factors affecting RAG's confidence in its predictions: the quality of the retrieved results and the manner in which these results are utilized. To guide RAG models in assessing their own confidence based on these two latent factors, we develop a counterfactual prompting framework that induces the models to alter these factors and analyzes the effect on their answers. We also introduce a benchmarking procedure to collect answers with the option to abstain, facilitating a series of experiments. For evaluation, we introduce several risk-related metrics and the experimental results demonstrate the effectiveness of our approach.

As LLMs grow more powerful, their most profound achievement may be recognising when to say "I don't know". Existing studies on LLM self-knowledge have been largely constrained by human-defined notions of feasibility, often neglecting the reasons behind unanswerability by LLMs and failing to study deficient types of self-knowledge. This study aims to obtain intrinsic insights into different types of LLM self-knowledge with a novel methodology: allowing them the flexibility to set their own feasibility boundaries and then analysing the consistency of these limits. We find that even frontier models like GPT-4o and Mistral Large are not sure of their own capabilities more than 80% of the time, highlighting a significant lack of trustworthiness in responses. Our analysis of confidence balance in LLMs indicates that models swing between overconfidence and conservatism in feasibility boundaries depending on task categories and that the most significant self-knowledge weaknesses lie in temporal awareness and contextual understanding. These difficulties in contextual comprehension additionally lead models to question their operational boundaries, resulting in considerable confusion within the self-knowledge of LLMs. We make our code and results available publicly at https://github.com/knowledge-verse-ai/LLM-Self_Knowledge_Eval

Forecasting is an important task in many domains, such as technology and economics. However existing forecasting benchmarks largely lack comprehensive confidence assessment, focus on limited question types, and often consist of artificial questions that do not align with real-world human forecasting needs. To address these gaps, we introduce FOReCAst (Future Outcome Reasoning and Confidence Assessment), a benchmark that evaluates models' ability to make predictions and their confidence in them. FOReCAst spans diverse forecasting scenarios involving Boolean questions, timeframe prediction, and quantity estimation, enabling a comprehensive evaluation of both prediction accuracy and confidence calibration for real-world applications.

Retrieval-Augmented Generation (RAG) mitigates hallucinations in Large Language Models (LLMs) by integrating external knowledge. However, conflicts between parametric knowledge and retrieved context pose challenges, particularly when retrieved information is unreliable or the model's internal knowledge is outdated. In such cases, LLMs struggle to determine whether to rely more on their own parameters or the conflicted context. To address this, we propose **CK-PLUG**, a plug-and-play method for controlling LLMs' reliance on parametric and contextual knowledge. We introduce a novel knowledge consistency metric, Confidence Gain, which detects knowledge conflicts by measuring entropy shifts in token probability distributions after context insertion. CK-PLUG then enables fine-grained control over knowledge preference by adjusting the probability distribution of tokens with negative confidence gain through a single tuning parameter. Experiments demonstrate CK-PLUG's ability to significantly regulate knowledge reliance in counterfactual RAG scenarios while maintaining generation fluency and knowledge accuracy. For instance, on Llama3-8B, memory recall (MR) of RAG response can be adjusted within a broad range (9.9%-71.9%), compared to the baseline of 42.1%. Moreover, CK-PLUG supports adaptive control based on the model's confidence in both internal and external knowledge, achieving consistent performance improvements across various general RAG tasks. Our code is available at: https://github.com/byronBBL/CK-PLUG{this https URL}.

Recent language models have shown remarkable performance on natural language understanding (NLU) tasks. However, they are often sub-optimal when faced with ambiguous samples that can be interpreted in multiple ways, over-confidently predicting a single label without consideration for its correctness. To address this issue, we propose a novel self-knowledge distillation method that enables models to learn label distributions more accurately by leveraging knowledge distilled from their lower layers. This approach also includes a learning phase that re-calibrates the unnecessarily strengthened confidence for training samples judged as extremely ambiguous based on the distilled distribution knowledge. We validate our method on diverse NLU benchmark datasets and the experimental results demonstrate its effectiveness in producing better label distributions. Particularly, through the process of re-calibrating the confidence for highly ambiguous samples, the issue of over-confidence when predictions for unseen samples do not match with their ground-truth labels has been significantly alleviated. This has been shown to contribute to generating better distributions than the existing state-of-the-art method. Moreover, our method is more efficient in training the models compared to the existing method, as it does not involve additional training processes to refine label distributions.

Accurately predicting customer Lifetime Value (LTV) is crucial for companies to optimize their revenue strategies. Traditional deep learning models for LTV prediction are effective but typically provide only point estimates and fail to capture model uncertainty in modeling user behaviors. To address this limitation, we propose a novel approach that enhances the architecture of purely neural network models by incorporating the Monte Carlo Dropout (MCD) framework. We benchmarked the proposed method using data from one of the most downloaded mobile games in the world, and demonstrated a substantial improvement in predictive Top 5\% Mean Absolute Percentage Error compared to existing state-of-the-art methods. Additionally, our approach provides confidence metric as an extra dimension for performance evaluation across various neural network models, facilitating more informed business decisions.

Large Language Models (LLMs) can correct their self-generated responses, but a decline in accuracy after self-correction is also witnessed. To have a deeper understanding of self-correction, we endeavor to decompose, evaluate, and analyze the self-correction behaviors of LLMs. By enumerating and analyzing answer correctness before and after self-correction, we decompose the self-correction capability into confidence (being confident to correct answers) and critique (turning wrong answers to correct) capabilities, and propose two metrics from a probabilistic perspective to measure these 2 capabilities, along with another metric for overall self-correction capability evaluation. Based on our decomposition and evaluation metrics, we conduct extensive experiments and draw some empirical conclusions. For example, we find different models can exhibit distinct behaviors: some models are confident while others are more critical. We also find the trade-off between the two capabilities (i.e. improving one can lead to a decline in the other) when manipulating model self-correction behavior by prompts or in-context learning. Further, we find a simple yet efficient strategy to improve self-correction capability by transforming Supervision Fine-Tuning (SFT) data format, and our strategy outperforms vanilla SFT in both capabilities and achieves much higher accuracy after self-correction. Our code will be publicly available on GitHub.

Next token prediction paradigm has been prevailing for autoregressive models in the era of LLMs. The current default sampling choice for popular LLMs is temperature scaling together with nucleus sampling to balance diversity and coherence. Nevertheless, such approach leads to inferior performance in various NLP tasks when the model is not certain about testing questions. To this end, we propose a brand new training-free decoding strategy, dubbed as Cautious Next Token Prediction (CNTP). In the decoding process, if the model has comparatively high prediction entropy at a certain step, we sample multiple trials starting from the step independently and stop when encountering any punctuation. Then we select the trial with the lowest perplexity score viewed as the most probable and reliable trial path given the model's capacity. The trial number is negatively correlated with the prediction confidence, i.e., the less confident the model is, the more trials it should sample. This is consistent with human beings' behaviour: when feeling uncertain or unconfident, one tends to think more creatively, exploring multiple thinking paths, to cautiously select the path one feels most confident about. Extensive experiments on both LLMs and MLLMs show that our proposed CNTP approach outperforms existing standard decoding strategies consistently by a clear margin. Moreover, the integration of CNTP with self consistency can further improve over vanilla self consistency. We believe our proposed CNTP has the potential to become one of the default choices for LLM decoding. Code is available at https://github.com/wyzjack/CNTP.

Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model calibration, the rigorous statistical evaluation of model calibration remains less explored. In this work, we develop confidence intervals the ell_2 Expected Calibration Error (ECE). We consider top-1-to-k calibration, which includes both the popular notion of confidence calibration as well as full calibration. For a debiased estimator of the ECE, we show asymptotic normality, but with different convergence rates and asymptotic variances for calibrated and miscalibrated models. We develop methods to construct asymptotically valid confidence intervals for the ECE, accounting for this behavior as well as non-negativity. Our theoretical findings are supported through extensive experiments, showing that our methods produce valid confidence intervals with shorter lengths compared to those obtained by resampling-based methods.

We expect the generalization error to improve with more samples from a similar task, and to deteriorate with more samples from an out-of-distribution (OOD) task. In this work, we show a counter-intuitive phenomenon: the generalization error of a task can be a non-monotonic function of the number of OOD samples. As the number of OOD samples increases, the generalization error on the target task improves before deteriorating beyond a threshold. In other words, there is value in training on small amounts of OOD data. We use Fisher's Linear Discriminant on synthetic datasets and deep networks on computer vision benchmarks such as MNIST, CIFAR-10, CINIC-10, PACS and DomainNet to demonstrate and analyze this phenomenon. In the idealistic setting where we know which samples are OOD, we show that these non-monotonic trends can be exploited using an appropriately weighted objective of the target and OOD empirical risk. While its practical utility is limited, this does suggest that if we can detect OOD samples, then there may be ways to benefit from them. When we do not know which samples are OOD, we show how a number of go-to strategies such as data-augmentation, hyper-parameter optimization, and pre-training are not enough to ensure that the target generalization error does not deteriorate with the number of OOD samples in the dataset.

Continual learning and few-shot learning are important frontiers in progress towards broader Machine Learning (ML) capabilities. There is a growing body of work in both, but few works combining the two. One exception is the Continual few-shot Learning (CFSL) framework of Antoniou et al. arXiv:2004.11967. In this study, we extend CFSL in two ways that capture a broader range of challenges, important for intelligent agent behaviour in real-world conditions. First, we modify CFSL to make it more comparable to standard continual learning experiments, where usually a much larger number of classes are presented. Second, we introduce an 'instance test' which requires recognition of specific instances of classes -- a capability of animal cognition that is usually neglected in ML. For an initial exploration of ML model performance under these conditions, we selected representative baseline models from the original CFSL work and added a model variant with replay. As expected, learning more classes is more difficult than the original CFSL experiments, and interestingly, the way in which image instances and classes are presented affects classification performance. Surprisingly, accuracy in the baseline instance test is comparable to other classification tasks, but poor given significant occlusion and noise. The use of replay for consolidation improves performance substantially for both types of tasks, but particularly the instance test.

Ensuring safe and effective use of AI requires understanding and anticipating its performance on novel tasks, from advanced scientific challenges to transformed workplace activities. So far, benchmarking has guided progress in AI, but it has offered limited explanatory and predictive power for general-purpose AI systems, given the low transferability across diverse tasks. In this paper, we introduce general scales for AI evaluation that can explain what common AI benchmarks really measure, extract ability profiles of AI systems, and predict their performance for new task instances, in- and out-of-distribution. Our fully-automated methodology builds on 18 newly-crafted rubrics that place instance demands on general scales that do not saturate. Illustrated for 15 large language models and 63 tasks, high explanatory power is unleashed from inspecting the demand and ability profiles, bringing insights on the sensitivity and specificity exhibited by different benchmarks, and how knowledge, metacognition and reasoning are affected by model size, chain-of-thought and distillation. Surprisingly, high predictive power at the instance level becomes possible using these demand levels, providing superior estimates over black-box baseline predictors based on embeddings or finetuning, especially in out-of-distribution settings (new tasks and new benchmarks). The scales, rubrics, battery, techniques and results presented here represent a major step for AI evaluation, underpinning the reliable deployment of AI in the years ahead. (Collaborative platform: https://kinds-of-intelligence-cfi.github.io/ADELE.)

We study the tradeoff between computational effort and classification accuracy in a cascade of deep neural networks. During inference, the user sets the acceptable accuracy degradation which then automatically determines confidence thresholds for the intermediate classifiers. As soon as the confidence threshold is met, inference terminates immediately without having to compute the output of the complete network. Confidence levels are derived directly from the softmax outputs of intermediate classifiers, as we do not train special decision functions. We show that using a softmax output as a confidence measure in a cascade of deep neural networks leads to a reduction of 15%-50% in the number of MAC operations while degrading the classification accuracy by roughly 1%. Our method can be easily incorporated into pre-trained non-cascaded architectures, as we exemplify on ResNet. Our main contribution is a method that dynamically adjusts the tradeoff between accuracy and computation without retraining the model.

