Daily Papers

Large language models (LLMs) are documented to struggle in settings that require complex reasoning. Nevertheless, instructing the model to break down the problem into smaller reasoning steps (Wei et al., 2022), or ensembling various generations through modifying decoding steps (Wang et al., 2023) boosts performance. Current methods assume that the input prompt is fixed and expect the decoding strategies to introduce the diversity needed for ensembling. In this work, we relax this assumption and discuss how one can create and leverage variations of the input prompt as a means to diversity of thought to improve model performance. We propose a method that automatically improves prompt diversity by soliciting feedback from the LLM to ideate approaches that fit for the problem. We then ensemble the diverse prompts in our method DIV-SE (DIVerse reasoning path Self-Ensemble) across multiple inference calls. We also propose a cost-effective alternative where diverse prompts are used within a single inference call; we call this IDIV-SE (In-call DIVerse reasoning path Self-Ensemble). Under a fixed generation budget, DIV-SE and IDIV-SE outperform the previously discussed baselines using both GPT-3.5 and GPT-4 on several reasoning benchmarks, without modifying the decoding process. Additionally, DIV-SE advances state-of-the-art performance on recent planning benchmarks (Valmeekam et al., 2023), exceeding the highest previously reported accuracy by at least 29.6 percentage points on the most challenging 4/5 Blocksworld task. Our results shed light on how to enforce prompt diversity toward LLM reasoning and thereby improve the pareto frontier of the accuracy-cost trade-off.

Large language models (LLMs) excel in natural language generation but often confidently produce incorrect responses, especially in tasks like mathematical reasoning. Chain-of-thought prompting, self-verification, and multi-agent debate are among the strategies proposed to improve the reasoning and factual accuracy of LLMs. Building on Du et al.'s multi-agent debate framework, we find that multi-agent debate helps at any model scale, and that diversity of thought elicits stronger reasoning in debating LLMs. Across various model sizes, performance on mathematical reasoning tasks benefits most when diverse trained models are used. Remarkably, after 4 rounds of debate, a diverse set of medium-capacity models (Gemini-Pro, Mixtral 7BX8, and PaLM 2-M) outperforms GPT-4 on the GSM-8K benchmark, scoring 91% accuracy. By comparison, when 3 instances of Gemini-Pro are used, performance only reaches 82%. Finally, this diverse set of medium-capacity models sets a new state-of-the-art performance on the ASDiv benchmark (94%). These results underscore the idea that the future of AI is agentic, with diverse cooperating agents yielding emergent capabilities beyond even the most powerful individual models.

We test whether Large Language Models (LLMs) can be used to simulate human participants in social-science studies. To do this, we run replications of 14 studies from the Many Labs 2 replication project with OpenAI's text-davinci-003 model, colloquially known as GPT3.5. Based on our pre-registered analyses, we find that among the eight studies we could analyse, our GPT sample replicated 37.5% of the original results and 37.5% of the Many Labs 2 results. However, we were unable to analyse the remaining six studies due to an unexpected phenomenon we call the "correct answer" effect. Different runs of GPT3.5 answered nuanced questions probing political orientation, economic preference, judgement, and moral philosophy with zero or near-zero variation in responses: with the supposedly "correct answer." In one exploratory follow-up study, we found that a "correct answer" was robust to changing the demographic details that precede the prompt. In another, we found that most but not all "correct answers" were robust to changing the order of answer choices. One of our most striking findings occurred in our replication of the Moral Foundations Theory survey results, where we found GPT3.5 identifying as a political conservative in 99.6% of the cases, and as a liberal in 99.3% of the cases in the reverse-order condition. However, both self-reported 'GPT conservatives' and 'GPT liberals' showed right-leaning moral foundations. Our results cast doubts on the validity of using LLMs as a general replacement for human participants in the social sciences. Our results also raise concerns that a hypothetical AI-led future may be subject to a diminished diversity-of-thought.

The advancement of Large Language Models(LLMs) has brought substantial attention to the Chain of Thought(CoT) approach, primarily due to its ability to enhance the capability of LLMs on tasks requiring complex reasoning. Moreover, the significance of CoT approaches extends to the application of LLMs for multi-modal tasks, such as multi-modal question answering. However, the selection of optimal CoT demonstration examples in multi-modal reasoning for LLMs remains less explored for LLMs due to the inherent complexity of multi-modal examples. In this paper, we introduce a novel approach that addresses this challenge by using retrieval mechanisms to dynamically and automatically select demonstration examples based on cross-modal similarities. This method aims to refine the CoT reasoning process in multi-modal scenarios via informing LLMs with more relevant and informative examples. Furthermore, we employ a stratified sampling method categorising demonstration examples into groups based on their types and retrieving examples from different groups respectively to promote the diversity of demonstration examples. Through a series of experiments, we demonstrate that our approach significantly improves the performance of LLMs, achieving state-of-the-art results in multi-modal reasoning tasks. Specifically, our methods demonstrate significant advancements on the ScienceQA dataset. While our method based on ChatGPT outperforms the Chameleon(ChatGPT) by 2.74% with an accuracy of 82.67%, the GPT4-based approach surpasses the Chameleon(GPT-4) by 0.89%, achieving 87.43% on accuracy under the same setting. Moreover, our best performing show a 6.05% increase over Chameleon for ChatGPT-based models and a 4.57% increase for GPT-4-based models.

We introduce CoT-ICL Lab, a framework and methodology to generate synthetic tokenized datasets and systematically study chain-of-thought (CoT) in-context learning (ICL) in language models. CoT-ICL Lab allows fine grained control over the complexity of in-context examples by decoupling (1) the causal structure involved in chain token generation from (2) the underlying token processing functions. We train decoder-only transformers (up to 700M parameters) on these datasets and show that CoT accelerates the accuracy transition to higher values across model sizes. In particular, we find that model depth is crucial for leveraging CoT with limited in-context examples, while more examples help shallow models match deeper model performance. Additionally, limiting the diversity of token processing functions throughout training improves causal structure learning via ICL. We also interpret these transitions by analyzing transformer embeddings and attention maps. Overall, CoT-ICL Lab serves as a simple yet powerful testbed for theoretical and empirical insights into ICL and CoT in language models.

Recent advancements in large language models (LLMs) have shown remarkable potential in automating machine learning tasks. However, existing LLM-based agents often struggle with low-diversity and suboptimal code generation. While recent work has introduced Monte Carlo Tree Search (MCTS) to address these issues, limitations persist in the quality and diversity of thoughts generated, as well as in the scalar value feedback mechanisms used for node selection. In this study, we introduce Introspective Monte Carlo Tree Search (I-MCTS), a novel approach that iteratively expands tree nodes through an introspective process that meticulously analyzes solutions and results from parent and sibling nodes. This facilitates a continuous refinement of the node in the search tree, thereby enhancing the overall decision-making process. Furthermore, we integrate a Large Language Model (LLM)-based value model to facilitate direct evaluation of each node's solution prior to conducting comprehensive computational rollouts. A hybrid rewarding mechanism is implemented to seamlessly transition the Q-value from LLM-estimated scores to actual performance scores. This allows higher-quality nodes to be traversed earlier. Applied to the various ML tasks, our approach demonstrates a 6% absolute improvement in performance compared to the strong open-source AutoML agents, showcasing its effectiveness in enhancing agentic AutoML systems. Resource available at https://github.com/jokieleung/I-MCTS

This work aims at decreasing the end-to-end generation latency of large language models (LLMs). One of the major causes of the high generation latency is the sequential decoding approach adopted by almost all state-of-the-art LLMs. In this work, motivated by the thinking and writing process of humans, we propose "Skeleton-of-Thought" (SoT), which guides LLMs to first generate the skeleton of the answer, and then conducts parallel API calls or batched decoding to complete the contents of each skeleton point in parallel. Not only does SoT provide considerable speed-up (up to 2.39x across 11 different LLMs), but it can also potentially improve the answer quality on several question categories in terms of diversity and relevance. SoT is an initial attempt at data-centric optimization for efficiency, and reveal the potential of pushing LLMs to think more like a human for answer quality.

A prevailing view holds that supervised fine-tuning (SFT) memorizes training data and fails to generalize, whereas reinforcement learning (RL) attains broader robustness. We revisit this claim through a systematic evaluation on two decision-making benchmarks, Sokoban and General Points, and arrive at a different conclusion. We show that much of SFT's perceived failure stems from frozen-prompt artifacts: when trained on fixed instruction templates, SFT models cling to training semantics rather than adapting to new ones. Introducing prompt diversity during training breaks this shortcut and yields strong generalization to unseen instruction variants without harming in-distribution performance. Beyond instruction shifts, we ask whether SFT can generalize to strictly harder tasks. Here, chain-of-thought (CoT) supervision provides an algorithmic scaffold that markedly improves transfer to more difficult regimes, such as larger Sokoban grids with additional boxes and arithmetic with out-of-distribution values or five-card compositions that increase combinatorial complexity. Finally, combining prompt diversity with CoT achieves the best of both worlds: robust generalization across both instruction-variant and difficulty-variant settings, matching or surpassing RL baselines on our benchmarks while retaining SFT's simplicity and stability. These findings challenge the narrative that SFT is inherently inferior to RL and support a data-centric perspective: with appropriately curated demonstrations, vanilla SFT can generalize as strongly as RL. Code reproducing the results in the paper can be found at: https://github.com/XiaofengLin7/debunking-sft-generalization.

Chain-of-thought (CoT) reasoning is critical for improving the interpretability and reliability of Large Vision-Language Models (LVLMs). However, existing training algorithms such as SFT, PPO, and GRPO may not generalize well across unseen reasoning tasks and heavily rely on a biased reward model. To address this challenge, we reformulate reasoning in LVLMs as posterior inference and propose a scalable training algorithm based on amortized variational inference. By leveraging diversity-seeking reinforcement learning algorithms, we introduce a novel sparse reward function for token-level learning signals that encourage diverse, high-likelihood latent CoT, overcoming deterministic sampling limitations and avoiding reward hacking. Additionally, we implement a Bayesian inference-scaling strategy that replaces costly Best-of-N and Beam Search with a marginal likelihood to efficiently rank optimal rationales and answers. We empirically demonstrate that the proposed method enhances the state-of-the-art LVLMs on seven reasoning benchmarks, in terms of effectiveness, generalization, and interpretability.

Large language models (LLMs) can perform complex reasoning by generating intermediate reasoning steps. Providing these steps for prompting demonstrations is called chain-of-thought (CoT) prompting. CoT prompting has two major paradigms. One leverages a simple prompt like "Let's think step by step" to facilitate step-by-step thinking before answering a question. The other uses a few manual demonstrations one by one, each composed of a question and a reasoning chain that leads to an answer. The superior performance of the second paradigm hinges on the hand-crafting of task-specific demonstrations one by one. We show that such manual efforts may be eliminated by leveraging LLMs with the "Let's think step by step" prompt to generate reasoning chains for demonstrations one by one, i.e., let's think not just step by step, but also one by one. However, these generated chains often come with mistakes. To mitigate the effect of such mistakes, we find that diversity matters for automatically constructing demonstrations. We propose an automatic CoT prompting method: Auto-CoT. It samples questions with diversity and generates reasoning chains to construct demonstrations. On ten public benchmark reasoning tasks with GPT-3, Auto-CoT consistently matches or exceeds the performance of the CoT paradigm that requires manual designs of demonstrations. Code is available at https://github.com/amazon-research/auto-cot

Chain-of-Thought (CoT) plays a crucial role in reasoning for math problem solving. We conduct a comprehensive examination of methods for designing CoT, comparing conventional natural language CoT with various program CoTs, including the self-describing program, the comment-describing program, and the non-describing program. Furthermore, we investigate the impact of programming language on program CoTs, comparing Python and Wolfram Language. Through extensive experiments on GSM8K, MATHQA, and SVAMP, we find that program CoTs often have superior effectiveness in math problem solving. Notably, the best performing combination with 30B parameters beats GPT-3.5-turbo by a significant margin. The results show that self-describing program offers greater diversity and thus can generally achieve higher performance. We also find that Python is a better choice of language than Wolfram for program CoTs. The experimental results provide a valuable guideline for future CoT designs that take into account both programming language and coding style for further advancements. Our datasets and code are publicly available.