FOLD-RM is an explainable machine learning classification algorithm that uses training data to create a set of classification rules. In this paper we introduce CON-FOLD which extends FOLD-RM in several ways. CON-FOLD assigns probability-based confidence scores to rules learned for a classification task. This allows users to know how confident they should be in a prediction made by the model. We present a confidence-based pruning algorithm that uses the unique structure of FOLD-RM rules to efficiently prune rules and prevent overfitting. Furthermore, CON-FOLD enables the user to provide pre-existing knowledge in the form of logic program rules that are either (fixed) background knowledge or (modifiable) initial rule candidates. The paper describes our method in detail and reports on practical experiments. We demonstrate the performance of the algorithm on benchmark datasets from the UCI Machine Learning Repository. For that, we introduce a new metric, Inverse Brier Score, to evaluate the accuracy of the produced confidence scores. Finally we apply this extension to a real world example that requires explainability: marking of student responses to a short answer question from the Australian Physics Olympiad.

Quality Estimation (QE) is estimating the quality of model output when the ground truth reference is not available. Looking at model uncertainty from its own output probabilities is the most trivial and low-effort way to estimate the output quality. However, for generative model, output probabilities might not be the best quality estimator. At an output step, there can be multiple correct options, making the probability distribution spread out more. Thus, lower token probability does not necessarily mean lower output quality. In other words, the model can be considered underconfident. In this paper, we propose a QE approach called Dominant Mass Probability (DMP}, that boosts the model confidence in cases where there are multiple viable output options. We show that, with no increase in complexity, DMP is notably better than sequence probability when estimating the quality of different models (Whisper, Llama, etc.) on different tasks (translation, summarization, etc.). Compared to sequence probability, DMP achieves on average +0.208 improvement in Pearson correlation to ground-truth quality.

As machine learning technology gets applied to actual products and solutions, new challenges have emerged. Models unexpectedly fail to generalize to small changes in the distribution, tend to be confident on novel data they have never seen, or cannot communicate the rationale behind their decisions effectively with the end users. Collectively, we face a trustworthiness issue with the current machine learning technology. This textbook on Trustworthy Machine Learning (TML) covers a theoretical and technical background of four key topics in TML: Out-of-Distribution Generalization, Explainability, Uncertainty Quantification, and Evaluation of Trustworthiness. We discuss important classical and contemporary research papers of the aforementioned fields and uncover and connect their underlying intuitions. The book evolved from the homonymous course at the University of T\"ubingen, first offered in the Winter Semester of 2022/23. It is meant to be a stand-alone product accompanied by code snippets and various pointers to further sources on topics of TML. The dedicated website of the book is https://trustworthyml.io/.

Recent advances in long chain-of-thought (CoT) reasoning have largely prioritized answer accuracy and token efficiency, while overlooking aspects critical to trustworthiness. We argue that usable reasoning systems must be trustworthy, characterized by three properties: interpretability, faithfulness, and reliability. To this end, we propose ReFIne, a new training framework that integrates supervised fine-tuning with GRPO to encourage models to: (i) improve interpretability by producing structured, tag-based traces with high-level planning that are easier for humans to follow; (ii) enhance faithfulness by explicitly disclosing the decisive information guiding each solution, with consistent cross-section references; and (iii) promote reliability by providing self-assessments of both the derivation's soundness and the confidence of the final answer. We apply ReFIne to the Qwen3 models at multiple scales (1.7B/4B/8B) and evaluate across mathematical benchmarks of varying difficulty. Our experimental results show that ReFIne models generate clearer and better-structured reasoning traces (interpretability +44.0%), more faithfully expose their underlying decision process (faithfulness +18.8%), and offer informative confidence estimates (reliability +42.4%). These findings highlight an overlooked but important direction: reasoning models should be optimized not only for accuracy, but also for broader dimensions of trustworthiness. Our code is available at: https://github.com/Trustworthy-ML-Lab/Training_Trustworthy_LRM_with_Refine

Estimating the difficulty of a dataset typically involves comparing state-of-the-art models to humans; the bigger the performance gap, the harder the dataset is said to be. However, this comparison provides little understanding of how difficult each instance in a given distribution is, or what attributes make the dataset difficult for a given model. To address these questions, we frame dataset difficulty -- w.r.t. a model V -- as the lack of V-usable information (Xu et al., 2019), where a lower value indicates a more difficult dataset for V. We further introduce pointwise \mathcal{V-information} (PVI) for measuring the difficulty of individual instances w.r.t. a given distribution. While standard evaluation metrics typically only compare different models for the same dataset, V-usable information and PVI also permit the converse: for a given model V, we can compare different datasets, as well as different instances/slices of the same dataset. Furthermore, our framework allows for the interpretability of different input attributes via transformations of the input, which we use to discover annotation artefacts in widely-used NLP benchmarks.

Large Language Models (LLMs) often generate outputs that lack grounding in real-world facts, a phenomenon known as hallucinations. Prior research has associated hallucinations with model uncertainty, leveraging this relationship for hallucination detection and mitigation. In this paper, we challenge the underlying assumption that all hallucinations are associated with uncertainty. Using knowledge detection and uncertainty measurement methods, we demonstrate that models can hallucinate with high certainty even when they have the correct knowledge. We further show that high-certainty hallucinations are consistent across models and datasets, distinctive enough to be singled out, and challenge existing mitigation methods. Our findings reveal an overlooked aspect of hallucinations, emphasizing the need to understand their origins and improve mitigation strategies to enhance LLM safety. The code is available at https://github.com/technion-cs-nlp/Trust_me_Im_wrong .

The recent proliferation of research into transformer based natural language processing has led to a number of studies which attempt to detect the presence of human-like cognitive behavior in the models. We contend that, as is true of human psychology, the investigation of cognitive behavior in language models must be conducted in an appropriate population of an appropriate size for the results to be meaningful. We leverage work in uncertainty estimation in a novel approach to efficiently construct experimental populations. The resultant tool, PopulationLM, has been made open source. We provide theoretical grounding in the uncertainty estimation literature and motivation from current cognitive work regarding language models. We discuss the methodological lessons from other scientific communities and attempt to demonstrate their application to two artificial population studies. Through population based experimentation we find that language models exhibit behavior consistent with typicality effects among categories highly represented in training. However, we find that language models don't tend to exhibit structural priming effects. Generally, our results show that single models tend to over estimate the presence of cognitive behaviors in neural models.

This study investigates the metacognitive capabilities of Large Language Models relative to human metacognition in the context of the International Coaching Federation ICF mimicking exam, a situational judgment test related to coaching competencies. Using a mixed method approach, we assessed the metacognitive performance, including sensitivity, accuracy in probabilistic predictions, and bias, of human participants and five advanced LLMs (GPT-4, Claude-3-Opus 3, Mistral Large, Llama 3, and Gemini 1.5 Pro). The results indicate that LLMs outperformed humans across all metacognitive metrics, particularly in terms of reduced overconfidence, compared to humans. However, both LLMs and humans showed less adaptability in ambiguous scenarios, adhering closely to predefined decision frameworks. The study suggests that Generative AI can effectively engage in human-like metacognitive processing without conscious awareness. Implications of the study are discussed in relation to development of AI simulators that scaffold cognitive and metacognitive aspects of mastering coaching competencies. More broadly, implications of these results are discussed in relation to development of metacognitive modules that lead towards more autonomous and intuitive AI systems.

The ability to acknowledge the inevitable uncertainty in their knowledge and reasoning is a prerequisite for AI systems to be truly truthful and reliable. In this paper, we present a taxonomy of uncertainty specific to vision-language AI systems, distinguishing between epistemic uncertainty (arising from a lack of information) and aleatoric uncertainty (due to inherent unpredictability), and further explore finer categories within. Based on this taxonomy, we synthesize a benchmark dataset, CertainlyUncertain, featuring 178K visual question answering (VQA) samples as contrastive pairs. This is achieved by 1) inpainting images to make previously answerable questions into unanswerable ones; and 2) using image captions to prompt large language models for both answerable and unanswerable questions. Additionally, we introduce a new metric confidence-weighted accuracy, that is well correlated with both accuracy and calibration error, to address the shortcomings of existing metrics.

Large language models frequently encounter conflicts between their parametric knowledge and contextual input, often resulting in factual inconsistencies or hallucinations. We propose Self-Reflective Debate for Contextual Reliability (SR-DCR), a lightweight framework that integrates token-level self-confidence with an asymmetric multi-agent debate to adjudicate such conflicts. A critic, deprived of context, challenges a defender who argues from the given passage; a judge model evaluates the debate and determines the context's reliability. The final answer is selected by combining the verdict with model confidence. Experiments on the ClashEval benchmark demonstrate that SR-DCR consistently enhances robustness to misleading context while maintaining accuracy on trustworthy inputs, outperforming both classical debate and confidence-only baselines with minimal computational overhead. The code is available at https://github.com/smiles724/Self-Reflective-Debates.

Uncertainty quantification is essential for assessing the reliability and trustworthiness of modern AI systems. Among existing approaches, verbalized uncertainty, where models express their confidence through natural language, has emerged as a lightweight and interpretable solution in large language models (LLMs). However, its effectiveness in vision-language models (VLMs) remains insufficiently studied. In this work, we conduct a comprehensive evaluation of verbalized confidence in VLMs, spanning three model categories, four task domains, and three evaluation scenarios. Our results show that current VLMs often display notable miscalibration across diverse tasks and settings. Notably, visual reasoning models (i.e., thinking with images) consistently exhibit better calibration, suggesting that modality-specific reasoning is critical for reliable uncertainty estimation. To further address calibration challenges, we introduce Visual Confidence-Aware Prompting, a two-stage prompting strategy that improves confidence alignment in multimodal settings. Overall, our study highlights the inherent miscalibration in VLMs across modalities. More broadly, our findings underscore the fundamental importance of modality alignment and model faithfulness in advancing reliable multimodal systems.

Evaluating the accuracy of outputs generated by Large Language Models (LLMs) is especially important in the climate science and policy domain. We introduce the Expert Confidence in Climate Statements (ClimateX) dataset, a novel, curated, expert-labeled dataset consisting of 8094 climate statements collected from the latest Intergovernmental Panel on Climate Change (IPCC) reports, labeled with their associated confidence levels. Using this dataset, we show that recent LLMs can classify human expert confidence in climate-related statements, especially in a few-shot learning setting, but with limited (up to 47%) accuracy. Overall, models exhibit consistent and significant over-confidence on low and medium confidence statements. We highlight implications of our results for climate communication, LLMs evaluation strategies, and the use of LLMs in information retrieval systems.

Large language models (LLMs) specializing in natural language generation (NLG) have recently started exhibiting promising capabilities across a variety of domains. However, gauging the trustworthiness of responses generated by LLMs remains an open challenge, with limited research on uncertainty quantification (UQ) for NLG. Furthermore, existing literature typically assumes white-box access to language models, which is becoming unrealistic either due to the closed-source nature of the latest LLMs or computational constraints. In this work, we investigate UQ in NLG for black-box LLMs. We first differentiate uncertainty vs confidence: the former refers to the "dispersion" of the potential predictions for a fixed input, and the latter refers to the confidence on a particular prediction/generation. We then propose and compare several confidence/uncertainty metrics, applying them to selective NLG where unreliable results could either be ignored or yielded for further assessment. Experiments were carried out with several popular LLMs on question-answering datasets (for evaluation purposes). Results reveal that a simple metric for the semantic dispersion can be a reliable predictor of the quality of LLM responses, providing valuable insights for practitioners on uncertainty management when adopting LLMs. The code to replicate our experiments is available at https://github.com/zlin7/UQ-NLG.

Training data attribution (TDA) techniques find influential training data for the model's prediction on the test data of interest. They approximate the impact of down- or up-weighting a particular training sample. While conceptually useful, they are hardly applicable to deep models in practice, particularly because of their sensitivity to different model initialisation. In this paper, we introduce a Bayesian perspective on the TDA task, where the learned model is treated as a Bayesian posterior and the TDA estimates as random variables. From this novel viewpoint, we observe that the influence of an individual training sample is often overshadowed by the noise stemming from model initialisation and SGD batch composition. Based on this observation, we argue that TDA can only be reliably used for explaining deep model predictions that are consistently influenced by certain training data, independent of other noise factors. Our experiments demonstrate the rarity of such noise-independent training-test data pairs but confirm their existence. We recommend that future researchers and practitioners trust TDA estimates only in such cases. Further, we find a disagreement between ground truth and estimated TDA distributions and encourage future work to study this gap. Code is provided at https://github.com/ElisaNguyen/bayesian-tda.