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to break down complex problems into interpretable intermediate steps, significantly enhancing model transparency and performance in reasoning tasks. However, conventional CoT methods rely on heuristic sampling without structured modeling of reasoning transitions, constraining their ability to systematically explore and discover diverse and effective reasoning trajectories. In this work, we introduce CTRLS, a framework that formulates CoT reasoning as a Markov decision process (MDP) with latent state transitions, enabling principled and state-aware exploration via distributional reinforcement learning. By modelling reasoning actions as explicit probability distributions in latent space, our approach explicitly models epistemic uncertainty, facilitating robust exploration of the reasoning space. As part of our framework, we introduce an on-policy reinforcement learning strategy incorporating epsilon-greedy exploration and entropy-based regularization to iteratively refine latent state transitions without requiring additional fine-tuning of the underlying LLM. Theoretical analyses provide evidence lower bounds (ELBO), theoretically grounding our transition-aware modeling of latent reasoning dynamics. Further experiments demonstrate improvements in reasoning accuracy, diversity, and exploration efficiency across benchmark reasoning tasks.

Reasoning capability is pivotal for Large Language Models (LLMs) to solve complex tasks, yet achieving reliable and scalable reasoning remains challenging. While Chain-of-Thought (CoT) prompting has become a mainstream approach, existing methods often suffer from uncontrolled generation, insufficient quality, and limited diversity in reasoning paths. Recent efforts leverage code to enhance CoT by grounding reasoning in executable steps, but such methods are typically constrained to predefined mathematical problems, hindering scalability and generalizability. In this work, we propose Caco (Code-Assisted Chain-of-ThOught), a novel framework that automates the synthesis of high-quality, verifiable, and diverse instruction-CoT reasoning data through code-driven augmentation. Unlike prior work, Caco first fine-tunes a code-based CoT generator on existing math and programming solutions in a unified code format, then scales the data generation to a large amount of diverse reasoning traces. Crucially, we introduce automated validation via code execution and rule-based filtering to ensure logical correctness and structural diversity, followed by reverse-engineering filtered outputs into natural language instructions and language CoTs to enrich task adaptability. This closed-loop process enables fully automated, scalable synthesis of reasoning data with guaranteed executability. Experiments on our created Caco-1.3M dataset demonstrate that Caco-trained models achieve strong competitive performance on mathematical reasoning benchmarks, outperforming existing strong baselines. Further analysis reveals that Caco's code-anchored verification and instruction diversity contribute to superior generalization across unseen tasks. Our work establishes a paradigm for building self-sustaining, trustworthy reasoning systems without human intervention.

Chain-of-thought prompting (e.g., "Let's think step-by-step") primes large language models to verbalize rationalization for their predictions. While chain-of-thought can lead to dramatic performance gains, benefits appear to emerge only for sufficiently large models (beyond 50B parameters). We show that orders-of-magnitude smaller models (125M -- 1.3B parameters) can still benefit from chain-of-thought prompting. To achieve this, we introduce Symbolic Chain-of-Thought Distillation (SCoTD), a method to train a smaller student model on rationalizations sampled from a significantly larger teacher model. Experiments across several commonsense benchmarks show that: 1) SCoTD enhances the performance of the student model in both supervised and few-shot settings, and especially for challenge sets; 2) sampling many reasoning chains per instance from the teacher is paramount; and 3) after distillation, student chain-of-thoughts are judged by humans as comparable to the teacher, despite orders of magnitude fewer parameters. We test several hypotheses regarding what properties of chain-of-thought samples are important, e.g., diversity vs. teacher likelihood vs. open-endedness. We release our corpus of chain-of-thought samples and code.

Implicit Chain-of-Thought (CoT) methods present a promising, token-efficient alternative to explicit CoT reasoning in Large Language Models (LLMs), but a persistent performance gap has limited the application of implicit CoT. We identify a core latent instability issue by scaling the computational budget of implicit CoT approaches: as we increase the number of implicit reasoning tokens to enhance performance, the training process often becomes unstable and collapses. Our analysis reveals that this instability arises from the latent representations becoming homogeneous and losing their semantic diversity, a failure caused by insufficient step-level supervision in existing implicit CoT approaches. To address this issue, we propose SIM-CoT, a plug-and-play training module that introduces step-level supervision to stabilize and enrich the latent reasoning space. Specifically, SIM-CoT employs an auxiliary decoder during training to align each implicit token with its corresponding explicit reasoning step, ensuring that latent states capture distinct and meaningful information. The proposed auxiliary decoder is removed during inference, preserving the computational efficiency of implicit CoT methods with no added overhead. In addition, the auxiliary decoder affords interpretability of implicit reasoning by projecting each latent token onto an explicit reasoning vocabulary, enabling per-step visualization of semantic roles and diagnosis. SIM-CoT significantly enhances both the in-domain accuracy and out-of-domain stability of various implicit CoT methods, boosting baselines like Coconut by +8.2% on GPT-2 and CODI by +3.0% on LLaMA-3.1 8B. Demonstrating strong scalability, SIM-CoT also surpasses the explicit CoT baseline on GPT-2 by 2.1% with 2.3\times greater token efficiency, while substantially closing the performance gap on larger models like LLaMA-3.1 8B.

Test-Time Scaling (TTS) refers to approaches that improve reasoning performance by allocating extra computation during inference, without altering the model's parameters. While existing TTS methods operate in a discrete token space by generating more intermediate steps, recent studies in Coconut and SoftCoT have demonstrated that thinking in the continuous latent space can further enhance the reasoning performance. Such latent thoughts encode informative thinking without the information loss associated with autoregressive token generation, sparking increased interest in continuous-space reasoning. Unlike discrete decoding, where repeated sampling enables exploring diverse reasoning paths, latent representations in continuous space are fixed for a given input, which limits diverse exploration, as all decoded paths originate from the same latent thought. To overcome this limitation, we introduce SoftCoT++ to extend SoftCoT to the Test-Time Scaling paradigm by enabling diverse exploration of thinking paths. Specifically, we perturb latent thoughts via multiple specialized initial tokens and apply contrastive learning to promote diversity among soft thought representations. Experiments across five reasoning benchmarks and two distinct LLM architectures demonstrate that SoftCoT++ significantly boosts SoftCoT and also outperforms SoftCoT with self-consistency scaling. Moreover, it shows strong compatibility with conventional scaling techniques such as self-consistency. Source code is available at https://github.com/xuyige/SoftCoT.

In the domain of text-to-image generative models, biases inherent in training datasets often propagate into generated content, posing significant ethical challenges, particularly in socially sensitive contexts. We introduce FairCoT, a novel framework that enhances fairness in diffusion models through Chain-of-Thought (CoT) reasoning within multimodal generative large language models (LLMs). FairCoT employs iterative CoT refinement and attire-based attribute prediction to systematically mitigate biases, ensuring diverse and equitable representation in generated images. By integrating iterative reasoning processes, FairCoT addresses the limitations of zero-shot CoT in sensitive scenarios, balancing creativity with ethical responsibility. Experimental evaluations across multiple models, including DALL-E and various Stable Diffusion variants, demonstrate that FairCoT significantly improves fairness and diversity metrics without compromising image quality or relevance. Our approach advances ethical AI practices in generative modeling, promoting socially responsible content generation and setting new standards for fairness in AI-generated imagery.

Large Language Models (LLMs) excel in reasoning tasks through Chain-of-Thought (CoT) prompting. However, CoT prompting greatly increases computational demands, which has prompted growing interest in distilling CoT capabilities into Small Language Models (SLMs). This study systematically examines the factors influencing CoT distillation, including the choice of granularity, format and teacher model. Through experiments involving four teacher models and seven student models across seven mathematical and commonsense reasoning datasets, we uncover three key findings: (1) Unlike LLMs, SLMs exhibit a non-monotonic relationship with granularity, with stronger models benefiting from finer-grained reasoning and weaker models performing better with simpler CoT supervision; (2) CoT format significantly impacts LLMs but has minimal effect on SLMs, likely due to their reliance on supervised fine-tuning rather than pretraining preferences; (3) Stronger teacher models do NOT always produce better student models, as diversity and complexity in CoT supervision can outweigh accuracy alone. These findings emphasize the need to tailor CoT strategies to specific student model, offering actionable insights for optimizing CoT distillation in SLMs. The code and datasets are available at https://github.com/EIT-NLP/Distilling-CoT-Reasoning.

Large reasoning models (LRM) with long chain-of-thought (CoT) capabilities have shown strong performance on objective tasks, such as math reasoning and coding. However, their effectiveness on subjective questions that may have different responses from different perspectives is still limited by a tendency towards homogeneous reasoning, introduced by the reliance on a single ground truth in supervised fine-tuning and verifiable reward in reinforcement learning. Motivated by the finding that increasing role perspectives consistently improves performance, we propose MultiRole-R1, a diversity-enhanced framework with multiple role perspectives, to improve the accuracy and diversity in subjective reasoning tasks. MultiRole-R1 features an unsupervised data construction pipeline that generates reasoning chains that incorporate diverse role perspectives. We further employ reinforcement learning via Group Relative Policy Optimization (GRPO) with reward shaping, by taking diversity as a reward signal in addition to the verifiable reward. With specially designed reward functions, we successfully promote perspective diversity and lexical diversity, uncovering a positive relation between reasoning diversity and accuracy. Our experiment on six benchmarks demonstrates MultiRole-R1's effectiveness and generalizability in enhancing both subjective and objective reasoning, showcasing the potential of diversity-enhanced training in LRMs.

Exploiting the recent advancements in artificial intelligence, showcased by ChatGPT and DALL-E, in real-world applications necessitates vast, domain-specific, and publicly accessible datasets. Unfortunately, the scarcity of such datasets poses a significant challenge for researchers aiming to apply these breakthroughs in engineering design. Synthetic datasets emerge as a viable alternative. However, practitioners are often uncertain about generating high-quality datasets that accurately represent real-world data and are suitable for the intended downstream applications. This study aims to fill this knowledge gap by proposing comprehensive guidelines for generating, annotating, and validating synthetic datasets. The trade-offs and methods associated with each of these aspects are elaborated upon. Further, the practical implications of these guidelines are illustrated through the creation of a turbo-compressors dataset. The study underscores the importance of thoughtful sampling methods to ensure the appropriate size, diversity, utility, and realism of a dataset. It also highlights that design diversity does not equate to performance diversity or realism. By employing test sets that represent uniform, real, or task-specific samples, the influence of sample size and sampling strategy is scrutinized. Overall, this paper offers valuable insights for researchers intending to create and publish synthetic datasets for engineering design, thereby paving the way for more effective applications of AI advancements in the field. The code and data for the dataset and methods are made publicly accessible at https://github.com/cyrilpic/radcomp .

Conventional language model (LM) safety alignment relies on a reactive, disjoint procedure: attackers exploit a static model, followed by defensive fine-tuning to patch exposed vulnerabilities. This sequential approach creates a mismatch -- attackers overfit to obsolete defenses, while defenders perpetually lag behind emerging threats. To address this, we propose Self-RedTeam, an online self-play reinforcement learning algorithm where an attacker and defender agent co-evolve through continuous interaction. We cast safety alignment as a two-player zero-sum game, where a single model alternates between attacker and defender roles -- generating adversarial prompts and safeguarding against them -- while a reward LM adjudicates outcomes. This enables dynamic co-adaptation. Grounded in the game-theoretic framework of zero-sum games, we establish a theoretical safety guarantee which motivates the design of our method: if self-play converges to a Nash Equilibrium, the defender will reliably produce safe responses to any adversarial input. Empirically, Self-RedTeam uncovers more diverse attacks (+21.8% SBERT) compared to attackers trained against static defenders and achieves higher robustness on safety benchmarks (e.g., +65.5% on WildJailBreak) than defenders trained against static attackers. We further propose hidden Chain-of-Thought, allowing agents to plan privately, which boosts adversarial diversity and reduces over-refusals. Our results motivate a shift from reactive patching to proactive co-evolution in LM safety training, enabling scalable, autonomous, and robust self-improvement of LMs via multi-agent reinforcement learning (MARL).

The use of continuous instead of discrete tokens during the Chain-of-Thought (CoT) phase of reasoning LLMs has garnered attention recently, based on the intuition that a continuous mixture of discrete tokens could simulate a superposition of several reasoning paths simultaneously. Theoretical results have formally proven that continuous tokens have much greater expressivity and can solve specific problems more efficiently. However, practical use of continuous tokens has been limited by strong training difficulties: previous works either just use continuous tokens at inference time on a pre-trained discrete-token model, or must distill the continuous CoT from ground-truth discrete CoTs and face computational costs that limit the CoT to very few tokens. This is the first work introducing a scalable method to learn continuous CoTs via reinforcement learning (RL), without distilling from reference discrete CoTs. We use "soft" tokens: mixtures of tokens together with noise on the input embedding to provide RL exploration. Computational overhead is minimal, enabling us to learn continuous CoTs with hundreds of tokens. On math reasoning benchmarks with Llama and Qwen models up to 8B, training with continuous CoTs match discrete-token CoTs for pass@1 and surpass them for pass@32, showing greater CoT diversity. In systematic comparisons, the best-performing scenario is to train with continuous CoT tokens then use discrete tokens for inference, meaning the "soft" models can be deployed in a standard way. Finally, we show continuous CoT RL training better preserves the predictions of the base model on out-of-domain tasks, thus providing a softer touch to the base model.

Large language models (LLMs) are often equipped with multi-sample decoding strategies. An LLM implicitly defines an arithmetic code book, facilitating efficient and embarrassingly parallelizable arithmetic sampling to produce multiple samples using quasi-random codes. Traditional text generation methods, such as beam search and sampling-based techniques, have notable limitations: they lack parallelizability or diversity of sampled sequences. This study explores the potential of arithmetic sampling, contrasting it with ancestral sampling across two decoding tasks that employ multi-sample inference: chain-of-thought reasoning with self-consistency and machine translation with minimum Bayes risk decoding. Our results demonstrate that arithmetic sampling produces more diverse samples, significantly improving reasoning and translation performance as the sample size increases. We observe a 3text{-5%} point increase in accuracy on the GSM8K dataset and a 0.45text{-0.89%} point increment in COMET score for WMT19 tasks using arithmetic sampling without any significant computational overhead.

Autoregressive large language models (LLMs) compress knowledge from their training data through next-token conditional distributions. This limits tractable querying of this knowledge to start-to-end autoregressive sampling. However, many tasks of interest -- including sequence continuation, infilling, and other forms of constrained generation -- involve sampling from intractable posterior distributions. We address this limitation by using amortized Bayesian inference to sample from these intractable posteriors. Such amortization is algorithmically achieved by fine-tuning LLMs via diversity-seeking reinforcement learning algorithms: generative flow networks (GFlowNets). We empirically demonstrate that this distribution-matching paradigm of LLM fine-tuning can serve as an effective alternative to maximum-likelihood training and reward-maximizing policy optimization. As an important application, we interpret chain-of-thought reasoning as a latent variable modeling problem and demonstrate that our approach enables data-efficient adaptation of LLMs to tasks that require multi-step rationalization and tool use.

Large language models demonstrate exceptional performance in simple code generation tasks but still face challenges in tackling complex problems. These challenges may stem from insufficient reasoning and problem decomposition capabilities. To address this issue, we propose a reasoning-augmented data generation process, SRA-MCTS, which guides the model to autonomously generate high-quality intermediate reasoning paths. This creates a positive feedback loop, enabling continuous improvement. Our method operates entirely through the model itself without requiring additional supervision. By synthesizing natural language reasoning paths and translating them into executable code, the approach ensures analytical accuracy and enhances the success rate in solving complex tasks. Experimental results show that, even without additional supervisory signals, our method achieves performance improvements across different model scales, demonstrating the significant potential of self-improvement in small models. Furthermore, the method remains robust when traditional Chain-of-Thought (CoT) approaches exhibit performance degradation, with notable improvements observed in diversity metrics such as pass@10. We encourage further exploration of reasoning processes within training data to enhance the ability of language models to address complex problems. Our code and data are public at https://github.com/DIRECT-BIT/SRA-MCTS.

Reinforcement Learning with Verifiable Rewards (RLVR) is a promising paradigm for enhancing the reasoning ability in Large Language Models (LLMs). However, prevailing methods primarily rely on self-exploration or a single off-policy teacher to elicit long chain-of-thought (LongCoT) reasoning, which may introduce intrinsic model biases and restrict exploration, ultimately limiting reasoning diversity and performance. Drawing inspiration from multi-teacher strategies in knowledge distillation, we introduce Adaptive Multi-Guidance Policy Optimization (AMPO), a novel framework that adaptively leverages guidance from multiple proficient teacher models, but only when the on-policy model fails to generate correct solutions. This "guidance-on-demand" approach expands exploration while preserving the value of self-discovery. Moreover, AMPO incorporates a comprehension-based selection mechanism, prompting the student to learn from the reasoning paths that it is most likely to comprehend, thus balancing broad exploration with effective exploitation. Extensive experiments show AMPO substantially outperforms a strong baseline (GRPO), with a 4.3% improvement on mathematical reasoning tasks and 12.2% on out-of-distribution tasks, while significantly boosting Pass@k performance and enabling more diverse exploration. Notably, using four peer-sized teachers, our method achieves comparable results to approaches that leverage a single, more powerful teacher (e.g., DeepSeek-R1) with more data. These results demonstrate a more efficient and scalable path to superior reasoning and generalizability. Our code is available at https://github.com/SII-Enigma/AMPO.

We present QuantumLLMInstruct (QLMMI), an innovative dataset featuring over 500,000 meticulously curated instruction-following problem-solution pairs designed specifically for quantum computing - the largest and most comprehensive dataset of its kind. Originating from over 90 primary seed domains and encompassing hundreds of subdomains autonomously generated by LLMs, QLMMI marks a transformative step in the diversity and richness of quantum computing datasets. Designed for instruction fine-tuning, QLMMI seeks to significantly improve LLM performance in addressing complex quantum computing challenges across a wide range of quantum physics topics. While Large Language Models (LLMs) have propelled advancements in computational science with datasets like Omni-MATH and OpenMathInstruct, these primarily target Olympiad-level mathematics, leaving quantum computing largely unexplored. The creation of QLMMI follows a rigorous four-stage methodology. Initially, foundational problems are developed using predefined templates, focusing on critical areas such as synthetic Hamiltonians, QASM code generation, Jordan-Wigner transformations, and Trotter-Suzuki quantum circuit decompositions. Next, detailed and domain-specific solutions are crafted to ensure accuracy and relevance. In the third stage, the dataset is enriched through advanced reasoning techniques, including Chain-of-Thought (CoT) and Task-Oriented Reasoning and Action (ToRA), which enhance problem-solution diversity while adhering to strict mathematical standards. Lastly, a zero-shot Judge LLM performs self-assessments to validate the dataset's quality and reliability, minimizing human oversight requirements.

Transferring the reasoning capability from stronger large language models (LLMs) to smaller ones has been quite appealing, as smaller LLMs are more flexible to deploy with less expense. Among the existing solutions, knowledge distillation stands out due to its outstanding efficiency and generalization. However, existing methods suffer from several drawbacks, including limited knowledge diversity and the lack of rich contextual information. To solve the problems and facilitate the learning of compact language models, we propose TinyLLM, a novel knowledge distillation paradigm to learn a small student LLM from multiple large teacher LLMs. In particular, we encourage the student LLM to not only generate the correct answers but also understand the rationales behind these answers. Given that different LLMs possess diverse reasoning skills, we guide the student model to assimilate knowledge from various teacher LLMs. We further introduce an in-context example generator and a teacher-forcing Chain-of-Thought strategy to ensure that the rationales are accurate and grounded in contextually appropriate scenarios. Extensive experiments on six datasets across two reasoning tasks demonstrate the superiority of our method. Results show that TinyLLM can outperform large teacher LLMs significantly, despite having a considerably smaller model size.

Reinforcement learning with verifiable outcome rewards (RLVR) has effectively scaled up chain-of-thought (CoT) reasoning in large language models (LLMs). Yet, its efficacy in training vision-language model (VLM) agents for goal-directed action reasoning in visual environments is less established. This work investigates this problem through extensive experiments on complex card games, such as 24 points, and embodied tasks from ALFWorld. We find that when rewards are based solely on action outcomes, RL fails to incentivize CoT reasoning in VLMs, instead leading to a phenomenon we termed thought collapse, characterized by a rapid loss of diversity in the agent's thoughts, state-irrelevant and incomplete reasoning, and subsequent invalid actions, resulting in negative rewards. To counteract thought collapse, we highlight the necessity of process guidance and propose an automated corrector that evaluates and refines the agent's reasoning at each RL step. This simple and scalable GTR (Guided Thought Reinforcement) framework trains reasoning and action simultaneously without the need for dense, per-step human labeling. Our experiments demonstrate that GTR significantly enhances the performance and generalization of the LLaVA-7b model across various visual environments, achieving 3-5 times higher task success rates compared to SoTA models with notably smaller model sizes.

It is widely accepted that information derived from analyzing speech (the acoustic signal) and language production (words and sentences) serves as a useful window into the health of an individual's cognitive ability. In fact, most neuropsychological testing batteries have a component related to speech and language where clinicians elicit speech from patients for subjective evaluation across a broad set of dimensions. With advances in speech signal processing and natural language processing, there has been recent interest in developing tools to detect more subtle changes in cognitive-linguistic function. This work relies on extracting a set of features from recorded and transcribed speech for objective assessments of speech and language, early diagnosis of neurological disease, and tracking of disease after diagnosis. With an emphasis on cognitive and thought disorders, in this paper we provide a review of existing speech and language features used in this domain, discuss their clinical application, and highlight their advantages and disadvantages. Broadly speaking, the review is split into two categories: language features based on natural language processing and speech features based on speech signal processing. Within each category, we consider features that aim to measure complementary dimensions of cognitive-linguistics, including language diversity, syntactic complexity, semantic coherence, and timing. We conclude the review with a proposal of new research directions to further advance the field.

Cognitive diversity, reflected in variations of language, perspective, and reasoning, is essential to creativity and collective intelligence. This diversity is rich and grounded in culture, history, and individual experience. Yet as large language models (LLMs) become deeply embedded in people's lives, they risk standardizing language and reasoning. This Review synthesizes evidence across linguistics, cognitive, and computer science to show how LLMs reflect and reinforce dominant styles while marginalizing alternative voices and reasoning strategies. We examine how their design and widespread use contribute to this effect by mirroring patterns in their training data and amplifying convergence as all people increasingly rely on the same models across contexts. Unchecked, this homogenization risks flattening the cognitive landscapes that drive collective intelligence and adaptability.

Large language models exhibit systematic deficiencies in creative writing, particularly in non-English contexts where training data is scarce and lacks process-level supervision. We present COIG-Writer, a novel Chinese creative writing dataset that captures both diverse outputs and their underlying thought processes through systematic reverse-engineering of high-quality texts. Unlike existing datasets that provide only input-output pairs, COIG-Writer comprises 1,665 meticulously curated triplets spanning 51 genres, each containing: (1) a reverse-engineered prompt, (2) detailed creative reasoning documenting decision-making processes, and (3) the final text. Through comprehensive experiments, we identify a two-component model of creative writing: narrative logic (provided by process supervision) and linguistic expression (maintained by general-purpose data). Our findings reveal three critical insights: (1) Process supervision is highly effective but requires stabilization with general data. A ratio of at least one creative sample to twelve general samples is needed to achieve optimal performance; below this threshold, the win rate progressively degrades (from 62.75% down to 35.78%)., (2) creative capabilities are culturally-bound with no cross-lingual transfer (89.26pp gap between Chinese and English performance), and (3) lexical diversity inversely correlates with creative quality (TTR paradox), suggesting high diversity signals compensatory behavior for logical deficiencies. These findings establish that creative excellence emerges from the interaction between logical scaffolding and linguistic grounding, analogous to how mathematical reasoning enhances but cannot replace linguistic competence in foundation models.

Large language models (LLMs) have shown promising potential in persuasion, but existing works on training LLM persuaders are still preliminary. Notably, while humans are skilled in modeling their opponent's thoughts and opinions proactively and dynamically, current LLMs struggle with such Theory of Mind (ToM) reasoning, resulting in limited diversity and opponent awareness. To address this limitation, we introduce Theory of Mind Augmented Persuader (ToMAP), a novel approach for building more flexible persuader agents by incorporating two theory of mind modules that enhance the persuader's awareness and analysis of the opponent's mental state. Specifically, we begin by prompting the persuader to consider possible objections to the target central claim, and then use a text encoder paired with a trained MLP classifier to predict the opponent's current stance on these counterclaims. Our carefully designed reinforcement learning schema enables the persuader learns how to analyze opponent-related information and utilize it to generate more effective arguments. Experiments show that the ToMAP persuader, while containing only 3B parameters, outperforms much larger baselines, like GPT-4o, with a relative gain of 39.4% across multiple persuadee models and diverse corpora. Notably, ToMAP exhibits complex reasoning chains and reduced repetition during training, which leads to more diverse and effective arguments. The opponent-aware feature of ToMAP also makes it suitable for long conversations and enables it to employ more logical and opponent-aware strategies. These results underscore our method's effectiveness and highlight its potential for developing more persuasive language agents. Code is available at: https://github.com/ulab-uiuc/ToMAP.