We introduce BSDetector, a method for detecting bad and speculative answers from a pretrained Large Language Model by estimating a numeric confidence score for any output it generated. Our uncertainty quantification technique works for any LLM accessible only via a black-box API, whose training data remains unknown. By expending a bit of extra computation, users of any LLM API can now get the same response as they would ordinarily, as well as a confidence estimate that cautions when not to trust this response. Experiments on both closed and open-form Question-Answer benchmarks reveal that BSDetector more accurately identifies incorrect LLM responses than alternative uncertainty estimation procedures (for both GPT-3 and ChatGPT). By sampling multiple responses from the LLM and considering the one with the highest confidence score, we can additionally obtain more accurate responses from the same LLM, without any extra training steps. In applications involving automated evaluation with LLMs, accounting for our confidence scores leads to more reliable evaluation in both human-in-the-loop and fully-automated settings (across both GPT 3.5 and 4).

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.

The trustworthiness of machine learning has emerged as a critical topic in the field, encompassing various applications and research areas such as robustness, security, interpretability, and fairness. The last decade saw the development of numerous methods addressing these challenges. In this survey, we systematically review these advancements from a data-centric perspective, highlighting the shortcomings of traditional empirical risk minimization (ERM) training in handling challenges posed by the data. Interestingly, we observe a convergence of these methods, despite being developed independently across trustworthy machine learning subfields. Pearl's hierarchy of causality offers a unifying framework for these techniques. Accordingly, this survey presents the background of trustworthy machine learning development using a unified set of concepts, connects this language to Pearl's causal hierarchy, and finally discusses methods explicitly inspired by causality literature. We provide a unified language with mathematical vocabulary to link these methods across robustness, adversarial robustness, interpretability, and fairness, fostering a more cohesive understanding of the field. Further, we explore the trustworthiness of large pretrained models. After summarizing dominant techniques like fine-tuning, parameter-efficient fine-tuning, prompting, and reinforcement learning with human feedback, we draw connections between them and the standard ERM. This connection allows us to build upon the principled understanding of trustworthy methods, extending it to these new techniques in large pretrained models, paving the way for future methods. Existing methods under this perspective are also reviewed. Lastly, we offer a brief summary of the applications of these methods and discuss potential future aspects related to our survey. For more information, please visit http://trustai.one.

Large Language Models (LLMs) are often described as being instances of foundation models - that is, models that transfer strongly across various tasks and conditions in few-show or zero-shot manner, while exhibiting scaling laws that predict function improvement when increasing the pre-training scale. These claims of excelling in different functions and tasks rely on measurements taken across various sets of standardized benchmarks showing high scores for such models. We demonstrate here a dramatic breakdown of function and reasoning capabilities of state-of-the-art models trained at the largest available scales which claim strong function, using a simple, short, conventional common sense problem formulated in concise natural language, easily solvable by humans. The breakdown is dramatic, as models also express strong overconfidence in their wrong solutions, while providing often non-sensical "reasoning"-like explanations akin to confabulations to justify and backup the validity of their clearly failed responses, making them sound plausible. Various standard interventions in an attempt to get the right solution, like various type of enhanced prompting, or urging the models to reconsider the wrong solutions again by multi step re-evaluation, fail. We take these initial observations to the scientific and technological community to stimulate urgent re-assessment of the claimed capabilities of current generation of LLMs, Such re-assessment also requires common action to create standardized benchmarks that would allow proper detection of such basic reasoning deficits that obviously manage to remain undiscovered by current state-of-the-art evaluation procedures and benchmarks. Code for reproducing experiments in the paper and raw experiments data can be found at https://github.com/LAION-AI/AIW

Despite the success of convolutional neural networks (CNNs) in many academic benchmarks for computer vision tasks, their application in the real-world is still facing fundamental challenges. One of these open problems is the inherent lack of robustness, unveiled by the striking effectiveness of adversarial attacks. Current attack methods are able to manipulate the network's prediction by adding specific but small amounts of noise to the input. In turn, adversarial training (AT) aims to achieve robustness against such attacks and ideally a better model generalization ability by including adversarial samples in the trainingset. However, an in-depth analysis of the resulting robust models beyond adversarial robustness is still pending. In this paper, we empirically analyze a variety of adversarially trained models that achieve high robust accuracies when facing state-of-the-art attacks and we show that AT has an interesting side-effect: it leads to models that are significantly less overconfident with their decisions, even on clean data than non-robust models. Further, our analysis of robust models shows that not only AT but also the model's building blocks (like activation functions and pooling) have a strong influence on the models' prediction confidences. Data & Project website: https://github.com/GeJulia/robustness_confidences_evaluation

LLM-judged benchmarks are increasingly used to evaluate complex model behaviors, yet their design introduces failure modes absent in conventional ground-truth based benchmarks. We argue that without tight objectives and verifiable constructions, benchmark rankings can produce high-confidence rankings that are in fact largely noise. We introduce two mechanisms to diagnose these issues. Schematic adherence quantifies how much of a judge's overall verdict is explained by the explicit evaluation schema, revealing unexplained variance when judges deviate from their own rubric. Psychometric validity aggregates internal consistency and discriminant validity signals to quantify irreducible uncertainty in any benchmarking run. Applying these tools to Arena-Hard Auto, we find severe schema incoherence and factor collapse across popular judges: for example, unexplained variance exceeding 90 percent for DeepSeek-R1-32B and factor correlations above 0.93 for most criteria. We also show that the ELO-style aggregation used by Arena-Hard Auto collapses and masks genuine ranking uncertainty. Our results highlight design failures that undermine validity and offer actionable principles for building better-scoped, reliability-aware LLM-judged benchmarks. We release our code at https://anonymous.4open.science/r/judgment-to-noise-947D/README.md

Recent studies have put into question the belief that emergent abilities in language models are exclusive to large models. This skepticism arises from two observations: 1) smaller models can also exhibit high performance on emergent abilities and 2) there is doubt on the discontinuous metrics used to measure these abilities. In this paper, we propose to study emergent abilities in the lens of pre-training loss, instead of model size or training compute. We demonstrate that the models with the same pre-training loss, but different model and data sizes, generate the same performance on various downstream tasks. We also discover that a model exhibits emergent abilities on certain tasks -- regardless of the continuity of metrics -- when its pre-training loss falls below a specific threshold. Before reaching this threshold, its performance remains at the level of random guessing. This inspires us to redefine emergent abilities as those that manifest in models with lower pre-training losses, highlighting that these abilities cannot be predicted by merely extrapolating the performance trends of models with higher pre-training losses.

Widely deployed large language models (LLMs) can produce convincing yet incorrect outputs, potentially misleading users who may rely on them as if they were correct. To reduce such overreliance, there have been calls for LLMs to communicate their uncertainty to end users. However, there has been little empirical work examining how users perceive and act upon LLMs' expressions of uncertainty. We explore this question through a large-scale, pre-registered, human-subject experiment (N=404) in which participants answer medical questions with or without access to responses from a fictional LLM-infused search engine. Using both behavioral and self-reported measures, we examine how different natural language expressions of uncertainty impact participants' reliance, trust, and overall task performance. We find that first-person expressions (e.g., "I'm not sure, but...") decrease participants' confidence in the system and tendency to agree with the system's answers, while increasing participants' accuracy. An exploratory analysis suggests that this increase can be attributed to reduced (but not fully eliminated) overreliance on incorrect answers. While we observe similar effects for uncertainty expressed from a general perspective (e.g., "It's not clear, but..."), these effects are weaker and not statistically significant. Our findings suggest that using natural language expressions of uncertainty may be an effective approach for reducing overreliance on LLMs, but that the precise language used matters. This highlights the importance of user testing before deploying LLMs at scale.

Recent work in language modeling has raised the possibility of self-improvement, where a language models evaluates and refines its own generations to achieve higher performance without external feedback. It is impossible for this self-improvement to create information that is not already in the model, so why should we expect that this will lead to improved capabilities? We offer a new perspective on the capabilities of self-improvement through a lens we refer to as sharpening. Motivated by the observation that language models are often better at verifying response quality than they are at generating correct responses, we formalize self-improvement as using the model itself as a verifier during post-training in order to ``sharpen'' the model to one placing large mass on high-quality sequences, thereby amortizing the expensive inference-time computation of generating good sequences. We begin by introducing a new statistical framework for sharpening in which the learner aims to sharpen a pre-trained base policy via sample access, and establish fundamental limits. Then we analyze two natural families of self-improvement algorithms based on SFT and RLHF. We find that (i) the SFT-based approach is minimax optimal whenever the initial model has sufficient coverage, but (ii) the RLHF-based approach can improve over SFT-based self-improvement by leveraging online exploration, bypassing the need for coverage. Finally, we empirically validate the sharpening mechanism via inference-time and amortization experiments. We view these findings as a starting point toward a foundational understanding that can guide the design and evaluation of self-improvement algorithms.

Many cognitive approaches to well-being, such as recognizing and reframing unhelpful thoughts, have received considerable empirical support over the past decades, yet still lack truly widespread adoption in self-help format. A barrier to that adoption is a lack of adequately specific and diverse dedicated practice material. This work examines whether current language models can be leveraged to both produce a virtually unlimited quantity of practice material illustrating standard unhelpful thought patterns matching specific given contexts, and generate suitable positive reframing proposals. We propose PATTERNREFRAME, a novel dataset of about 10k examples of thoughts containing unhelpful thought patterns conditioned on a given persona, accompanied by about 27k positive reframes. By using this dataset to train and/or evaluate current models, we show that existing models can already be powerful tools to help generate an abundance of tailored practice material and hypotheses, with no or minimal additional model training required.

Large Language Models (LLMs) have shown remarkable capabilities across various tasks, but their deployment in high-stake domains requires consistent performance across multiple interaction rounds. This paper introduces a comprehensive framework for evaluating and improving LLM response consistency, making three key contributions. First, we propose a novel Position-Weighted Consistency (PWC) score that captures both the importance of early-stage stability and recovery patterns in multi-turn interactions. Second, we present a carefully curated benchmark dataset spanning diverse domains and difficulty levels, specifically designed to evaluate LLM consistency under various challenging follow-up scenarios. Third, we introduce Confidence-Aware Response Generation (CARG), a framework that significantly improves response stability by incorporating model confidence signals into the generation process. Empirical results demonstrate that CARG significantly improves response stability without sacrificing accuracy, underscoring its potential for reliable LLM deployment in critical applications.

We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers). In particular, we derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large, in which case the output of the model is unreliable. This condition can be computed based solely on the output of the model obtained simply by some special iterative prompting based on the previous responses. Such quantification, for instance, allows to detect hallucinations (cases when epistemic uncertainty is high) in both single- and multi-answer responses. This is in contrast to many standard uncertainty quantification strategies (such as thresholding the log-likelihood of a response) where hallucinations in the multi-answer case cannot be detected. We conduct a series of experiments which demonstrate the advantage of our formulation. Further, our investigations shed some light on how the probabilities assigned to a given output by an LLM can be amplified by iterative prompting, which might be of independent interest.

While numerous works have assessed the generative performance of language models (LMs) on tasks requiring Theory of Mind reasoning, research into the models' internal representation of mental states remains limited. Recent work has used probing to demonstrate that LMs can represent beliefs of themselves and others. However, these claims are accompanied by limited evaluation, making it difficult to assess how mental state representations are affected by model design and training choices. We report an extensive benchmark with various LM types with different model sizes, fine-tuning approaches, and prompt designs to study the robustness of mental state representations and memorisation issues within the probes. Our results show that the quality of models' internal representations of the beliefs of others increases with model size and, more crucially, with fine-tuning. We are the first to study how prompt variations impact probing performance on theory of mind tasks. We demonstrate that models' representations are sensitive to prompt variations, even when such variations should be beneficial. Finally, we complement previous activation editing experiments on Theory of Mind tasks and show that it is possible to improve models' reasoning performance by steering their activations without the need to train any probe.

Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic uncertainty, we argue that this does not capture the part of lack of knowledge induced by model misspecification. We discuss how the excess risk, which is the gap between the generalization error of a predictor and the Bayes predictor, is a sound measure of epistemic uncertainty which captures the effect of model misspecification. We thus propose a principled framework for directly estimating the excess risk by learning a secondary predictor for the generalization error and subtracting an estimate of aleatoric uncertainty, i.e., intrinsic unpredictability. We discuss the merits of this novel measure of epistemic uncertainty, and highlight how it differs from variance-based measures of epistemic uncertainty and addresses its major pitfall. Our framework, Direct Epistemic Uncertainty Prediction (DEUP) is particularly interesting in interactive learning environments, where the learner is allowed to acquire novel examples in each round. Through a wide set of experiments, we illustrate how existing methods in sequential model optimization can be improved with epistemic uncertainty estimates from DEUP, and how DEUP can be used to drive exploration in reinforcement learning. We also evaluate the quality of uncertainty estimates from DEUP for probabilistic image classification and predicting synergies of drug combinations.

Generative search engines directly generate responses to user queries, along with in-line citations. A prerequisite trait of a trustworthy generative search engine is verifiability, i.e., systems should cite comprehensively (high citation recall; all statements are fully supported by citations) and accurately (high citation precision; every cite supports its associated statement). We conduct human evaluation to audit four popular generative search engines -- Bing Chat, NeevaAI, perplexity.ai, and YouChat -- across a diverse set of queries from a variety of sources (e.g., historical Google user queries, dynamically-collected open-ended questions on Reddit, etc.). We find that responses from existing generative search engines are fluent and appear informative, but frequently contain unsupported statements and inaccurate citations: on average, a mere 51.5% of generated sentences are fully supported by citations and only 74.5% of citations support their associated sentence. We believe that these results are concerningly low for systems that may serve as a primary tool for information-seeking users, especially given their facade of trustworthiness. We hope that our results further motivate the development of trustworthy generative search engines and help researchers and users better understand the shortcomings of existing commercial systems.

With the recent emergence of foundation models trained on internet-scale data and demonstrating remarkable generalization capabilities, such foundation models have become more widely adopted, leading to an expanding range of application domains. Despite this rapid proliferation, the trustworthiness of foundation models remains underexplored. Specifically, the out-of-distribution detection (OoDD) capabilities of large vision-language models (LVLMs), such as GPT-4o, which are trained on massive multi-modal data, have not been sufficiently addressed. The disparity between their demonstrated potential and practical reliability raises concerns regarding the safe and trustworthy deployment of foundation models. To address this gap, we evaluate and analyze the OoDD capabilities of various proprietary and open-source LVLMs. Our investigation contributes to a better understanding of how these foundation models represent confidence scores through their generated natural language responses. Based on our observations, we propose a self-guided prompting approach, termed Reflexive Guidance (ReGuide), aimed at enhancing the OoDD capability of LVLMs by leveraging self-generated image-adaptive concept suggestions. Experimental results demonstrate that our ReGuide enhances the performance of current LVLMs in both image classification and OoDD tasks.

To answer a question, language models often need to integrate prior knowledge learned during pretraining and new information presented in context. We hypothesize that models perform this integration in a predictable way across different questions and contexts: models will rely more on prior knowledge for questions about entities (e.g., persons, places, etc.) that they are more familiar with due to higher exposure in the training corpus, and be more easily persuaded by some contexts than others. To formalize this problem, we propose two mutual information-based metrics to measure a model's dependency on a context and on its prior about an entity: first, the persuasion score of a given context represents how much a model depends on the context in its decision, and second, the susceptibility score of a given entity represents how much the model can be swayed away from its original answer distribution about an entity. Following well-established measurement modeling methods, we empirically test for the validity and reliability of these metrics. Finally, we explore and find a relationship between the scores and the model's expected familiarity with an entity, and provide two use cases to illustrate their benefits.

Production assertions are statements embedded in the code to help developers validate their assumptions about the code. They assist developers in debugging, provide valuable documentation, and enhance code comprehension. Current research in this area primarily focuses on assertion generation for unit tests using techniques, such as static analysis and deep learning. While these techniques have shown promise, they fall short when it comes to generating production assertions, which serve a different purpose. This preprint addresses the gap by introducing Assertify, an automated end-to-end tool that leverages Large Language Models (LLMs) and prompt engineering with few-shot learning to generate production assertions. By creating context-rich prompts, the tool emulates the approach developers take when creating production assertions for their code. To evaluate our approach, we compiled a dataset of 2,810 methods by scraping 22 mature Java repositories from GitHub. Our experiments demonstrate the effectiveness of few-shot learning by producing assertions with an average ROUGE-L score of 0.526, indicating reasonably high structural similarity with the assertions written by developers. This research demonstrates the potential of LLMs in automating the generation of production assertions that resemble the original assertions.

The field of AI research is advancing at an unprecedented pace, enabling automated hypothesis generation and experimental design across diverse domains such as biology, mathematics, and artificial intelligence. Despite these advancements, there remains a significant gap in the availability of scalable advising systems capable of providing high-quality, well-reasoned feedback to refine proposed hypotheses and experimental designs. To address this challenge, we explore key factors that underlie the development of robust advising systems, including model size, context length, confidence estimation, and structured reasoning processes. Our findings reveal that a relatively small model, when equipped with a well-compressed literature database and a structured reasoning framework, can outperform powerful general-purpose language models such as Deepseek-R1 in terms of acceptance rates for self-ranked top-30% submissions to ICLR 2025. Moreover, when limited to high-confidence predictions, our system achieves an acceptance rate exceeding 90% on the ICLR 2025 test set, underscoring its potential to significantly enhance the quality and efficiency of hypothesis generation and experimental design. The code is released at https://github.com/HowardLiu0830/GUIDE-Research-Idea-Evaluation.

A crucial requirement for reliable deployment of deep learning models for safety-critical applications is the ability to identify out-of-distribution (OOD) data points, samples which differ from the training data and on which a model might underperform. Previous work has attempted to tackle this problem using uncertainty estimation techniques. However, there is empirical evidence that a large family of these techniques do not detect OOD reliably in classification tasks. This paper gives a theoretical explanation for said experimental findings and illustrates it on synthetic data. We prove that such techniques are not able to reliably identify OOD samples in a classification setting, since their level of confidence is generalized to unseen areas of the feature space. This result stems from the interplay between the representation of ReLU networks as piece-wise affine transformations, the saturating nature of activation functions like softmax, and the most widely-used uncertainty metrics.

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-m rate, where m is the number of simulated samples. This can lead to significant computational challenges since a large m is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.

The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We study the use of bootstraps in high-dimensional environments with a small number of resamples. In particular, we show that with a recent "cheap" bootstrap perspective, using a number of resamples as small as one could attain valid coverage even when the dimension grows closely with the sample size, thus strongly supporting the implementability of the bootstrap for large-scale problems. We validate our theoretical results and compare the performance of our approach with other benchmarks via a range of experiments.

Monitoring machine learning models once they are deployed is challenging. It is even more challenging to decide when to retrain models in real-case scenarios when labeled data is beyond reach, and monitoring performance metrics becomes unfeasible. In this work, we use non-parametric bootstrapped uncertainty estimates and SHAP values to provide explainable uncertainty estimation as a technique that aims to monitor the deterioration of machine learning models in deployment environments, as well as determine the source of model deterioration when target labels are not available. Classical methods are purely aimed at detecting distribution shift, which can lead to false positives in the sense that the model has not deteriorated despite a shift in the data distribution. To estimate model uncertainty we construct prediction intervals using a novel bootstrap method, which improves upon the work of Kumar & Srivastava (2012). We show that both our model deterioration detection system as well as our uncertainty estimation method achieve better performance than the current state-of-the-art. Finally, we use explainable AI techniques to gain an understanding of the drivers of model deterioration. We release an open source Python package, doubt, which implements our proposed methods, as well as the code used to reproduce our experiments.

As AI grows more powerful, it will increasingly shape how we understand the world. But with this influence comes the risk of amplifying misinformation and deepening social divides-especially on consequential topics like public health where factual accuracy directly impacts well-being. Scalable Oversight aims to ensure AI truthfulness by enabling humans to supervise systems that may exceed human capabilities--yet humans themselves hold different beliefs and biases that impair their judgment. We study whether AI debate can guide biased judges toward the truth by having two AI systems debate opposing sides of controversial COVID-19 factuality claims where people hold strong prior beliefs. We conduct two studies: one with human judges holding either mainstream or skeptical beliefs evaluating factuality claims through AI-assisted debate or consultancy protocols, and a second examining the same problem with personalized AI judges designed to mimic these different human belief systems. In our human study, we find that debate-where two AI advisor systems present opposing evidence-based arguments-consistently improves judgment accuracy and confidence calibration, outperforming consultancy with a single-advisor system by 10% overall. The improvement is most significant for judges with mainstream beliefs (+15.2% accuracy), though debate also helps skeptical judges who initially misjudge claims move toward accurate views (+4.7% accuracy). In our AI judge study, we find that AI judges with human-like personas achieve even higher accuracy (78.5%) than human judges (70.1%) and default AI judges without personas (69.8%), suggesting their potential for supervising frontier AI models. These findings highlight AI debate as a promising path toward scalable, bias-resilient oversight--leveraging both diverse human and AI judgments to move closer to truth in contested domains.

Trust is an important factor in people's interactions with AI systems. However, there is a lack of empirical studies examining how real end-users trust or distrust the AI system they interact with. Most research investigates one aspect of trust in lab settings with hypothetical end-users. In this paper, we provide a holistic and nuanced understanding of trust in AI through a qualitative case study of a real-world computer vision application. We report findings from interviews with 20 end-users of a popular, AI-based bird identification app where we inquired about their trust in the app from many angles. We find participants perceived the app as trustworthy and trusted it, but selectively accepted app outputs after engaging in verification behaviors, and decided against app adoption in certain high-stakes scenarios. We also find domain knowledge and context are important factors for trust-related assessment and decision-making. We discuss the implications of our findings and provide recommendations for future research on trust in AI.

Despite their vast capabilities, Large Language Models (LLMs) often struggle with generating reliable outputs, frequently producing high-confidence inaccuracies known as hallucinations. Addressing this challenge, our research introduces InternalInspector, a novel framework designed to enhance confidence estimation in LLMs by leveraging contrastive learning on internal states including attention states, feed-forward states, and activation states of all layers. Unlike existing methods that primarily focus on the final activation state, InternalInspector conducts a comprehensive analysis across all internal states of every layer to accurately identify both correct and incorrect prediction processes. By benchmarking InternalInspector against existing confidence estimation methods across various natural language understanding and generation tasks, including factual question answering, commonsense reasoning, and reading comprehension, InternalInspector achieves significantly higher accuracy in aligning the estimated confidence scores with the correctness of the LLM's predictions and lower calibration error. Furthermore, InternalInspector excels at HaluEval, a hallucination detection benchmark, outperforming other internal-based confidence estimation methods in this task.

Recent advancements in large language models (LLMs) often rely on generating intermediate reasoning steps to enhance accuracy. However, little work has examined how reasoning utility contributes to the final answer's correctness. Due to the stochastic nature of autoregressive generation, generating more context does not guarantee increased confidence in the answer. If we could predict, during generation, whether a reasoning step will be useful, we could stop early or prune ineffective steps, avoiding distractions in the final decision. We present an oracle study on MATH dataset, using Qwen2.5-32B and GPT-4o to generate reasoning chains, and then employing a separate model (Qwen3-8B) to quantify the utility of these chains for final accuracy. Specifically, we measure the model's uncertainty on the answer span Y at each reasoning step using conditional entropy (expected negative log-likelihood over the vocabulary) with context expanding step by step. Our results show a clear pattern: conditional entropy that decreases over steps is strongly associated with correct answers, whereas flat or increasing entropy often results in wrong answers. We also corroborate that incorrect reasoning paths tend to be longer than correct ones, suggesting that longer reasoning does not necessarily yield better outcomes. These findings serve as a foundation to inspire future work on designing efficient reasoning pipelines that detect and avoid unproductive reasoning early.