Chain-of-Thought (CoT) prompting reveals that large language models are capable of performing complex reasoning via intermediate steps. CoT prompting is primarily categorized into three approaches. The first approach utilizes straightforward prompts like ``Let's think step by step'' to generate a sequential thought process before yielding an answer. The second approach makes use of human-crafted, step-by-step demonstrations to guide the model's reasoning process. The third automates the generation of reasoned demonstrations with the 'Let's think step by step'.This approach sometimes leads to reasoning errors, highlighting the need to diversify demonstrations to mitigate its misleading effects. However, diverse demonstrations pose challenges for effective representations. In this work, we propose ECHO, a self-harmonized chain-of-thought prompting method. It consolidates diverse solution paths into a uniform and effective solution pattern.ECHO demonstrates the best overall performance across three reasoning domains.

Existing Large Multimodal Models (LMMs) struggle with mathematical geometric reasoning due to a lack of high-quality image-text paired data. Current geometric data generation approaches, which apply preset templates to generate geometric data or use Large Language Models (LLMs) to rephrase questions and answers (Q&A), unavoidably limit data accuracy and diversity. To synthesize higher-quality data, we propose a two-stage Reverse Chain-of-Thought (R-CoT) geometry problem generation pipeline. First, we introduce GeoChain to produce high-fidelity geometric images and corresponding descriptions highlighting relations among geometric elements. We then design a Reverse A&Q method that reasons step-by-step based on the descriptions and generates questions in reverse from the reasoning results. Experiments demonstrate that the proposed method brings significant and consistent improvements on multiple LMM baselines, achieving new performance records in the 2B, 7B, and 8B settings. Notably, R-CoT-8B significantly outperforms previous state-of-the-art open-source mathematical models by 16.6% on MathVista and 9.2% on GeoQA, while also surpassing the closed-source model GPT-4o by an average of 13% across both datasets. The code is available at https://github.com/dle666/R-CoT.

Recent advances in Large Language Models (LLMs) have shown that their reasoning capabilities can be significantly improved through Reinforcement Learning with Verifiable Reward (RLVR), particularly in domains like mathematics and programming, where ground-truth correctness can be automatically evaluated. However, extending this success to other reasoning-intensive domains remains challenging due to the scarcity of high-quality, verifiable datasets and the high cost of human supervision. In this work, we introduce the Loong Project: an open-source framework for scalable synthetic data generation and verification across a diverse range of reasoning-intensive domains. The framework consists of two key components: (1) LoongBench, a curated seed dataset containing 8,729 human-vetted examples across 12 domains (e.g., Advanced Mathematics, Chemistry, Logic), each paired with executable code and rich metadata; and (2) LoongEnv, a modular synthetic data generation environment that supports multiple prompting strategies to produce new question-answer-code triples. Together, these components form an agent-environment loop that enables reinforcement learning, where an LLM-based agent is rewarded for generating Chain-of-Thought (CoT) solutions that align with code-executed answers. Empirically, we benchmark LoongBench on a broad suite of both open-source and proprietary LLMs to evaluate domain coverage and reveal performance bottlenecks. In addition, we conduct a comprehensive analysis of synthetic data generated by LoongEnv, examining correctness, difficulty, and diversity. Code and documentation are available at https://github.com/camel-ai/loong.

Zero-shot capability has been considered as a new revolution of deep learning, letting machines work on tasks without curated training data. As a good start and the only existing outcome of zero-shot image captioning (IC), ZeroCap abandons supervised training and sequentially searches every word in the caption using the knowledge of large-scale pretrained models. Though effective, its autoregressive generation and gradient-directed searching mechanism limit the diversity of captions and inference speed, respectively. Moreover, ZeroCap does not consider the controllability issue of zero-shot IC. To move forward, we propose a framework for Controllable Zero-shot IC, named ConZIC. The core of ConZIC is a novel sampling-based non-autoregressive language model named GibbsBERT, which can generate and continuously polish every word. Extensive quantitative and qualitative results demonstrate the superior performance of our proposed ConZIC for both zero-shot IC and controllable zero-shot IC. Especially, ConZIC achieves about 5x faster generation speed than ZeroCap, and about 1.5x higher diversity scores, with accurate generation given different control signals.

We address the challenge of developing a generalizable neural tracking controller for dexterous manipulation from human references. This controller aims to manage a dexterous robot hand to manipulate diverse objects for various purposes defined by kinematic human-object interactions. Developing such a controller is complicated by the intricate contact dynamics of dexterous manipulation and the need for adaptivity, generalizability, and robustness. Current reinforcement learning and trajectory optimization methods often fall short due to their dependence on task-specific rewards or precise system models. We introduce an approach that curates large-scale successful robot tracking demonstrations, comprising pairs of human references and robot actions, to train a neural controller. Utilizing a data flywheel, we iteratively enhance the controller's performance, as well as the number and quality of successful tracking demonstrations. We exploit available tracking demonstrations and carefully integrate reinforcement learning and imitation learning to boost the controller's performance in dynamic environments. At the same time, to obtain high-quality tracking demonstrations, we individually optimize per-trajectory tracking by leveraging the learned tracking controller in a homotopy optimization method. The homotopy optimization, mimicking chain-of-thought, aids in solving challenging trajectory tracking problems to increase demonstration diversity. We showcase our success by training a generalizable neural controller and evaluating it in both simulation and real world. Our method achieves over a 10% improvement in success rates compared to leading baselines. The project website with animated results is available at https://meowuu7.github.io/DexTrack/.

Transcriptomic foundation models (TFMs) have recently emerged as powerful tools for analyzing gene expression in cells and tissues, supporting key tasks such as cell-type annotation, batch correction, and perturbation prediction. However, the diversity of model implementations and training strategies across recent TFMs, though promising, makes it challenging to isolate the contribution of individual design choices or evaluate their potential synergies. This hinders the field's ability to converge on best practices and limits the reproducibility of insights across studies. We present BMFM-RNA, an open-source, modular software package that unifies diverse TFM pretraining and fine-tuning objectives within a single framework. Leveraging this capability, we introduce a novel training objective, whole cell expression decoder (WCED), which captures global expression patterns using an autoencoder-like CLS bottleneck representation. In this paper, we describe the framework, supported input representations, and training objectives. We evaluated four model checkpoints pretrained on CELLxGENE using combinations of masked language modeling (MLM), WCED and multitask learning. Using the benchmarking capabilities of BMFM-RNA, we show that WCED-based models achieve performance that matches or exceeds state-of-the-art approaches like scGPT across more than a dozen datasets in both zero-shot and fine-tuning tasks. BMFM-RNA, available as part of the biomed-multi-omics project ( https://github.com/BiomedSciAI/biomed-multi-omic ), offers a reproducible foundation for systematic benchmarking and community-driven exploration of optimal TFM training strategies, enabling the development of more effective tools to leverage the latest advances in AI for understanding cell biology.

While closed-source Large Language Models (LLMs) demonstrate strong mathematical problem-solving abilities, open-source models continue to struggle with such tasks. To bridge this gap, we propose a data augmentation approach and introduce PersonaMathQA, a dataset derived from MATH and GSM8K, on which we train the PersonaMath models. Our approach consists of two stages: the first stage is learning from Persona Diversification, and the second stage is learning from Reflection. In the first stage, we regenerate detailed chain-of-thought (CoT) solutions as instructions using a closed-source LLM and introduce a novel persona-driven data augmentation technique to enhance the dataset's quantity and diversity. In the second stage, we incorporate reflection to fully leverage more challenging and valuable questions. Evaluation of our PersonaMath models on MATH and GSM8K reveals that the PersonaMath-7B model (based on LLaMA-2-7B) achieves an accuracy of 24.2% on MATH and 68.7% on GSM8K, surpassing all baseline methods and achieving state-of-the-art performance. Notably, our dataset contains only 70.3K data points-merely 17.8% of MetaMathQA and 27% of MathInstruct-yet our model outperforms these baselines, demonstrating the high quality and diversity of our dataset, which enables more efficient model training. We open-source the PersonaMathQA dataset, PersonaMath models, and our code for public usage.

Research on LLM technologies is rapidly emerging, with most of them employing a 'fast thinking' approach to inference. Most LLMs generate the final result based solely on a single query and LLM's reasoning capabilities. However, with the advent of OpenAI-o1, 'slow thinking' techniques have garnered increasing attention because its process is closer to the human thought process. Inspired by the human ability to constantly associate and replenish knowledge during thinking, we developed the novel Chain-of-Associated-Thoughts (CoAT) framework, which introduces an innovative synergy between the Monte Carlo Tree Search (MCTS) algorithm and a dynamic mechanism for integrating new key information, termed 'associative memory'. By combining the structured exploration capabilities of MCTS with the adaptive learning capacity of associative memory, CoAT significantly expands the LLM search space, enabling our framework to explore diverse reasoning pathways and dynamically update its knowledge base in real-time. This allows the framework to not only revisit and refine earlier inferences but also adaptively incorporate evolving information, ensuring that the final output is both accurate and comprehensive. To validate the effectiveness of our framework, we conducted extensive experiments across a range of generative and reasoning tasks. These experiments demonstrated that our framework outperforms conventional inference processes on accuracy, coherence, and diversity. The framework's ability to iteratively expand its search space while retaining contextually relevant information results.

Large language models (LLMs) have demonstrated remarkable performance in diverse tasks using zero-shot and few-shot prompting. Even though their capabilities of data synthesis have been studied well in recent years, the generated data suffers from a lack of diversity, less adherence to the prompt, and potential biases that creep into the data from the generator model. In this work, we tackle the challenge of generating datasets with high diversity, upon which a student model is trained for downstream tasks. Taking the route of decoding-time guidance-based approaches, we propose CorrSynth, which generates data that is more diverse and faithful to the input prompt using a correlated sampling strategy. Further, our method overcomes the complexity drawbacks of some other guidance-based techniques like classifier-based guidance. With extensive experiments, we show the effectiveness of our approach and substantiate our claims. In particular, we perform intrinsic evaluation to show the improvements in diversity. Our experiments show that CorrSynth improves both student metrics and intrinsic metrics upon competitive baselines across four datasets, showing the innate advantage of our method.

Instruction tuning -- fine-tuning a large language model (LLM) on pairs of instructions and desired outcomes -- is an approach that enables pre-trained language models to perform real-world tasks and follow human instructions. Its practical success depends on the model learning a broader set of instructions than those it was trained on. Yet the factors that determine model generalization to such unseen tasks are not well understood. %To understand the driving factors of generalization, In this paper, we experiment with string rewrites, a symbolic task that serves as a building block for Turing complete Markov algorithms while allowing experimental control of "inputs" and "instructions". We investigate the trade-off between the number of instructions the model is trained on and the number of training samples provided for each instruction and observe that the diversity of the instruction set determines generalization. Generalization emerges once a diverse enough set of tasks is provided, even though very few examples are provided for each task. Instruction diversity also ensures robustness with respect to non-uniform distributions of instructions in the training set.

We systematically study a wide variety of image-based generative models spanning semantically-diverse datasets to understand and improve the feature extractors and metrics used to evaluate them. Using best practices in psychophysics, we measure human perception of image realism for generated samples by conducting the largest experiment evaluating generative models to date, and find that no existing metric strongly correlates with human evaluations. Comparing to 16 modern metrics for evaluating the overall performance, fidelity, diversity, and memorization of generative models, we find that the state-of-the-art perceptual realism of diffusion models as judged by humans is not reflected in commonly reported metrics such as FID. This discrepancy is not explained by diversity in generated samples, though one cause is over-reliance on Inception-V3. We address these flaws through a study of alternative self-supervised feature extractors, find that the semantic information encoded by individual networks strongly depends on their training procedure, and show that DINOv2-ViT-L/14 allows for much richer evaluation of generative models. Next, we investigate data memorization, and find that generative models do memorize training examples on simple, smaller datasets like CIFAR10, but not necessarily on more complex datasets like ImageNet. However, our experiments show that current metrics do not properly detect memorization; none in the literature is able to separate memorization from other phenomena such as underfitting or mode shrinkage. To facilitate further development of generative models and their evaluation we release all generated image datasets, human evaluation data, and a modular library to compute 16 common metrics for 8 different encoders at https://github.com/layer6ai-labs/dgm-eval.