We propose a new test to measure a text model's multitask accuracy. The test covers 57 tasks including elementary mathematics, US history, computer science, law, and more. To attain high accuracy on this test, models must possess extensive world knowledge and problem solving ability. We find that while most recent models have near random-chance accuracy, the very largest GPT-3 model improves over random chance by almost 20 percentage points on average. However, on every one of the 57 tasks, the best models still need substantial improvements before they can reach expert-level accuracy. Models also have lopsided performance and frequently do not know when they are wrong. Worse, they still have near-random accuracy on some socially important subjects such as morality and law. By comprehensively evaluating the breadth and depth of a model's academic and professional understanding, our test can be used to analyze models across many tasks and to identify important shortcomings.

Words of estimative probability (WEP) are expressions of a statement's plausibility (probably, maybe, likely, doubt, likely, unlikely, impossible...). Multiple surveys demonstrate the agreement of human evaluators when assigning numerical probability levels to WEP. For example, highly likely corresponds to a median chance of 0.90+-0.08 in Fagen-Ulmschneider (2015)'s survey. In this work, we measure the ability of neural language processing models to capture the consensual probability level associated to each WEP. Firstly, we use the UNLI dataset (Chen et al., 2020) which associates premises and hypotheses with their perceived joint probability p, to construct prompts, e.g. "[PREMISE]. [WEP], [HYPOTHESIS]." and assess whether language models can predict whether the WEP consensual probability level is close to p. Secondly, we construct a dataset of WEP-based probabilistic reasoning, to test whether language models can reason with WEP compositions. When prompted "[EVENTA] is likely. [EVENTB] is impossible.", a causal language model should not express that [EVENTA&B] is likely. We show that both tasks are unsolved by off-the-shelf English language models, but that fine-tuning leads to transferable improvement.

Benchmarks shape scientific conclusions about model capabilities and steer model development. This creates a feedback loop: stronger benchmarks drive better models, and better models demand more discriminative benchmarks. Ensuring benchmark reliability is therefore essential for trustworthy evaluation and meaningful progress. In this work, we study benchmark reliability from a distributional perspective and introduce benchmark harmony, which measures how uniformly a model's performance is distributed across the subdomains of a benchmark. We posit that high harmony is a desirable benchmark property, indicating that the aggregate metric reflects uniform competence across subdomains. Across 19 multiple-choice benchmarks and five model families, we map each benchmark onto a mean-variance plane of harmony computed across models, where high mean and low variance signal more reliable evaluation. Our analysis shows that less harmonious benchmarks can give misleading results, since overall accuracy may be disproportionately influenced by specific subdomains. For instance, ARC-Easy is overwhelmed by questions on Biological Concepts, overshadowing other critical subdomains such as Geography, Physics, Chemistry, and Environmental Science. By recommending that harmony should be reported alongside accuracy, we reframe evaluation from simple performance averages to a more robust, distributionally reliable measurement of performance.

We propose a new definition of instance optimality for differentially private estimation algorithms. Our definition requires an optimal algorithm to compete, simultaneously for every dataset D, with the best private benchmark algorithm that (a) knows D in advance and (b) is evaluated by its worst-case performance on large subsets of D. That is, the benchmark algorithm need not perform well when potentially extreme points are added to D; it only has to handle the removal of a small number of real data points that already exist. This makes our benchmark significantly stronger than those proposed in prior work. We nevertheless show, for real-valued datasets, how to construct private algorithms that achieve our notion of instance optimality when estimating a broad class of dataset properties, including means, quantiles, and ell_p-norm minimizers. For means in particular, we provide a detailed analysis and show that our algorithm simultaneously matches or exceeds the asymptotic performance of existing algorithms under a range of distributional assumptions.

Recent large language models often answer factual questions correctly. But users can't trust any given claim a model makes without fact-checking, because language models can hallucinate convincing nonsense. In this work we use reinforcement learning from human preferences (RLHP) to train "open-book" QA models that generate answers whilst also citing specific evidence for their claims, which aids in the appraisal of correctness. Supporting evidence is drawn from multiple documents found via a search engine, or from a single user-provided document. Our 280 billion parameter model, GopherCite, is able to produce answers with high quality supporting evidence and abstain from answering when unsure. We measure the performance of GopherCite by conducting human evaluation of answers to questions in a subset of the NaturalQuestions and ELI5 datasets. The model's response is found to be high-quality 80\% of the time on this Natural Questions subset, and 67\% of the time on the ELI5 subset. Abstaining from the third of questions for which it is most unsure improves performance to 90\% and 80\% respectively, approaching human baselines. However, analysis on the adversarial TruthfulQA dataset shows why citation is only one part of an overall strategy for safety and trustworthiness: not all claims supported by evidence are true.

The Neural Arithmetic Logic Unit (NALU) is a neural network layer that can learn exact arithmetic operations between the elements of a hidden state. The goal of NALU is to learn perfect extrapolation, which requires learning the exact underlying logic of an unknown arithmetic problem. Evaluating the performance of the NALU is non-trivial as one arithmetic problem might have many solutions. As a consequence, single-instance MSE has been used to evaluate and compare performance between models. However, it can be hard to interpret what magnitude of MSE represents a correct solution and models sensitivity to initialization. We propose using a success-criterion to measure if and when a model converges. Using a success-criterion we can summarize success-rate over many initialization seeds and calculate confidence intervals. We contribute a generalized version of the previous arithmetic benchmark to measure models sensitivity under different conditions. This is, to our knowledge, the first extensive evaluation with respect to convergence of the NALU and its sub-units. Using a success-criterion to summarize 4800 experiments we find that consistently learning arithmetic extrapolation is challenging, in particular for multiplication.

In this paper, we introduce the idea of decomposing the residuals of regression with respect to the data instances instead of features. This allows us to determine the effects of each individual instance on the model and each other, and in doing so makes for a model-agnostic method of identifying instances of interest. In doing so, we can also determine the appropriateness of the model and data in the wider context of a given study. The paper focuses on the possible applications that such a framework brings to the relatively unexplored field of instance analysis in the context of Explainable AI tasks.

Estimating the difficulty of multiple-choice questions would be great help for educators who must spend substantial time creating and piloting stimuli for their tests, and for learners who want to practice. Supervised approaches to difficulty estimation have yielded to date mixed results. In this contribution we leverage an aspect of generative large models which might be seen as a weakness when answering questions, namely their uncertainty, and exploit it towards exploring correlations between two different metrics of uncertainty, and the actual student response distribution. While we observe some present but weak correlations, we also discover that the models' behaviour is different in the case of correct vs wrong answers, and that correlations differ substantially according to the different question types which are included in our fine-grained, previously unused dataset of 451 questions from a Biopsychology course. In discussing our findings, we also suggest potential avenues to further leverage model uncertainty as an additional proxy for item difficulty.

Do large language models (LLMs) anticipate when they will answer correctly? To study this, we extract activations after a question is read but before any tokens are generated, and train linear probes to predict whether the model's forthcoming answer will be correct. Across three open-source model families ranging from 7 to 70 billion parameters, projections on this "in-advance correctness direction" trained on generic trivia questions predict success in distribution and on diverse out-of-distribution knowledge datasets, outperforming black-box baselines and verbalised predicted confidence. Predictive power saturates in intermediate layers, suggesting that self-assessment emerges mid-computation. Notably, generalisation falters on questions requiring mathematical reasoning. Moreover, for models responding "I don't know", doing so strongly correlates with the probe score, indicating that the same direction also captures confidence. By complementing previous results on truthfulness and other behaviours obtained with probes and sparse auto-encoders, our work contributes essential findings to elucidate LLM internals.

Despite its importance to experimental design, statistical power (the probability that, given a real effect, an experiment will reject the null hypothesis) has largely been ignored by the NLP community. Underpowered experiments make it more difficult to discern the difference between statistical noise and meaningful model improvements, and increase the chances of exaggerated findings. By meta-analyzing a set of existing NLP papers and datasets, we characterize typical power for a variety of settings and conclude that underpowered experiments are common in the NLP literature. In particular, for several tasks in the popular GLUE benchmark, small test sets mean that most attempted comparisons to state of the art models will not be adequately powered. Similarly, based on reasonable assumptions, we find that the most typical experimental design for human rating studies will be underpowered to detect small model differences, of the sort that are frequently studied. For machine translation, we find that typical test sets of 2000 sentences have approximately 75% power to detect differences of 1 BLEU point. To improve the situation going forward, we give an overview of best practices for power analysis in NLP and release a series of notebooks to assist with future power analyses.

The deployment of pre-trained perception models in novel environments often leads to performance degradation due to distributional shifts. Although recent artificial intelligence approaches for metacognition use logical rules to characterize and filter model errors, improving precision often comes at the cost of reduced recall. This paper addresses the hypothesis that leveraging multiple pre-trained models can mitigate this recall reduction. We formulate the challenge of identifying and managing conflicting predictions from various models as a consistency-based abduction problem. The input predictions and the learned error detection rules derived from each model are encoded in a logic program. We then seek an abductive explanation--a subset of model predictions--that maximizes prediction coverage while ensuring the rate of logical inconsistencies (derived from domain constraints) remains below a specified threshold. We propose two algorithms for this knowledge representation task: an exact method based on Integer Programming (IP) and an efficient Heuristic Search (HS). Through extensive experiments on a simulated aerial imagery dataset featuring controlled, complex distributional shifts, we demonstrate that our abduction-based framework outperforms individual models and standard ensemble baselines, achieving, for instance, average relative improvements of approximately 13.6% in F1-score and 16.6% in accuracy across 15 diverse test datasets when compared to the best individual model. Our results validate the use of consistency-based abduction as an effective mechanism to robustly integrate knowledge from multiple imperfect reasoners in challenging, novel scenarios.

Natural language is an appealing medium for explaining how large language models process and store information, but evaluating the faithfulness of such explanations is challenging. To help address this, we develop two modes of evaluation for natural language explanations that claim individual neurons represent a concept in a text input. In the observational mode, we evaluate claims that a neuron a activates on all and only input strings that refer to a concept picked out by the proposed explanation E. In the intervention mode, we construe E as a claim that the neuron a is a causal mediator of the concept denoted by E. We apply our framework to the GPT-4-generated explanations of GPT-2 XL neurons of Bills et al. (2023) and show that even the most confident explanations have high error rates and little to no causal efficacy. We close the paper by critically assessing whether natural language is a good choice for explanations and whether neurons are the best level of analysis.

Machine learning models in modern mass-market applications are often updated over time. One of the foremost challenges faced is that, despite increasing overall performance, these updates may flip specific model predictions in unpredictable ways. In practice, researchers quantify the number of unstable predictions between models pre and post update -- i.e., predictive churn. In this paper, we study this effect through the lens of predictive multiplicity -- i.e., the prevalence of conflicting predictions over the set of near-optimal models (the Rashomon set). We show how traditional measures of predictive multiplicity can be used to examine expected churn over this set of prospective models -- i.e., the set of models that may be used to replace a baseline model in deployment. We present theoretical results on the expected churn between models within the Rashomon set from different perspectives. And we characterize expected churn over model updates via the Rashomon set, pairing our analysis with empirical results on real-world datasets -- showing how our approach can be used to better anticipate, reduce, and avoid churn in consumer-facing applications. Further, we show that our approach is useful even for models enhanced with uncertainty awareness.

Recent research has focused on enhancing the capability of smaller models through imitation learning, drawing on the outputs generated by large foundation models (LFMs). A number of issues impact the quality of these models, ranging from limited imitation signals from shallow LFM outputs; small scale homogeneous training data; and most notably a lack of rigorous evaluation resulting in overestimating the small model's capability as they tend to learn to imitate the style, but not the reasoning process of LFMs. To address these challenges, we develop Orca (We are working with our legal team to publicly release a diff of the model weights in accordance with LLaMA's release policy to be published at https://aka.ms/orca-lm), a 13-billion parameter model that learns to imitate the reasoning process of LFMs. Orca learns from rich signals from GPT-4 including explanation traces; step-by-step thought processes; and other complex instructions, guided by teacher assistance from ChatGPT. To promote this progressive learning, we tap into large-scale and diverse imitation data with judicious sampling and selection. Orca surpasses conventional state-of-the-art instruction-tuned models such as Vicuna-13B by more than 100% in complex zero-shot reasoning benchmarks like Big-Bench Hard (BBH) and 42% on AGIEval. Moreover, Orca reaches parity with ChatGPT on the BBH benchmark and shows competitive performance (4 pts gap with optimized system message) in professional and academic examinations like the SAT, LSAT, GRE, and GMAT, both in zero-shot settings without CoT; while trailing behind GPT-4. Our research indicates that learning from step-by-step explanations, whether these are generated by humans or more advanced AI models, is a promising direction to improve model capabilities and skills.