Divergent thinking, the cognitive process of generating diverse solutions, is a hallmark of human creativity and problem-solving. For machines, sampling diverse solution trajectories in complex reasoning problems is crucial for robust outcomes, data augmentation, and enhanced model generalization. Large language models (LLMs) often struggle with generating high-quality, diverse reasoning. While supervised fine-tuning helps with quality, it requires extensive supervision data to capture the full diversity of solutions. Alternatively, reinforcement learning methods like PPO aim to find limited highest-reward solutions while neglecting the solution diversity, akin to convergent thinking. To address these limitations, we propose Flow of Reasoning (FoR) -- an efficient LLM training approach enabling diverse reasoning with minimal data. FoR formulates multi-step LLM reasoning as a Markovian flow from an initial state to terminal states. The formulation allows to adapt principled GFlowNet approaches to train the LLM as a policy, which is able to sample multiple reasoning paths with probabilities proportional to the unnormalized reward. Empirical results show that, with limited training data (e.g., 15 examples), FoR can discover diverse high-quality solutions that excel greatly beyond current state-of-the-art methods across three tasks, including embodied reasoning (BlocksWorld), math puzzle solving (Game24), and logical reasoning (PrOntoQA). Code is available at https://github.com/Yu-Fangxu/FoR.

Presenting high-level arguments is a crucial task for fostering participation in online societal discussions. Current argument summarization approaches miss an important facet of this task -- capturing diversity -- which is important for accommodating multiple perspectives. We introduce three aspects of diversity: those of opinions, annotators, and sources. We evaluate approaches to a popular argument summarization task called Key Point Analysis, which shows how these approaches struggle to (1) represent arguments shared by few people, (2) deal with data from various sources, and (3) align with subjectivity in human-provided annotations. We find that both general-purpose LLMs and dedicated KPA models exhibit this behavior, but have complementary strengths. Further, we observe that diversification of training data may ameliorate generalization. Addressing diversity in argument summarization requires a mix of strategies to deal with subjectivity.

Recent advancements in Large Language Models (LLMs) have revolutionized decision-making by breaking down complex problems into more manageable language sequences referred to as ``thoughts''. An effective thought design should consider three key perspectives: performance, efficiency, and flexibility. However, existing thought can at most exhibit two of these attributes. To address these limitations, we introduce a novel thought prompting approach called ``Everything of Thoughts'' (XoT) to defy the law of ``Penrose triangle of existing thought paradigms. XoT leverages pretrained reinforcement learning and Monte Carlo Tree Search (MCTS) to incorporate external domain knowledge into thoughts, thereby enhancing LLMs' capabilities and enabling them to generalize to unseen problems efficiently. Through the utilization of the MCTS-LLM collaborative thought revision framework, this approach autonomously produces high-quality comprehensive cognitive mappings with minimal LLM interactions. Additionally, XoT empowers LLMs to engage in unconstrained thinking, allowing for flexible cognitive mappings for problems with multiple solutions.

In this work, we focus on the problem of retrieving relevant arguments for a query claim covering diverse aspects. State-of-the-art methods rely on explicit mappings between claims and premises, and thus are unable to utilize large available collections of premises without laborious and costly manual annotation. Their diversity approach relies on removing duplicates via clustering which does not directly ensure that the selected premises cover all aspects. This work introduces a new multi-step approach for the argument retrieval problem. Rather than relying on ground-truth assignments, our approach employs a machine learning model to capture semantic relationships between arguments. Beyond that, it aims to cover diverse facets of the query, instead of trying to identify duplicates explicitly. Our empirical evaluation demonstrates that our approach leads to a significant improvement in the argument retrieval task even though it requires less data.

Collecting diverse human opinions is costly and challenging. This leads to a recent trend in exploiting large language models (LLMs) for generating diverse data for potential scalable and efficient solutions. However, the extent to which LLMs can generate diverse perspectives on subjective topics is still unclear. In this study, we explore LLMs' capacity of generating diverse perspectives and rationales on subjective topics such as social norms and argumentative texts. We introduce the problem of extracting maximum diversity from LLMs. Motivated by how humans form opinions based on values, we propose a criteria-based prompting technique to ground diverse opinions. To see how far we can extract diverse perspectives from LLMs, or called diversity coverage, we employ a step-by-step recall prompting to generate more outputs from the model iteratively. Our methods, applied to various tasks, show that LLMs can indeed produce diverse opinions according to the degree of task subjectivity. We also find that LLM's performance of extracting maximum diversity is on par with human.

While AI agents show potential in scientific ideation, most existing frameworks rely on single-agent refinement, limiting creativity due to bounded knowledge and perspective. Inspired by real-world research dynamics, this paper investigates whether structured multi-agent discussions can surpass solitary ideation. We propose a cooperative multi-agent framework for generating research proposals and systematically compare configurations including group size, leaderled versus leaderless structures, and team compositions varying in interdisciplinarity and seniority. To assess idea quality, we employ a comprehensive protocol with agent-based scoring and human review across dimensions such as novelty, strategic vision, and integration depth. Our results show that multi-agent discussions substantially outperform solitary baselines. A designated leader acts as a catalyst, transforming discussion into more integrated and visionary proposals. Notably, we find that cognitive diversity is a primary driver of quality, yet expertise is a non-negotiable prerequisite, as teams lacking a foundation of senior knowledge fail to surpass even a single competent agent. These findings offer actionable insights for designing collaborative AI ideation systems and shed light on how team structure influences creative outcomes.

Classic results establish that encouraging predictive diversity improves performance in ensembles of low-capacity models, e.g. through bagging or boosting. Here we demonstrate that these intuitions do not apply to high-capacity neural network ensembles (deep ensembles), and in fact the opposite is often true. In a large scale study of nearly 600 neural network classification ensembles, we examine a variety of interventions that trade off component model performance for predictive diversity. While such interventions can improve the performance of small neural network ensembles (in line with standard intuitions), they harm the performance of the large neural network ensembles most often used in practice. Surprisingly, we also find that discouraging predictive diversity is often benign in large-network ensembles, fully inverting standard intuitions. Even when diversity-promoting interventions do not sacrifice component model performance (e.g. using heterogeneous architectures and training paradigms), we observe an opportunity cost associated with pursuing increased predictive diversity. Examining over 1000 ensembles, we observe that the performance benefits of diverse architectures/training procedures are easily dwarfed by the benefits of simply using higher-capacity models, despite the fact that such higher capacity models often yield significantly less predictive diversity. Overall, our findings demonstrate that standard intuitions around predictive diversity, originally developed for low-capacity ensembles, do not directly apply to modern high-capacity deep ensembles. This work clarifies fundamental challenges to the goal of improving deep ensembles by making them more diverse, while suggesting an alternative path: simply forming ensembles from ever more powerful (and less diverse) component models.

Few-shot learning is a challenging task that requires language models to generalize from limited examples. Large language models like GPT-3 and PaLM have made impressive progress in this area, but they still face difficulties in reasoning tasks such as GSM8K, a benchmark for arithmetic problems. To improve their reasoning skills, previous work has proposed to guide the language model with prompts that elicit a series of reasoning steps before giving the final answer, achieving a significant improvement on GSM8K from 17.9% to 58.1% in problem-solving rate. In this paper, we present DIVERSE (Diverse Verifier on Reasoning Step), a novel approach that further enhances the reasoning capability of language models. DIVERSE has three main components: first, it generates diverse prompts to explore different reasoning paths for the same question; second, it uses a verifier to filter out incorrect answers based on a weighted voting scheme; and third, it verifies each reasoning step individually instead of the whole chain. We evaluate DIVERSE on the latest language model code-davinci-002 and show that it achieves new state-of-the-art results on six of eight reasoning benchmarks (e.g., GSM8K 74.4% to 83.2%).

Large language models (LLMs) have led to a surge in collaborative writing with model assistance. As different users incorporate suggestions from the same model, there is a risk of decreased diversity in the produced content, potentially limiting diverse perspectives in public discourse. In this work, we measure the impact of co-writing on diversity via a controlled experiment, where users write argumentative essays in three setups -- using a base LLM (GPT3), a feedback-tuned LLM (InstructGPT), and writing without model help. We develop a set of diversity metrics and find that writing with InstructGPT (but not the GPT3) results in a statistically significant reduction in diversity. Specifically, it increases the similarity between the writings of different authors and reduces the overall lexical and content diversity. We additionally find that this effect is mainly attributable to InstructGPT contributing less diverse text to co-written essays. In contrast, the user-contributed text remains unaffected by model collaboration. This suggests that the recent improvement in generation quality from adapting models to human feedback might come at the cost of more homogeneous and less diverse content.

Despite advances in generation quality, current text-to-image (T2I) models often lack diversity, generating homogeneous outputs. This work introduces a framework to address the need for robust diversity evaluation in T2I models. Our framework systematically assesses diversity by evaluating individual concepts and their relevant factors of variation. Key contributions include: (1) a novel human evaluation template for nuanced diversity assessment; (2) a curated prompt set covering diverse concepts with their identified factors of variation (e.g. prompt: An image of an apple, factor of variation: color); and (3) a methodology for comparing models in terms of human annotations via binomial tests. Furthermore, we rigorously compare various image embeddings for diversity measurement. Notably, our principled approach enables ranking of T2I models by diversity, identifying categories where they particularly struggle. This research offers a robust methodology and insights, paving the way for improvements in T2I model diversity and metric development.

Diverse language model responses are crucial for creative generation, open-ended tasks, and self-improvement training. We show that common diversity metrics, and even reward models used for preference optimization, systematically bias models toward shorter outputs, limiting expressiveness. To address this, we introduce Diverse, not Short (Diverse-NS), a length-controlled self-learning framework that improves response diversity while maintaining length parity. By generating and filtering preference data that balances diversity, quality, and length, Diverse-NS enables effective training using only 3,000 preference pairs. Applied to LLaMA-3.1-8B and the Olmo-2 family, Diverse-NS substantially enhances lexical and semantic diversity. We show consistent improvement in diversity with minor reduction or gains in response quality on four creative generation tasks: Divergent Associations, Persona Generation, Alternate Uses, and Creative Writing. Surprisingly, experiments with the Olmo-2 model family (7B, and 13B) show that smaller models like Olmo-2-7B can serve as effective "diversity teachers" for larger models. By explicitly addressing length bias, our method efficiently pushes models toward more diverse and expressive outputs.

In many text-generation problems, users may prefer not only a single response, but a diverse range of high-quality outputs from which to choose. Quality-diversity (QD) search algorithms aim at such outcomes, by continually improving and diversifying a population of candidates. However, the applicability of QD to qualitative domains, like creative writing, has been limited by the difficulty of algorithmically specifying measures of quality and diversity. Interestingly, recent developments in language models (LMs) have enabled guiding search through AI feedback, wherein LMs are prompted in natural language to evaluate qualitative aspects of text. Leveraging this development, we introduce Quality-Diversity through AI Feedback (QDAIF), wherein an evolutionary algorithm applies LMs to both generate variation and evaluate the quality and diversity of candidate text. When assessed on creative writing domains, QDAIF covers more of a specified search space with high-quality samples than do non-QD controls. Further, human evaluation of QDAIF-generated creative texts validates reasonable agreement between AI and human evaluation. Our results thus highlight the potential of AI feedback to guide open-ended search for creative and original solutions, providing a recipe that seemingly generalizes to many domains and modalities. In this way, QDAIF is a step towards AI systems that can independently search, diversify, evaluate, and improve, which are among the core skills underlying human society's capacity for innovation.

Generative commonsense reasoning (GCR) in natural language is to reason about the commonsense while generating coherent text. Recent years have seen a surge of interest in improving the generation quality of commonsense reasoning tasks. Nevertheless, these approaches have seldom investigated diversity in the GCR tasks, which aims to generate alternative explanations for a real-world situation or predict all possible outcomes. Diversifying GCR is challenging as it expects to generate multiple outputs that are not only semantically different but also grounded in commonsense knowledge. In this paper, we propose MoKGE, a novel method that diversifies the generative reasoning by a mixture of expert (MoE) strategy on commonsense knowledge graphs (KG). A set of knowledge experts seek diverse reasoning on KG to encourage various generation outputs. Empirical experiments demonstrated that MoKGE can significantly improve the diversity while achieving on par performance on accuracy on two GCR benchmarks, based on both automatic and human evaluations.