Pretrained language models have shown superior performance on many natural language processing tasks, yet they still struggle at multi-step formal reasoning tasks like grade school math problems. One key challenge of finetuning them to solve such math reasoning problems is that many existing datasets only contain one reference solution for each problem, despite the fact that there are often alternative solutions resembling different reasoning paths to the final answer. This way, the finetuned models are biased towards the limited reference solutions, which limits their generalization to unseen examples. To mitigate this issue, we propose to let the model perform sampling during training and learn from both self-sampled fully-correct solutions, which yield the correct answer upon execution, and partially-correct solutions, whose intermediate state matches an intermediate state of a known correct solution. We show that our use of self-sampled correct and partially-correct solutions can benefit learning and help guide the sampling process, leading to more efficient exploration of the solution space. Additionally, we explore various training objectives to support learning from multiple solutions per example and find they greatly affect the performance. Experiments on two math reasoning datasets show the effectiveness of our method compared to learning from a single reference solution with MLE, where we improve PASS@100 from 35.5% to 44.5% for GSM8K, and 27.6% to 36.2% PASS@80 for MathQA. Such improvements are also consistent across different model sizes. Our code is available at https://github.com/microsoft/TraceCodegen.

In their recent Nature Human Behaviour paper, "Emergent analogical reasoning in large language models," (Webb, Holyoak, and Lu, 2023) the authors argue that "large language models such as GPT-3 have acquired an emergent ability to find zero-shot solutions to a broad range of analogy problems." In this response, we provide counterexamples of the letter string analogies. In our tests, GPT-3 fails to solve even the easiest variants of the problems presented in the original paper. Zero-shot reasoning is an extraordinary claim that requires extraordinary evidence. We do not see that evidence in our experiments. To strengthen claims of humanlike reasoning such as zero-shot reasoning, it is important that the field develop approaches that rule out data memorization.

We propose an approach to estimate the number of samples required for a model to reach a target performance. We find that the power law, the de facto principle to estimate model performance, leads to large error when using a small dataset (e.g., 5 samples per class) for extrapolation. This is because the log-performance error against the log-dataset size follows a nonlinear progression in the few-shot regime followed by a linear progression in the high-shot regime. We introduce a novel piecewise power law (PPL) that handles the two data regimes differently. To estimate the parameters of the PPL, we introduce a random forest regressor trained via meta learning that generalizes across classification/detection tasks, ResNet/ViT based architectures, and random/pre-trained initializations. The PPL improves the performance estimation on average by 37% across 16 classification and 33% across 10 detection datasets, compared to the power law. We further extend the PPL to provide a confidence bound and use it to limit the prediction horizon that reduces over-estimation of data by 76% on classification and 91% on detection datasets.

Robust, faithful and harm-free pronoun use for individuals is an important goal for language models as their use increases, but prior work tends to study only one or two of these characteristics at a time. To measure progress towards the combined goal, we introduce the task of pronoun fidelity: given a context introducing a co-referring entity and pronoun, the task is to reuse the correct pronoun later. We present RUFF, a carefully-designed dataset of over 5 million instances to measure robust pronoun fidelity in English, and we evaluate 37 popular large language models across architectures (encoder-only, decoder-only and encoder-decoder) and scales (11M-70B parameters). When an individual is introduced with a pronoun, models can mostly faithfully reuse this pronoun in the next sentence, but they are significantly worse with she/her/her, singular they and neopronouns. Moreover, models are easily distracted by non-adversarial sentences discussing other people; even one additional sentence with a distractor pronoun causes accuracy to drop on average by 34%. Our results show that pronoun fidelity is neither robust, nor due to reasoning, in a simple, naturalistic setting where humans achieve nearly 100% accuracy. We encourage researchers to bridge the gaps we find and to carefully evaluate reasoning in settings where superficial repetition might inflate perceptions of model performance.

Suppose Alice trains an open-weight language model and Bob uses a blackbox derivative of Alice's model to produce text. Can Alice prove that Bob is using her model, either by querying Bob's derivative model (query setting) or from the text alone (observational setting)? We formulate this question as an independence testing problem--in which the null hypothesis is that Bob's model or text is independent of Alice's randomized training run--and investigate it through the lens of palimpsestic memorization in language models: models are more likely to memorize data seen later in training, so we can test whether Bob is using Alice's model using test statistics that capture correlation between Bob's model or text and the ordering of training examples in Alice's training run. If Alice has randomly shuffled her training data, then any significant correlation amounts to exactly quantifiable statistical evidence against the null hypothesis, regardless of the composition of Alice's training data. In the query setting, we directly estimate (via prompting) the likelihood Bob's model gives to Alice's training examples and order; we correlate the likelihoods of over 40 fine-tunes of various Pythia and OLMo base models ranging from 1B to 12B parameters with the base model's training data order, achieving a p-value on the order of at most 1e-8 in all but six cases. In the observational setting, we try two approaches based on estimating 1) the likelihood of Bob's text overlapping with spans of Alice's training examples and 2) the likelihood of Bob's text with respect to different versions of Alice's model we obtain by repeating the last phase (e.g., 1%) of her training run on reshuffled data. The second approach can reliably distinguish Bob's text from as little as a few hundred tokens; the first does not involve any retraining but requires many more tokens (several hundred thousand) to achieve high power.

This paper presents a new approach for assessing uncertainty in machine translation by simultaneously evaluating translation quality and providing a reliable confidence score. Our approach utilizes conformal predictive distributions to produce prediction intervals with guaranteed coverage, meaning that for any given significance level epsilon, we can expect the true quality score of a translation to fall out of the interval at a rate of 1-epsilon. In this paper, we demonstrate how our method outperforms a simple, but effective baseline on six different language pairs in terms of coverage and sharpness. Furthermore, we validate that our approach requires the data exchangeability assumption to hold for optimal performance.

The recent wave of generative AI has sparked unprecedented global attention, with both excitement and concern over potentially superhuman levels of artificial intelligence: models now take only seconds to produce outputs that would challenge or exceed the capabilities even of expert humans. At the same time, models still show basic errors in understanding that would not be expected even in non-expert humans. This presents us with an apparent paradox: how do we reconcile seemingly superhuman capabilities with the persistence of errors that few humans would make? In this work, we posit that this tension reflects a divergence in the configuration of intelligence in today's generative models relative to intelligence in humans. Specifically, we propose and test the Generative AI Paradox hypothesis: generative models, having been trained directly to reproduce expert-like outputs, acquire generative capabilities that are not contingent upon -- and can therefore exceed -- their ability to understand those same types of outputs. This contrasts with humans, for whom basic understanding almost always precedes the ability to generate expert-level outputs. We test this hypothesis through controlled experiments analyzing generation vs. understanding in generative models, across both language and image modalities. Our results show that although models can outperform humans in generation, they consistently fall short of human capabilities in measures of understanding, as well as weaker correlation between generation and understanding performance, and more brittleness to adversarial inputs. Our findings support the hypothesis that models' generative capability may not be contingent upon understanding capability, and call for caution in interpreting artificial intelligence by analogy to human intelligence.

Knowledge distillation methods have recently shown to be a promising direction to speedup the synthesis of large-scale diffusion models by requiring only a few inference steps. While several powerful distillation methods were recently proposed, the overall quality of student samples is typically lower compared to the teacher ones, which hinders their practical usage. In this work, we investigate the relative quality of samples produced by the teacher text-to-image diffusion model and its distilled student version. As our main empirical finding, we discover that a noticeable portion of student samples exhibit superior fidelity compared to the teacher ones, despite the ``approximate'' nature of the student. Based on this finding, we propose an adaptive collaboration between student and teacher diffusion models for effective text-to-image synthesis. Specifically, the distilled model produces the initial sample, and then an oracle decides whether it needs further improvements with a slow teacher model. Extensive experiments demonstrate that the designed pipeline surpasses state-of-the-art text-to-image alternatives for various inference budgets in terms of human preference. Furthermore, the proposed approach can be naturally used in popular applications such as text-guided image editing and controllable generation.

When language models (LMs) are trained to forget (or "unlearn'') a skill, how precisely does their behavior change? We study the behavior of transformer LMs in which tasks have been forgotten via fine-tuning on randomized labels. Such LMs learn to generate near-random predictions for individual examples in the "training'' set used for forgetting. Across tasks, however, LMs exhibit extreme variability in whether LM predictions change on examples outside the training set. In some tasks (like entailment classification), forgetting generalizes robustly, and causes models to produce uninformative predictions on new task instances; in other tasks (like physical commonsense reasoning and scientific question answering) forgetting affects only the training examples, and models continue to perform the "forgotten'' task accurately even for examples very similar to those that appeared in the training set. Dataset difficulty is not predictive of whether a behavior can be forgotten; instead, generalization in forgetting is (weakly) predicted by the confidence of LMs' initial task predictions and the variability of LM representations of training data, with low confidence and low variability both associated with greater generalization. Perhaps most surprisingly, random-label forgetting appears to be somewhat insensitive to the contents of the training set: for example, models trained on science questions with random labels continue to answer other science questions accurately, but begin to produce random labels on entailment classification tasks. Finally, we show that even generalizable forgetting is shallow: linear probes trained on LMs' representations can still perform tasks reliably after forgetting. Our results highlight the difficulty and unpredictability of performing targeted skill removal from models via fine-tuning.

Evaluation benchmarks are the cornerstone of measuring capabilities of large language models (LLMs), as well as driving progress in said capabilities. Originally designed to make claims about capabilities (or lack thereof) in fully pretrained models, evaluation benchmarks are now also extensively used to decide between various training choices. Despite this widespread usage, we rarely quantify the variance in our evaluation benchmarks, which dictates whether differences in performance are meaningful. Here, we define and measure a range of metrics geared towards measuring variance in evaluation benchmarks, including seed variance across initialisations, and monotonicity during training. By studying a large number of models -- both openly available and pretrained from scratch -- we provide empirical estimates for a variety of variance metrics, with considerations and recommendations for practitioners. We also evaluate the utility and tradeoffs of continuous versus discrete performance measures and explore options for better understanding and reducing this variance. We find that simple changes, such as framing choice tasks (like MMLU) as completion tasks, can often reduce variance for smaller scale (sim7B) models, while more involved methods inspired from human testing literature (such as item analysis and item response theory) struggle to meaningfully reduce variance. Overall, our work provides insights into variance in evaluation benchmarks, suggests LM-specific techniques to reduce variance, and more generally encourages practitioners to carefully factor in variance when comparing models.

We introduce a boosting algorithm to pre-process data for fairness. Starting from an initial fair but inaccurate distribution, our approach shifts towards better data fitting while still ensuring a minimal fairness guarantee. To do so, it learns the sufficient statistics of an exponential family with boosting-compliant convergence. Importantly, we are able to theoretically prove that the learned distribution will have a representation rate and statistical rate data fairness guarantee. Unlike recent optimization based pre-processing methods, our approach can be easily adapted for continuous domain features. Furthermore, when the weak learners are specified to be decision trees, the sufficient statistics of the learned distribution can be examined to provide clues on sources of (un)fairness. Empirical results are present to display the quality of result on real-world data.

Experts advising decision-makers are likely to display expertise which varies as a function of the problem instance. In practice, this may lead to sub-optimal or discriminatory decisions against minority cases. In this work we model such changes in depth and breadth of knowledge as a partitioning of the problem space into regions of differing expertise. We provide here new algorithms that explicitly consider and adapt to the relationship between problem instances and experts' knowledge. We first propose and highlight the drawbacks of a naive approach based on nearest neighbor queries. To address these drawbacks we then introduce a novel algorithm - expertise trees - that constructs decision trees enabling the learner to select appropriate models. We provide theoretical insights and empirically validate the improved performance of our novel approach on a range of problems for which existing methods proved to be inadequate.

We identify incremental learning dynamics in transformers, where the difference between trained and initial weights progressively increases in rank. We rigorously prove this occurs under the simplifying assumptions of diagonal weight matrices and small initialization. Our experiments support the theory and also show that phenomenon can occur in practice without the simplifying assumptions.