Recent advances in reinforcement learning for language model post-training, such as Group Relative Policy Optimization (GRPO), have shown promise in low-resource settings. However, GRPO typically relies on solution-level and scalar reward signals that fail to capture the semantic diversity among sampled completions. This leads to what we identify as a diversity-quality inconsistency, where distinct reasoning paths may receive indistinguishable rewards. To address this limitation, we propose Diversity-aware Reward Adjustment (DRA), a method that explicitly incorporates semantic diversity into the reward computation. DRA uses Submodular Mutual Information (SMI) to downweight redundant completions and amplify rewards for diverse ones. This encourages better exploration during learning, while maintaining stable exploitation of high-quality samples. Our method integrates seamlessly with both GRPO and its variant DR.~GRPO, resulting in DRA-GRPO and DGA-DR.~GRPO. We evaluate our method on five mathematical reasoning benchmarks and find that it outperforms recent strong baselines. It achieves state-of-the-art performance with an average accuracy of 58.2%, using only 7,000 fine-tuning samples and a total training cost of approximately $55. The code is available at https://github.com/xiwenc1/DRA-GRPO.

Generating diverse responses from large language models (LLMs) is crucial for applications such as planning/search and synthetic data generation, where diversity provides distinct answers across generations. Prior approaches rely on increasing temperature to increase diversity. However, contrary to popular belief, we show not only does this approach produce lower quality individual generations as temperature increases, but it depends on model's next-token probabilities being similar to the true distribution of answers. We propose , an alternative approach that uses the language model itself to partition the space into strata. At inference, a random stratum is selected and a sample drawn from within the strata. To measure diversity, we introduce CoverageQA, a dataset of underspecified questions with multiple equally plausible answers, and assess diversity by measuring KL Divergence between the output distribution and uniform distribution over valid ground truth answers. As computing probability per response/solution for proprietary models is infeasible, we measure recall on ground truth solutions. Our evaluation show using SimpleStrat achieves higher recall by 0.05 compared to GPT-4o and 0.36 average reduction in KL Divergence compared to Llama 3.

The primary goal in recommendation is to suggest relevant content to users, but optimizing for accuracy often results in recommendations that lack diversity. To remedy this, conventional approaches such as re-ranking improve diversity by presenting more diverse items. Here we argue that to promote inherent and prolonged diversity, the system must encourage its creation. Towards this, we harness the performative nature of recommendation, and show how learning can incentivize strategic content creators to create diverse content. Our approach relies on a novel form of regularization that anticipates strategic changes to content, and penalizes for content homogeneity. We provide analytic and empirical results that demonstrate when and how diversity can be incentivized, and experimentally demonstrate the utility of our approach on synthetic and semi-synthetic data.

Temperature sampling is a conventional approach to diversify large language model predictions. As temperature increases, the prediction becomes diverse but also vulnerable to hallucinations -- generating tokens that are sensible but not factual. One common approach to mitigate hallucinations is to provide source/grounding documents and the model is trained to produce predictions that bind to and are attributable to the provided source. It appears that there is a trade-off between diversity and attribution. To mitigate any such trade-off, we propose to relax the constraint of having a fixed temperature over decoding steps, and a mechanism to guide the dynamic temperature according to its relevance to the source through KL-divergence. Our experiments justifies the trade-off, and shows that our sampling algorithm outperforms the conventional top-k and top-p algorithms in conversational question-answering and summarization tasks.

Current trends to pre-train capable Large Language Models (LLMs) mostly focus on scaling of model and dataset size. However, the quality of pre-training data is an important factor for training powerful LLMs, yet it is a nebulous concept that has not been fully characterized. Therefore, we use the recently proposed Task2Vec diversity coefficient to ground and understand formal aspects of data quality, to go beyond scale alone. Specifically, we measure the diversity coefficient of publicly available pre-training datasets to demonstrate that their formal diversity is high when compared to theoretical lower and upper bounds. In addition, to build confidence in the diversity coefficient, we conduct interpretability experiments and find that the coefficient aligns with intuitive properties of diversity, e.g., it increases as the number of latent concepts increases. We conclude the diversity coefficient is reliable, show it's high for publicly available LLM datasets, and conjecture it can be used to build useful diverse datasets for LLMs.

Recent progress in single-image 3D generation highlights the importance of multi-view coherency, leveraging 3D priors from large-scale diffusion models pretrained on Internet-scale images. However, the aspect of novel-view diversity remains underexplored within the research landscape due to the ambiguity in converting a 2D image into 3D content, where numerous potential shapes can emerge. Here, we aim to address this research gap by simultaneously addressing both consistency and diversity. Yet, striking a balance between these two aspects poses a considerable challenge due to their inherent trade-offs. This work introduces HarmonyView, a simple yet effective diffusion sampling technique adept at decomposing two intricate aspects in single-image 3D generation: consistency and diversity. This approach paves the way for a more nuanced exploration of the two critical dimensions within the sampling process. Moreover, we propose a new evaluation metric based on CLIP image and text encoders to comprehensively assess the diversity of the generated views, which closely aligns with human evaluators' judgments. In experiments, HarmonyView achieves a harmonious balance, demonstrating a win-win scenario in both consistency and diversity.

Text-to-image (T2I) models are remarkable at generating realistic images based on textual descriptions. However, textual prompts are inherently underspecified: they do not specify all possible attributes of the required image. This raises two key questions: Do T2I models generate diverse outputs on underspecified prompts? How can we automatically measure diversity? We propose GRADE: Granular Attribute Diversity Evaluation, an automatic method for quantifying sample diversity. GRADE leverages the world knowledge embedded in large language models and visual question-answering systems to identify relevant concept-specific axes of diversity (e.g., ``shape'' and ``color'' for the concept ``cookie''). It then estimates frequency distributions of concepts and their attributes and quantifies diversity using (normalized) entropy. GRADE achieves over 90% human agreement while exhibiting weak correlation to commonly used diversity metrics. We use GRADE to measure the overall diversity of 12 T2I models using 400 concept-attribute pairs, revealing that all models display limited variation. Further, we find that these models often exhibit default behaviors, a phenomenon where the model consistently generates concepts with the same attributes (e.g., 98% of the cookies are round). Finally, we demonstrate that a key reason for low diversity is due to underspecified captions in training data. Our work proposes a modern, semantically-driven approach to measure sample diversity and highlights the stunning homogeneity in outputs by T2I models.

Effective generalization in language models depends critically on the diversity of their training data. Yet existing diversity metrics often fall short of this goal, relying on surface-level heuristics that are decoupled from model behavior. This motivates us to ask: What kind of diversity in training data actually drives generalization in language models -- and how can we measure and amplify it? Through large-scale empirical analyses spanning over 300 training runs, carefully controlled for data scale and quality, we show that data diversity can be a strong predictor of generalization in LLM reasoning -- as measured by average model performance on unseen out-of-distribution benchmarks. We introduce G-Vendi, a metric that quantifies diversity via the entropy of model-induced gradients. Despite using a small off-the-shelf proxy model for gradients, G-Vendi consistently outperforms alternative measures, achieving strong correlation (Spearman's rho approx 0.9) with out-of-distribution (OOD) performance on both natural language inference (NLI) and math reasoning tasks. Building on this insight, we present Prismatic Synthesis, a framework for generating diverse synthetic data by targeting underrepresented regions in gradient space. Experimental results show that Prismatic Synthesis consistently improves model performance as we scale synthetic data -- not just on in-distribution test but across unseen, out-of-distribution benchmarks -- significantly outperforming state-of-the-art models that rely on 20 times larger data generator than ours. For example, PrismMath-7B, our model distilled from a 32B LLM, outperforms R1-Distill-Qwen-7B -- the same base model trained on proprietary data generated by 671B R1 -- on 6 out of 7 challenging benchmarks.

AI research agents offer the promise to accelerate scientific progress by automating the design, implementation, and training of machine learning models. However, the field is still in its infancy, and the key factors driving the success or failure of agent trajectories are not fully understood. We examine the role that ideation diversity plays in agent performance. First, we analyse agent trajectories on MLE-bench, a well-known benchmark to evaluate AI research agents, across different models and agent scaffolds. Our analysis reveals that different models and agent scaffolds yield varying degrees of ideation diversity, and that higher-performing agents tend to have increased ideation diversity. Further, we run a controlled experiment where we modify the degree of ideation diversity, demonstrating that higher ideation diversity results in stronger performance. Finally, we strengthen our results by examining additional evaluation metrics beyond the standard medal-based scoring of MLE-bench, showing that our findings still hold across other agent performance metrics.

Reinforcement Learning from Human Feedback (RLHF) has shown potential in qualitative tasks where easily defined performance measures are lacking. However, there are drawbacks when RLHF is commonly used to optimize for average human preferences, especially in generative tasks that demand diverse model responses. Meanwhile, Quality Diversity (QD) algorithms excel at identifying diverse and high-quality solutions but often rely on manually crafted diversity metrics. This paper introduces Quality Diversity through Human Feedback (QDHF), a novel approach that progressively infers diversity metrics from human judgments of similarity among solutions, thereby enhancing the applicability and effectiveness of QD algorithms in complex and open-ended domains. Empirical studies show that QDHF significantly outperforms state-of-the-art methods in automatic diversity discovery and matches the efficacy of QD with manually crafted diversity metrics on standard benchmarks in robotics and reinforcement learning. Notably, in open-ended generative tasks, QDHF substantially enhances the diversity of text-to-image generation from a diffusion model and is more favorably received in user studies. We conclude by analyzing QDHF's scalability, robustness, and quality of derived diversity metrics, emphasizing its strength in open-ended optimization tasks. Code and tutorials are available at https://liding.info/qdhf.

Although LLMs have demonstrated improved performance by scaling parallel test-time compute, doing so relies on generating reasoning paths that are both diverse and accurate. For challenging problems, the forking tokens that trigger diverse yet correct reasoning modes are typically deep in the sampling tree. Consequently, common strategies to encourage diversity, such as temperature scaling, encounter a worsened trade-off between diversity and accuracy. Motivated by this challenge, we treat parallel reasoning as a set-of-next-token-prediction problem, and incorporate a set-based global loss into Supervised Fine-Tuning (SFT) using self-supervised bipartite matching between our global forking tokens and unique reasoning traces. We observe that, while naive fine-tuning with multiple reasoning traces collapses these unique reasoning modes, our proposed method, Set Supervised Fine-Tuning (SSFT), preserves these modes and produces emergent global forking tokens. Experiments on multiple reasoning benchmarks show that our SSFT consistently outperforms SFT under both Pass@1 and Cons@k metrics.

While scaling training compute has led to remarkable improvements in large language models (LLMs), scaling inference compute has not yet yielded analogous gains. We hypothesize that a core missing component is a lack of diverse LLM outputs, leading to inefficient search due to models repeatedly sampling highly similar, yet incorrect generations. We empirically demonstrate that this lack of diversity can be mitigated by searching over candidate plans for solving a problem in natural language. Based on this insight, we propose PLANSEARCH, a novel search algorithm which shows strong results across HumanEval+, MBPP+, and LiveCodeBench (a contamination-free benchmark for competitive coding). PLANSEARCH generates a diverse set of observations about the problem and then uses these observations to construct plans for solving the problem. By searching over plans in natural language rather than directly over code solutions, PLANSEARCH explores a significantly more diverse range of potential solutions compared to baseline search methods. Using PLANSEARCH on top of Claude 3.5 Sonnet achieves a state-of-the-art pass@200 of 77.0% on LiveCodeBench, outperforming both the best score achieved without search (pass@1 = 41.4%) and using standard repeated sampling (pass@200 = 60.6%). Finally, we show that, across all models, search algorithms, and benchmarks analyzed, we can accurately predict performance gains due to search as a direct function of the diversity over generated ideas.