Large language models (LLMs) have shown high agreement with human raters across a variety of tasks, demonstrating potential to ease the challenges of human data collection. In computational social science (CSS), researchers are increasingly leveraging LLM annotations to complement slow and expensive human annotations. Still, guidelines for collecting and using LLM annotations, without compromising the validity of downstream conclusions, remain limited. We introduce Confidence-Driven Inference: a method that combines LLM annotations and LLM confidence indicators to strategically select which human annotations should be collected, with the goal of producing accurate statistical estimates and provably valid confidence intervals while reducing the number of human annotations needed. Our approach comes with safeguards against LLM annotations of poor quality, guaranteeing that the conclusions will be both valid and no less accurate than if we only relied on human annotations. We demonstrate the effectiveness of Confidence-Driven Inference over baselines in statistical estimation tasks across three CSS settings--text politeness, stance, and bias--reducing the needed number of human annotations by over 25% in each. Although we use CSS settings for demonstration, Confidence-Driven Inference can be used to estimate most standard quantities across a broad range of NLP problems.

Generative AI, particularly Language Models (LMs), has the potential to transform real-world domains with societal impact, particularly where access to experts is limited. For example, in education, training novice educators with expert guidance is important for effectiveness but expensive, creating significant barriers to improving education quality at scale. This challenge disproportionately harms students from under-served communities, who stand to gain the most from high-quality education. We introduce Tutor CoPilot, a novel Human-AI approach that leverages a model of expert thinking to provide expert-like guidance to tutors as they tutor. This study is the first randomized controlled trial of a Human-AI system in live tutoring, involving 900 tutors and 1,800 K-12 students from historically under-served communities. Following a preregistered analysis plan, we find that students working with tutors that have access to Tutor CoPilot are 4 percentage points (p.p.) more likely to master topics (p<0.01). Notably, students of lower-rated tutors experienced the greatest benefit, improving mastery by 9 p.p. We find that Tutor CoPilot costs only $20 per-tutor annually. We analyze 550,000+ messages using classifiers to identify pedagogical strategies, and find that tutors with access to Tutor CoPilot are more likely to use high-quality strategies to foster student understanding (e.g., asking guiding questions) and less likely to give away the answer to the student. Tutor interviews highlight how Tutor CoPilot's guidance helps tutors to respond to student needs, though they flag issues in Tutor CoPilot, such as generating suggestions that are not grade-level appropriate. Altogether, our study of Tutor CoPilot demonstrates how Human-AI systems can scale expertise in real-world domains, bridge gaps in skills and create a future where high-quality education is accessible to all students.

Faithfulness hallucinations are claims generated by a Large Language Model (LLM) not supported by contexts provided to the LLM. Lacking assessment standards, existing benchmarks focus on "factual statements" that rephrase source materials while overlooking "cognitive statements" that involve making inferences from the given context. Consequently, evaluating and detecting the hallucination of cognitive statements remains challenging. Inspired by how evidence is assessed in the legal domain, we design a rigorous framework to assess different levels of faithfulness of cognitive statements and introduce the CogniBench dataset where we reveal insightful statistics. To keep pace with rapidly evolving LLMs, we further develop an automatic annotation pipeline that scales easily across different models. This results in a large-scale CogniBench-L dataset, which facilitates training accurate detectors for both factual and cognitive hallucinations. We release our model and datasets at: https://github.com/FUTUREEEEEE/CogniBench

When using large language models (LLMs) in high-stakes applications, we need to know when we can trust their predictions. Some works argue that prompting high-performance LLMs is sufficient to produce calibrated uncertainties, while others introduce sampling methods that can be prohibitively expensive. In this work, we first argue that prompting on its own is insufficient to achieve good calibration and then show that fine-tuning on a small dataset of correct and incorrect answers can create an uncertainty estimate with good generalization and small computational overhead. We show that a thousand graded examples are sufficient to outperform baseline methods and that training through the features of a model is necessary for good performance and tractable for large open-source models when using LoRA. We also investigate the mechanisms that enable reliable LLM uncertainty estimation, finding that many models can be used as general-purpose uncertainty estimators, applicable not just to their own uncertainties but also the uncertainty of other models. Lastly, we show that uncertainty estimates inform human use of LLMs in human-AI collaborative settings through a user study.

Despite increasingly fluent, relevant, and coherent language generation, major gaps remain between how humans and machines use language. We argue that a key dimension that is missing from our understanding of language models (LMs) is the model's ability to interpret and generate expressions of uncertainty. Whether it be the weatherperson announcing a chance of rain or a doctor giving a diagnosis, information is often not black-and-white and expressions of uncertainty provide nuance to support human-decision making. The increasing deployment of LMs in the wild motivates us to investigate whether LMs are capable of interpreting expressions of uncertainty and how LMs' behaviors change when learning to emit their own expressions of uncertainty. When injecting expressions of uncertainty into prompts (e.g., "I think the answer is..."), we discover that GPT3's generations vary upwards of 80% in accuracy based on the expression used. We analyze the linguistic characteristics of these expressions and find a drop in accuracy when naturalistic expressions of certainty are present. We find similar effects when teaching models to emit their own expressions of uncertainty, where model calibration suffers when teaching models to emit certainty rather than uncertainty. Together, these results highlight the challenges of building LMs that interpret and generate trustworthy expressions of uncertainty.

One way to increase confidence in the outputs of Large Language Models (LLMs) is to support them with reasoning that is clear and easy to check -- a property we call legibility. We study legibility in the context of solving grade-school math problems and show that optimizing chain-of-thought solutions only for answer correctness can make them less legible. To mitigate the loss in legibility, we propose a training algorithm inspired by Prover-Verifier Game from Anil et al. (2021). Our algorithm iteratively trains small verifiers to predict solution correctness, "helpful" provers to produce correct solutions that the verifier accepts, and "sneaky" provers to produce incorrect solutions that fool the verifier. We find that the helpful prover's accuracy and the verifier's robustness to adversarial attacks increase over the course of training. Furthermore, we show that legibility training transfers to time-constrained humans tasked with verifying solution correctness. Over course of LLM training human accuracy increases when checking the helpful prover's solutions, and decreases when checking the sneaky prover's solutions. Hence, training for checkability by small verifiers is a plausible technique for increasing output legibility. Our results suggest legibility training against small verifiers as a practical avenue for increasing legibility of large LLMs to humans, and thus could help with alignment of superhuman models.

Cascades are a classical strategy to enable inference cost to vary adaptively across samples, wherein a sequence of classifiers are invoked in turn. A deferral rule determines whether to invoke the next classifier in the sequence, or to terminate prediction. One simple deferral rule employs the confidence of the current classifier, e.g., based on the maximum predicted softmax probability. Despite being oblivious to the structure of the cascade -- e.g., not modelling the errors of downstream models -- such confidence-based deferral often works remarkably well in practice. In this paper, we seek to better understand the conditions under which confidence-based deferral may fail, and when alternate deferral strategies can perform better. We first present a theoretical characterisation of the optimal deferral rule, which precisely characterises settings under which confidence-based deferral may suffer. We then study post-hoc deferral mechanisms, and demonstrate they can significantly improve upon confidence-based deferral in settings where (i) downstream models are specialists that only work well on a subset of inputs, (ii) samples are subject to label noise, and (iii) there is distribution shift between the train and test set.

Large Language Models (LLMs) have shown great potential in reasoning tasks through test-time scaling methods like self-consistency with majority voting. However, this approach often leads to diminishing returns in accuracy and high computational overhead. To address these challenges, we introduce Deep Think with Confidence (DeepConf), a simple yet powerful method that enhances both reasoning efficiency and performance at test time. DeepConf leverages model-internal confidence signals to dynamically filter out low-quality reasoning traces during or after generation. It requires no additional model training or hyperparameter tuning and can be seamlessly integrated into existing serving frameworks. We evaluate DeepConf across a variety of reasoning tasks and the latest open-source models, including Qwen 3 and GPT-OSS series. Notably, on challenging benchmarks such as AIME 2025, DeepConf@512 achieves up to 99.9% accuracy and reduces generated tokens by up to 84.7% compared to full parallel thinking.

Large Language Models (LLMs) are often augmented with external information as contexts, but this external information can sometimes be inaccurate or even intentionally misleading. We argue that robust LLMs should demonstrate situated faithfulness, dynamically calibrating their trust in external information based on their confidence in the internal knowledge and the external context. To benchmark this capability, we evaluate LLMs across several QA datasets, including a newly created dataset called RedditQA featuring in-the-wild incorrect contexts sourced from Reddit posts. We show that when provided with both correct and incorrect contexts, both open-source and proprietary models tend to overly rely on external information, regardless of its factual accuracy. To enhance situated faithfulness, we propose two approaches: Self-Guided Confidence Reasoning (SCR) and Rule-Based Confidence Reasoning (RCR). SCR enables models to self-access the confidence of external information relative to their own internal knowledge to produce the most accurate answer. RCR, in contrast, extracts explicit confidence signals from the LLM and determines the final answer using predefined rules. Our results show that for LLMs with strong reasoning capabilities, such as GPT-4o and GPT-4o mini, SCR outperforms RCR, achieving improvements of up to 24.2% over a direct input augmentation baseline. Conversely, for a smaller model like Llama-3-8B, RCR outperforms SCR. Fine-tuning SCR with our proposed Confidence Reasoning Direct Preference Optimization (CR-DPO) method improves performance on both seen and unseen datasets, yielding an average improvement of 8.9% on Llama-3-8B. In addition to quantitative results, we offer insights into the relative strengths of SCR and RCR. Our findings highlight promising avenues for improving situated faithfulness in LLMs. The data and code are released.

Self-improvement is a mechanism in Large Language Model (LLM) pre-training, post-training and test-time inference. We explore a framework where the model verifies its own outputs, filters or reweights data based on this verification, and distills the filtered data. Despite several empirical successes, a fundamental understanding is still lacking. In this work, we initiate a comprehensive, modular and controlled study on LLM self-improvement. We provide a mathematical formulation for self-improvement, which is largely governed by a quantity which we formalize as the generation-verification gap. Through experiments with various model families and tasks, we discover a scaling phenomenon of self-improvement -- a variant of the generation-verification gap scales monotonically with the model pre-training flops. We also examine when self-improvement is possible, an iterative self-improvement procedure, and ways to improve its performance. Our findings not only advance understanding of LLM self-improvement with practical implications, but also open numerous avenues for future research into its capabilities and boundaries.

Sampling-based search, a simple paradigm for utilizing test-time compute, involves generating multiple candidate responses and selecting the best one -- typically by verifying each response for correctness. In this paper, we study the scaling trends governing sampling-based search. Among our findings is that simply scaling up a minimalist implementation that uses only random sampling and direct self-verification results in sustained performance improvements that, for example, elevate the Gemini v1.5 Pro model's reasoning capabilities past that of o1-Preview on popular benchmarks. We partially attribute the scalability of sampling-based search to a phenomenon of implicit scaling, where sampling a larger pool of responses in turn improves verification accuracy. We further identify two useful principles for improving self-verification capabilities with test-time compute: (1) comparing across responses provides helpful signals about the locations of errors and hallucinations, and (2) different model output styles are useful for different contexts -- chains of thought are useful for reasoning but harder to verify. We also find that, though accurate verification can be elicited, frontier models demonstrate remarkably weak out-of-box verification capabilities and introduce a benchmark to measure progress on these deficiencies.

As language models (LMs) become integral to fields like healthcare, law, and journalism, their ability to differentiate between fact, belief, and knowledge is essential for reliable decision-making. Failure to grasp these distinctions can lead to significant consequences in areas such as medical diagnosis, legal judgments, and dissemination of fake news. Despite this, current literature has largely focused on more complex issues such as theory of mind, overlooking more fundamental epistemic challenges. This study systematically evaluates the epistemic reasoning capabilities of modern LMs, including GPT-4, Claude-3, and Llama-3, using a new dataset, KaBLE, consisting of 13,000 questions across 13 tasks. Our results reveal key limitations. First, while LMs achieve 86% accuracy on factual scenarios, their performance drops significantly with false scenarios, particularly in belief-related tasks. Second, LMs struggle with recognizing and affirming personal beliefs, especially when those beliefs contradict factual data, which raises concerns for applications in healthcare and counseling, where engaging with a person's beliefs is critical. Third, we identify a salient bias in how LMs process first-person versus third-person beliefs, performing better on third-person tasks (80.7%) compared to first-person tasks (54.4%). Fourth, LMs lack a robust understanding of the factive nature of knowledge, namely, that knowledge inherently requires truth. Fifth, LMs rely on linguistic cues for fact-checking and sometimes bypass the deeper reasoning. These findings highlight significant concerns about current LMs' ability to reason about truth, belief, and knowledge while emphasizing the need for advancements in these areas before broad deployment in critical sectors.

One of the most profound challenges of modern machine learning is performing well on the long-tail of rare and underrepresented features. Large general-purpose models are trained for many tasks, but work best on high-frequency use cases. After training, it is hard to adapt a model to perform well on specific use cases underrepresented in the training corpus. Relying on prompt engineering or few-shot examples to maximize the output quality on a particular test case can be frustrating, as models can be highly sensitive to small changes, react in unpredicted ways or rely on a fixed system prompt for maintaining performance. In this work, we ask: "Can we optimize our training protocols to both improve controllability and performance on underrepresented use cases at inference time?" We revisit the divide between training and inference techniques to improve long-tail performance while providing users with a set of control levers the model is trained to be responsive to. We create a detailed taxonomy of data characteristics and task provenance to explicitly control generation attributes and implicitly condition generations at inference time. We fine-tune a base model to infer these markers automatically, which makes them optional at inference time. This principled and flexible approach yields pronounced improvements in performance, especially on examples from the long tail of the training distribution. While we observe an average lift of 5.7% win rates in open-ended generation quality with our markers, we see over 9.1% gains in underrepresented domains. We also observe relative lifts of up to 14.1% on underrepresented tasks like CodeRepair and absolute improvements of 35.3% on length instruction following evaluations.

When individuals encounter observations that violate their expectations, when will they adjust their expectations and when will they maintain them despite these observations? For example, when individuals expect objects of type A to be smaller than objects B, but observe the opposite, when will they adjust their expectation about the relationship between the two objects (to A being larger than B)? Naively, one would predict that the larger the violation, the greater the adaptation. However, experiments reveal that when violations are extreme, individuals are more likely to hold on to their prior expectations rather than adjust them. To address this puzzle, we tested the adaptation of artificial neural networks (ANNs) capable of relational learning and found a similar phenomenon: Standard learning dynamics dictates that small violations would lead to adjustments of expected relations while larger ones would be resolved using a different mechanism -- a change in object representation that bypasses the need for adaptation of the relational expectations. These results suggest that the experimentally-observed stability of prior expectations when facing large expectation violations is a natural consequence of learning dynamics and does not require any additional mechanisms. We conclude by discussing the effect of intermediate adaptation steps on this stability.

Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability distributions. In this paper, we focus on evaluating the probabilistic reasoning capabilities of LMs using idealized and real-world statistical distributions. We perform a systematic evaluation of state-of-the-art LMs on three tasks: estimating percentiles, drawing samples, and calculating probabilities. We evaluate three ways to provide context to LMs 1) anchoring examples from within a distribution or family of distributions, 2) real-world context, 3) summary statistics on which to base a Normal approximation. Models can make inferences about distributions, and can be further aided by the incorporation of real-world context, example shots and simplified assumptions, even if these assumptions are incorrect or misspecified. To conduct this work, we developed a comprehensive benchmark distribution dataset with associated question-answer pairs that we will release publicly.

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way.

We study whether Large Language Models (LLMs) latently perform multi-hop reasoning with complex prompts such as "The mother of the singer of 'Superstition' is". We look for evidence of a latent reasoning pathway where an LLM (1) latently identifies "the singer of 'Superstition'" as Stevie Wonder, the bridge entity, and (2) uses its knowledge of Stevie Wonder's mother to complete the prompt. We analyze these two hops individually and consider their co-occurrence as indicative of latent multi-hop reasoning. For the first hop, we test if changing the prompt to indirectly mention the bridge entity instead of any other entity increases the LLM's internal recall of the bridge entity. For the second hop, we test if increasing this recall causes the LLM to better utilize what it knows about the bridge entity. We find strong evidence of latent multi-hop reasoning for the prompts of certain relation types, with the reasoning pathway used in more than 80% of the prompts. However, the utilization is highly contextual, varying across different types of prompts. Also, on average, the evidence for the second hop and the full multi-hop traversal is rather moderate and only substantial for the first hop. Moreover, we find a clear scaling trend with increasing model size for the first hop of reasoning but not for the second hop. Our experimental findings suggest potential challenges and opportunities for future development and applications of LLMs.

The ecological validity of soundscape studies usually rests on a choice of soundscapes that are representative of the perceptual space under investigation. For example, a soundscape pleasantness study might investigate locations with soundscapes ranging from "pleasant" to "annoying". The choice of soundscapes is typically researcher-led, but a participant-led process can reduce selection bias and improve result reliability. Hence, we propose a robust participant-led method to pinpoint characteristic soundscapes possessing arbitrary perceptual attributes. We validate our method by identifying Singaporean soundscapes spanning the perceptual quadrants generated from the "Pleasantness" and "Eventfulness" axes of the ISO 12913-2 circumplex model of soundscape perception, as perceived by local experts. From memory and experience, 67 participants first selected locations corresponding to each perceptual quadrant in each major planning region of Singapore. We then performed weighted k-means clustering on the selected locations, with weights for each location derived from previous frequencies and durations spent in each location by each participant. Weights hence acted as proxies for participant confidence. In total, 62 locations were thereby identified as suitable locations with characteristic soundscapes for further research utilizing the ISO 12913-2 perceptual quadrants. Audio-visual recordings and acoustic characterization of the soundscapes will be made in a future study.

Large Language Models are trained on vast amounts of text from the internet, which contains both factual and misleading information about the world. Can language models discern truth from falsehood in this contradicting data? Expanding on the view that LLMs can model different agents producing the corpora, we hypothesize that they can cluster truthful text by modeling a truthful persona: a group of agents that are likely to produce truthful text and share similar features. For example, trustworthy sources like Wikipedia and Science usually use formal writing styles and make consistent claims. By modeling this persona, LLMs can generalize truthfulness beyond the specific contexts in which each agent generated the training text. For example, the model can infer that the agent "Wikipedia" will behave truthfully on topics that were only generated by "Science" because they share a persona. We first show evidence for the persona hypothesis via two observations: (1) we can probe whether a model's answer will be truthful before it is generated; (2) finetuning a model on a set of facts improves its truthfulness on unseen topics. Next, using arithmetics as a synthetic environment, we show that language models can separate true and false statements, and generalize truthfulness across agents; but only if agents in the training data share a truthful generative process that enables the creation of a truthful persona. Overall, our findings suggest that models can exploit hierarchical structures in the data to learn abstract concepts like truthfulness.

Uncertainty estimation is a significant issue for current large language models (LLMs) that are generally poorly calibrated and over-confident, especially with reinforcement learning from human feedback (RLHF). Unlike humans, whose decisions and confidences not only stem from intrinsic beliefs but can also be adjusted through daily observations, existing calibration methods for LLMs focus on estimating or eliciting individual confidence without taking full advantage of the "Collective Wisdom": the interaction among multiple LLMs that can collectively improve both accuracy and calibration. In this work, we propose Collaborative Calibration, a post-hoc training-free calibration strategy that leverages the collaborative and expressive capabilities of multiple tool-augmented LLM agents in a simulated group deliberation process. We demonstrate the effectiveness of Collaborative Calibration on generative QA tasks across various domains, showing its potential in harnessing the rationalization of collectively calibrated confidence assessments and improving the reliability of model predictions.

One paradigm of language model (LM) fine-tuning relies on creating large training datasets, under the assumption that high quantity and diversity will enable models to generalize to novel tasks after post-training. In practice, gathering large sets of data is inefficient, and training on them is prohibitively expensive; worse, there is no guarantee that the resulting model will handle complex scenarios or generalize better. Moreover, existing techniques rarely assess whether a training sample provides novel information or is redundant with the knowledge already acquired by the model, resulting in unnecessary costs. In this work, we explore a new test-time self-improvement method to create more effective and generalizable agentic LMs on-the-fly. The proposed algorithm can be summarized in three steps: (i) first it identifies the samples that model struggles with (self-awareness), (ii) then generates similar examples from detected uncertain samples (self-data augmentation), and (iii) uses these newly generated samples at test-time fine-tuning (self-improvement). We study two variants of this approach: Test-Time Self-Improvement (TT-SI), where the same model generates additional training examples from its own uncertain cases and then learns from them, and contrast this approach with Test-Time Distillation (TT-D), where a stronger model generates similar examples for uncertain cases, enabling student to adapt using distilled supervision. Empirical evaluations across different agent benchmarks demonstrate that TT-SI improves the performance with +5.48% absolute accuracy gain on average across all benchmarks and surpasses other standard learning methods, yet using 68x less training samples. Our findings highlight the promise of TT-SI, demonstrating the potential of self-improvement algorithms at test-time as a new paradigm for building more capable agents toward self-evolution.

Machine learning has been highly successful in data-intensive applications but is often hampered when the data set is small. Recently, Few-Shot Learning (FSL) is proposed to tackle this problem. Using prior knowledge, FSL can rapidly generalize to new tasks containing only a few samples with supervised information. In this paper, we conduct a thorough survey to fully understand FSL. Starting from a formal definition of FSL, we distinguish FSL from several relevant machine learning problems. We then point out that the core issue in FSL is that the empirical risk minimized is unreliable. Based on how prior knowledge can be used to handle this core issue, we categorize FSL methods from three perspectives: (i) data, which uses prior knowledge to augment the supervised experience; (ii) model, which uses prior knowledge to reduce the size of the hypothesis space; and (iii) algorithm, which uses prior knowledge to alter the search for the best hypothesis in the given hypothesis space. With this taxonomy, we review and discuss the pros and cons of each category. Promising directions, in the aspects of the FSL problem setups, techniques, applications and theories, are also proposed to provide insights for future research.

Common methods for aligning large language models (LLMs) with desired behaviour heavily rely on human-labelled data. However, as models grow increasingly sophisticated, they will surpass human expertise, and the role of human evaluation will evolve into non-experts overseeing experts. In anticipation of this, we ask: can weaker models assess the correctness of stronger models? We investigate this question in an analogous setting, where stronger models (experts) possess the necessary information to answer questions and weaker models (non-experts) lack this information. The method we evaluate is debate, where two LLM experts each argue for a different answer, and a non-expert selects the answer. We find that debate consistently helps both non-expert models and humans answer questions, achieving 76% and 88% accuracy respectively (naive baselines obtain 48% and 60%). Furthermore, optimising expert debaters for persuasiveness in an unsupervised manner improves non-expert ability to identify the truth in debates. Our results provide encouraging empirical evidence for the viability of aligning models with debate in the absence of ground truth.

AI explanations are often mentioned as a way to improve human-AI decision-making, but empirical studies have not found consistent evidence of explanations' effectiveness and, on the contrary, suggest that they can increase overreliance when the AI system is wrong. While many factors may affect reliance on AI support, one important factor is how decision-makers reconcile their own intuition -- beliefs or heuristics, based on prior knowledge, experience, or pattern recognition, used to make judgments -- with the information provided by the AI system to determine when to override AI predictions. We conduct a think-aloud, mixed-methods study with two explanation types (feature- and example-based) for two prediction tasks to explore how decision-makers' intuition affects their use of AI predictions and explanations, and ultimately their choice of when to rely on AI. Our results identify three types of intuition involved in reasoning about AI predictions and explanations: intuition about the task outcome, features, and AI limitations. Building on these, we summarize three observed pathways for decision-makers to apply their own intuition and override AI predictions. We use these pathways to explain why (1) the feature-based explanations we used did not improve participants' decision outcomes and increased their overreliance on AI, and (2) the example-based explanations we used improved decision-makers' performance over feature-based explanations and helped achieve complementary human-AI performance. Overall, our work identifies directions for further development of AI decision-support systems and explanation methods that help decision-makers effectively apply their intuition to achieve appropriate reliance on AI.