The training and deployment of large language models (LLMs) create a feedback loop with human users: models learn human beliefs from data, reinforce these beliefs with generated content, reabsorb the reinforced beliefs, and feed them back to users again and again. This dynamic resembles an echo chamber. We hypothesize that this feedback loop entrenches the existing values and beliefs of users, leading to a loss of diversity and potentially the lock-in of false beliefs. We formalize this hypothesis and test it empirically with agent-based LLM simulations and real-world GPT usage data. Analysis reveals sudden but sustained drops in diversity after the release of new GPT iterations, consistent with the hypothesized human-AI feedback loop. Code and data available at https://thelockinhypothesis.com

Language models (LMs) often struggle to generate diverse, human-like creative content, raising concerns about the long-term homogenization of human thought through repeated exposure to similar outputs. Yet scalable methods for evaluating LM output diversity remain limited, especially beyond narrow tasks such as random number or name generation, or beyond repeated sampling from a single model. We introduce Infinity-Chat, a large-scale dataset of 26K diverse, real-world, open-ended user queries that admit a wide range of plausible answers with no single ground truth. We introduce the first comprehensive taxonomy for characterizing the full spectrum of open-ended prompts posed to LMs, comprising 6 top-level categories (e.g., brainstorm & ideation) that further breaks down to 17 subcategories. Using Infinity-Chat, we present a large-scale study of mode collapse in LMs, revealing a pronounced Artificial Hivemind effect in open-ended generation of LMs, characterized by (1) intra-model repetition, where a single model consistently generates similar responses, and more so (2) inter-model homogeneity, where different models produce strikingly similar outputs. Infinity-Chat also includes 31,250 human annotations, across absolute ratings and pairwise preferences, with 25 independent human annotations per example. This enables studying collective and individual-specific human preferences in response to open-ended queries. Our findings show that LMs, reward models, and LM judges are less well calibrated to human ratings on model generations that elicit differing idiosyncratic annotator preferences, despite maintaining comparable overall quality. Overall, INFINITY-CHAT presents the first large-scale resource for systematically studying real-world open-ended queries to LMs, revealing critical insights to guide future research for mitigating long-term AI safety risks posed by the Artificial Hivemind.

We study retrieving a set of documents that covers various perspectives on a complex and contentious question (e.g., will ChatGPT do more harm than good?). We curate a Benchmark for Retrieval Diversity for Subjective questions (BERDS), where each example consists of a question and diverse perspectives associated with the question, sourced from survey questions and debate websites. On this data, retrievers paired with a corpus are evaluated to surface a document set that contains diverse perspectives. Our framing diverges from most retrieval tasks in that document relevancy cannot be decided by simple string matches to references. Instead, we build a language model based automatic evaluator that decides whether each retrieved document contains a perspective. This allows us to evaluate the performance of three different types of corpus (Wikipedia, web snapshot, and corpus constructed on the fly with retrieved pages from the search engine) paired with retrievers. Retrieving diverse documents remains challenging, with the outputs from existing retrievers covering all perspectives on only 33.74% of the examples. We further study the impact of query expansion and diversity-focused reranking approaches and analyze retriever sycophancy. Together, we lay the foundation for future studies in retrieval diversity handling complex queries.

Post-training of Large Language Models (LMs) often prioritizes accuracy and helpfulness at the expense of diversity. This creates a tension: while post-training improves response quality, it also sharpens output distributions and reduces the range of ideas, limiting the usefulness of LMs in creative and exploratory tasks such as brainstorming, storytelling, or problem solving. We address this challenge with Diversity-Aware Reinforcement Learning (DARLING), a framework that jointly optimizes for response quality and semantic diversity. At its core, DARLING introduces a learned partition function to measure diversity beyond surface-level lexical variations. This diversity signal is then combined with a quality reward during online reinforcement learning, encouraging models to generate outputs that are both high-quality and distinct. Experiments across multiple model families and sizes show that DARLING generalizes to two regimes: non-verifiable tasks (instruction following and creative writing) and verifiable tasks (competition math). On five benchmarks in the first setting, DARLING consistently outperforms quality-only RL baselines, producing outputs that are simultaneously of higher quality and novelty. In the second setting, DARLING achieves higher pass@1 (solution quality) and pass@k (solution variety). Most strikingly, explicitly optimizing for diversity catalyzes exploration in online RL, which manifests itself as higher-quality responses.

Measuring diversity accurately is important for many scientific fields, including machine learning (ML), ecology, and chemistry. The Vendi Score was introduced as a generic similarity-based diversity metric that extends the Hill number of order q=1 by leveraging ideas from quantum statistical mechanics. Contrary to many diversity metrics in ecology, the Vendi Score accounts for similarity and does not require knowledge of the prevalence of the categories in the collection to be evaluated for diversity. However, the Vendi Score treats each item in a given collection with a level of sensitivity proportional to the item's prevalence. This is undesirable in settings where there is a significant imbalance in item prevalence. In this paper, we extend the other Hill numbers using similarity to provide flexibility in allocating sensitivity to rare or common items. This leads to a family of diversity metrics -- Vendi scores with different levels of sensitivity -- that can be used in a variety of applications. We study the properties of the scores in a synthetic controlled setting where the ground truth diversity is known. We then test their utility in improving molecular simulations via Vendi Sampling. Finally, we use the Vendi scores to better understand the behavior of image generative models in terms of memorization, duplication, diversity, and sample quality.

As creative writing tasks do not have singular correct answers, large language models (LLMs) trained to perform these tasks should be able to generate diverse valid outputs. However, LLM post-training often focuses on improving generation quality but neglects to facilitate output diversity. Hence, in creative writing generation, we investigate post-training approaches to promote both output diversity and quality. Our core idea is to include deviation -- the degree of difference between a training sample and all other samples with the same prompt -- in the training objective to facilitate learning from rare high-quality instances. By adopting our approach to direct preference optimization (DPO) and odds ratio preference optimization (ORPO), we demonstrate that we can promote the output diversity of trained models while minimally decreasing quality. Our best model with 8B parameters could achieve on-par diversity as a human-created dataset while having output quality similar to the best instruction-tuned models we examined, GPT-4o and DeepSeek-R1. We further validate our approaches with a human evaluation, an ablation, and a comparison to an existing diversification approach, DivPO.

Reinforcement Learning with Verifiable Rewards (RLVR), particularly with algorithms like Group Relative Policy Optimization (GRPO), has proven highly effective in enhancing the reasoning capabilities of large language models. However, a critical bottleneck in current pipelines lies in the limited diversity of sampled trajectories during group rollouts. Homogeneous trajectories and their associated rewards would diminish the return signals for policy updates, thereby hindering effective policy learning. This lack of diversity stems primarily from token-level stochastic sampling, where local variations are likely to collapse into near-identical reasoning paths. To address this limitation, we propose Lookahead Tree-Based Rollouts (LATR), a novel rollout strategy designed to explicitly promotes trajectory-level diversity by enforcing branching into different candidate tokens likely to yield distinct continuations. Specifically, LATR iteratively operates in three stages: (1) branching at high-uncertainty generation steps, (2) performing lookahead simulation for each new branch, and (3) pruning branches that exhibits prolonged similarity during simulation. Compared with stochastic Sampling, LATR accelerates policy learning by 131% on average and improves final pass@1 performance by 4.2% on both GRPO and Dynamic sAmpling Policy Optimization (DAPO) algorithms across different reasoning tasks. Our code and data are publicly available at https://github.com/starreeze/latr.

Exposure to large language model output is rapidly increasing. How will seeing AI-generated ideas affect human ideas? We conducted an experiment (800+ participants, 40+ countries) where participants viewed creative ideas that were from ChatGPT or prior experimental participants and then brainstormed their own idea. We varied the number of AI-generated examples (none, low, or high exposure) and if the examples were labeled as 'AI' (disclosure). Our dynamic experiment design -- ideas from prior participants in an experimental condition are used as stimuli for future participants in the same experimental condition -- mimics the interdependent process of cultural creation: creative ideas are built upon prior ideas. Hence, we capture the compounding effects of having LLMs 'in the culture loop'. We find that high AI exposure (but not low AI exposure) did not affect the creativity of individual ideas but did increase the average amount and rate of change of collective idea diversity. AI made ideas different, not better. There were no main effects of disclosure. We also found that self-reported creative people were less influenced by knowing an idea was from AI, and that participants were more likely to knowingly adopt AI ideas when the task was difficult. Our findings suggest that introducing AI ideas into society may increase collective diversity but not individual creativity.

Numerous applications of large language models (LLMs) rely on their ability to perform step-by-step reasoning. However, the reasoning behavior of LLMs remains poorly understood, posing challenges to research, development, and safety. To address this gap, we introduce landscape of thoughts-the first visualization tool for users to inspect the reasoning paths of chain-of-thought and its derivatives on any multi-choice dataset. Specifically, we represent the states in a reasoning path as feature vectors that quantify their distances to all answer choices. These features are then visualized in two-dimensional plots using t-SNE. Qualitative and quantitative analysis with the landscape of thoughts effectively distinguishes between strong and weak models, correct and incorrect answers, as well as different reasoning tasks. It also uncovers undesirable reasoning patterns, such as low consistency and high uncertainty. Additionally, users can adapt our tool to a model that predicts the property they observe. We showcase this advantage by adapting our tool to a lightweight verifier that evaluates the correctness of reasoning paths. The code is publicly available at: https://github.com/tmlr-group/landscape-of-thoughts.

Distilled diffusion models suffer from a critical limitation: reduced sample diversity compared to their base counterparts. In this work, we uncover that despite this diversity loss, distilled models retain the fundamental concept representations of base models. We demonstrate control distillation - where control mechanisms like Concept Sliders and LoRAs trained on base models can be seamlessly transferred to distilled models and vice-versa, effectively distilling control without any retraining. This preservation of representational structure prompted our investigation into the mechanisms of diversity collapse during distillation. To understand how distillation affects diversity, we introduce Diffusion Target (DT) Visualization, an analysis and debugging tool that reveals how models predict final outputs at intermediate steps. Through DT-Visualization, we identify generation artifacts, inconsistencies, and demonstrate that initial diffusion timesteps disproportionately determine output diversity, while later steps primarily refine details. Based on these insights, we introduce diversity distillation - a hybrid inference approach that strategically employs the base model for only the first critical timestep before transitioning to the efficient distilled model. Our experiments demonstrate that this simple modification not only restores the diversity capabilities from base to distilled models but surprisingly exceeds it, while maintaining nearly the computational efficiency of distilled inference, all without requiring additional training or model modifications. Our code and data are available at https://distillation.baulab.info

Scientific idea generation lies at the heart of scientific discovery and has driven human progress-whether by solving unsolved problems or proposing novel hypotheses to explain unknown phenomena. Unlike standard scientific reasoning or general creative generation, idea generation in science is a multi-objective and open-ended task, where the novelty of a contribution is as essential as its empirical soundness. Large language models (LLMs) have recently emerged as promising generators of scientific ideas, capable of producing coherent and factual outputs with surprising intuition and acceptable reasoning, yet their creative capacity remains inconsistent and poorly understood. This survey provides a structured synthesis of methods for LLM-driven scientific ideation, examining how different approaches balance creativity with scientific soundness. We categorize existing methods into five complementary families: External knowledge augmentation, Prompt-based distributional steering, Inference-time scaling, Multi-agent collaboration, and Parameter-level adaptation. To interpret their contributions, we employ two complementary frameworks: Boden's taxonomy of Combinatorial, Exploratory and Transformational creativity to characterize the level of ideas each family expected to generate, and Rhodes' 4Ps framework-Person, Process, Press, and Product-to locate the aspect or source of creativity that each method emphasizes. By aligning methodological advances with creativity frameworks, this survey clarifies the state of the field and outlines key directions toward reliable, systematic, and transformative applications of LLMs in scientific discovery.

Supervised learning datasets may contain multiple cues that explain the training set equally well, i.e., learning any of them would lead to the correct predictions on the training data. However, many of them can be spurious, i.e., lose their predictive power under a distribution shift and consequently fail to generalize to out-of-distribution (OOD) data. Recently developed "diversification" methods (Lee et al., 2023; Pagliardini et al., 2023) approach this problem by finding multiple diverse hypotheses that rely on different features. This paper aims to study this class of methods and identify the key components contributing to their OOD generalization abilities. We show that (1) diversification methods are highly sensitive to the distribution of the unlabeled data used for diversification and can underperform significantly when away from a method-specific sweet spot. (2) Diversification alone is insufficient for OOD generalization. The choice of the used learning algorithm, e.g., the model's architecture and pretraining, is crucial. In standard experiments (classification on Waterbirds and Office-Home datasets), using the second-best choice leads to an up to 20\% absolute drop in accuracy. (3) The optimal choice of learning algorithm depends on the unlabeled data and vice versa i.e. they are co-dependent. (4) Finally, we show that, in practice, the above pitfalls cannot be alleviated by increasing the number of diverse hypotheses, the major feature of diversification methods. These findings provide a clearer understanding of the critical design factors influencing the OOD generalization abilities of diversification methods. They can guide practitioners in how to use the existing methods best and guide researchers in developing new, better ones.

The sharp increase in data-related expenses has motivated research into condensing datasets while retaining the most informative features. Dataset distillation has thus recently come to the fore. This paradigm generates synthetic datasets that are representative enough to replace the original dataset in training a neural network. To avoid redundancy in these synthetic datasets, it is crucial that each element contains unique features and remains diverse from others during the synthesis stage. In this paper, we provide a thorough theoretical and empirical analysis of diversity within synthesized datasets. We argue that enhancing diversity can improve the parallelizable yet isolated synthesizing approach. Specifically, we introduce a novel method that employs dynamic and directed weight adjustment techniques to modulate the synthesis process, thereby maximizing the representativeness and diversity of each synthetic instance. Our method ensures that each batch of synthetic data mirrors the characteristics of a large, varying subset of the original dataset. Extensive experiments across multiple datasets, including CIFAR, Tiny-ImageNet, and ImageNet-1K, demonstrate the superior performance of our method, highlighting its effectiveness in producing diverse and representative synthetic datasets with minimal computational expense. Our code is available at https://github.com/AngusDujw/Diversity-Driven-Synthesis.https://github.com/AngusDujw/Diversity-Driven-Synthesis.

Recent advances in large language models (LLMs) have demonstrated the effectiveness of Iterative Self-Improvement (ISI) techniques. However, continuous training on self-generated data leads to reduced output diversity, a limitation particularly critical in reasoning tasks where diverse solution paths are essential. We present DIVE (Diversified Iterative Self-Improvement), a novel framework that addresses this challenge through two key components: Sample Pool Expansion for broader solution exploration, and Data Selection for balancing diversity and quality in preference pairs. Experiments on MATH and GSM8k datasets show that DIVE achieves a 10% to 45% relative increase in output diversity metrics while maintaining performance quality compared to vanilla ISI. Our ablation studies confirm both components' significance in achieving these improvements. Code is available at https://github.com/qinyiwei/DIVE.

Neural sequence models are widely used to model time-series data. Equally ubiquitous is the usage of beam search (BS) as an approximate inference algorithm to decode output sequences from these models. BS explores the search space in a greedy left-right fashion retaining only the top-B candidates - resulting in sequences that differ only slightly from each other. Producing lists of nearly identical sequences is not only computationally wasteful but also typically fails to capture the inherent ambiguity of complex AI tasks. To overcome this problem, we propose Diverse Beam Search (DBS), an alternative to BS that decodes a list of diverse outputs by optimizing for a diversity-augmented objective. We observe that our method finds better top-1 solutions by controlling for the exploration and exploitation of the search space - implying that DBS is a better search algorithm. Moreover, these gains are achieved with minimal computational or memory over- head as compared to beam search. To demonstrate the broad applicability of our method, we present results on image captioning, machine translation and visual question generation using both standard quantitative metrics and qualitative human studies. Further, we study the role of diversity for image-grounded language generation tasks as the complexity of the image changes. We observe that our method consistently outperforms BS and previously proposed techniques for diverse decoding from neural sequence models.

Many studies on scaling laws consider basic factors such as model size, model shape, dataset size, and compute power. These factors are easily tunable and represent the fundamental elements of any machine learning setup. But researchers have also employed more complex factors to estimate the test error and generalization performance with high predictability. These factors are generally specific to the domain or application. For example, feature diversity was primarily used for promoting syn-to-real transfer by Chen et al. (2021). With numerous scaling factors defined in previous works, it would be interesting to investigate how these factors may affect overall generalization performance in the context of self-supervised learning with CNN models. How do individual factors promote generalization, which includes varying depth, width, or the number of training epochs with early stopping? For example, does higher feature diversity result in higher accuracy held in complex settings other than a syn-to-real transfer? How do these factors depend on each other? We found that the last layer is the most diversified throughout the training. However, while the model's test error decreases with increasing epochs, its diversity drops. We also discovered that diversity is directly related to model width.

Generalization is arguably the most important goal of statistical language modeling research. Publicly available benchmarks and papers published with an open-source code have been critical to advancing the field. However, it is often very difficult, and sometimes even impossible, to reproduce the results fully as reported in publications. In this paper, we propose a simple framework that should help advance the state of the art in language modeling in terms of generalization. We propose to publish not just the code, but also probabilities on dev and test sets with future publications so that one can easily add the new model into an ensemble. This has crucial advantages: it is much easier to determine whether a newly proposed model is actually complementary to the current baseline. Therefore, instead of inventing new names for the old tricks, the scientific community can advance faster. Finally, this approach promotes diversity of ideas: one does not need to create an individual model that is the new state of the art to attract attention; it will be sufficient to develop a new model that learns patterns which other models do not. Thus, even a suboptimal model can be found to have value. Remarkably, our approach has yielded new state-of-the-art results across various language modeling benchmarks up to 10%.

Artificial intelligence (AI) systems, and Large Language Models (LLMs) in particular, are increasingly employed for creative tasks like scientific idea generation, constituting a form of generalization from training data unaddressed by existing conceptual frameworks. Despite its similarities to compositional generalization (CG), combinatorial creativity (CC) is an open-ended ability. Instead of evaluating for accuracy or correctness against fixed targets, which would contradict the open-ended nature of CC, we propose a theoretical framework and algorithmic task for evaluating outputs by their degrees of novelty and utility. From here, we make several important empirical contributions: (1) We obtain the first insights into the scaling behavior of creativity for LLMs. (2) We discover that, for fixed compute budgets, there exist optimal model depths and widths for creative ability. (3) We find that the ideation-execution gap, whereby LLMs excel at generating novel scientific ideas but struggle to ensure their practical feasibility, may be explained by a more fundamental novelty-utility tradeoff characteristic of creativity algorithms in general. Importantly, this tradeoff remains persistent even at scale, casting doubt on the long-term creative potential of LLMs in their current form. Together, our conceptual framework and empirical findings provide a foundation for understanding and improving creativity in modern AI models, bridging the gap between human and machine intelligence.

A shared goal of several machine learning communities like continual learning, meta-learning and transfer learning, is to design algorithms and models that efficiently and robustly adapt to unseen tasks. An even more ambitious goal is to build models that never stop adapting, and that become increasingly more efficient through time by suitably transferring the accrued knowledge. Beyond the study of the actual learning algorithm and model architecture, there are several hurdles towards our quest to build such models, such as the choice of learning protocol, metric of success and data needed to validate research hypotheses. In this work, we introduce the Never-Ending VIsual-classification Stream (NEVIS'22), a benchmark consisting of a stream of over 100 visual classification tasks, sorted chronologically and extracted from papers sampled uniformly from computer vision proceedings spanning the last three decades. The resulting stream reflects what the research community thought was meaningful at any point in time, and it serves as an ideal test bed to assess how well models can adapt to new tasks, and do so better and more efficiently as time goes by. Despite being limited to classification, the resulting stream has a rich diversity of tasks from OCR, to texture analysis, scene recognition, and so forth. The diversity is also reflected in the wide range of dataset sizes, spanning over four orders of magnitude. Overall, NEVIS'22 poses an unprecedented challenge for current sequential learning approaches due to the scale and diversity of tasks, yet with a low entry barrier as it is limited to a single modality and well understood supervised learning problems. Moreover, we provide a reference implementation including strong baselines and an evaluation protocol to compare methods in terms of their trade-off between accuracy and compute.

While the field of Quality-Diversity (QD) has grown into a distinct branch of stochastic optimization, a few problems, in particular locomotion and navigation tasks, have become de facto standards. Are such benchmarks sufficient? Are they representative of the key challenges faced by QD algorithms? Do they provide the ability to focus on one particular challenge by properly disentangling it from others? Do they have much predictive power in terms of scalability and generalization? Existing benchmarks are not standardized, and there is currently no MNIST equivalent for QD. Inspired by recent works on Reinforcement Learning benchmarks, we argue that the identification of challenges faced by QD methods and the development of targeted, challenging, scalable but affordable benchmarks is an important step. As an initial effort, we identify three problems that are challenging in sparse reward settings, and propose associated benchmarks: (1) Behavior metric bias, which can result from the use of metrics that do not match the structure of the behavior space. (2) Behavioral Plateaus, with varying characteristics, such that escaping them would require adaptive QD algorithms and (3) Evolvability Traps, where small variations in genotype result in large behavioral changes. The environments that we propose satisfy the properties listed above.

Text-to-image (T2I) diffusion models have demonstrated impressive performance in generating high-fidelity images, largely enabled by text-guided inference. However, this advantage often comes with a critical drawback: limited diversity, as outputs tend to collapse into similar modes under strong text guidance. Existing approaches typically optimize intermediate latents or text conditions during inference, but these methods deliver only modest gains or remain sensitive to hyperparameter tuning. In this work, we introduce Contrastive Noise Optimization, a simple yet effective method that addresses the diversity issue from a distinct perspective. Unlike prior techniques that adapt intermediate latents, our approach shapes the initial noise to promote diverse outputs. Specifically, we develop a contrastive loss defined in the Tweedie data space and optimize a batch of noise latents. Our contrastive optimization repels instances within the batch to maximize diversity while keeping them anchored to a reference sample to preserve fidelity. We further provide theoretical insights into the mechanism of this preprocessing to substantiate its effectiveness. Extensive experiments across multiple T2I backbones demonstrate that our approach achieves a superior quality-diversity Pareto frontier while remaining robust to hyperparameter choices.

We are born with the ability to learn concepts by comparing diverse observations. This helps us to understand the new world in a compositional manner and facilitates extrapolation, as objects naturally consist of multiple concepts. In this work, we argue that the cognitive mechanism of comparison, fundamental to human learning, is also vital for machines to recover true concepts underlying the data. This offers correctness guarantees for the field of concept learning, which, despite its impressive empirical successes, still lacks general theoretical support. Specifically, we aim to develop a theoretical framework for the identifiability of concepts with multiple classes of observations. We show that with sufficient diversity across classes, hidden concepts can be identified without assuming specific concept types, functional relations, or parametric generative models. Interestingly, even when conditions are not globally satisfied, we can still provide alternative guarantees for as many concepts as possible based on local comparisons, thereby extending the applicability of our theory to more flexible scenarios. Moreover, the hidden structure between classes and concepts can also be identified nonparametrically. We validate our theoretical results in both synthetic and real-world settings.

Clustering has been a major research topic in the field of machine learning, one to which Deep Learning has recently been applied with significant success. However, an aspect of clustering that is not addressed by existing deep clustering methods, is that of efficiently producing multiple, diverse partitionings for a given dataset. This is particularly important, as a diverse set of base clusterings are necessary for consensus clustering, which has been found to produce better and more robust results than relying on a single clustering. To address this gap, we propose DivClust, a diversity controlling loss that can be incorporated into existing deep clustering frameworks to produce multiple clusterings with the desired degree of diversity. We conduct experiments with multiple datasets and deep clustering frameworks and show that: a) our method effectively controls diversity across frameworks and datasets with very small additional computational cost, b) the sets of clusterings learned by DivClust include solutions that significantly outperform single-clustering baselines, and c) using an off-the-shelf consensus clustering algorithm, DivClust produces consensus clustering solutions that consistently outperform single-clustering baselines, effectively improving the performance of the base deep clustering framework.

Inference-Time Scaling (ITS) improves language models by allocating more computation at generation time. Particle Filtering (PF) has emerged as a strong ITS method for complex mathematical reasoning tasks, but it is vulnerable when guided by process reward models, which often assign overconfident scores early in the reasoning process. This causes PF to suffer from premature exploitation: it myopically commits to locally promising trajectories, prunes potentially correct hypotheses, and converges to suboptimal solutions. This failure mode, known as particle impoverishment, is especially severe under constrained computational budgets. To address this, we analyze the problem and identify two root causes: a lack of diversity in the particle set due to overconfident resampling and consequent inability to assess the potential of a reasoning path. We introduce Entropic Particle Filtering (ePF), an algorithm that integrates two new techniques to solve these issues. The first technique, Entropic Annealing (EA), directly mitigates particle impoverishment by monitoring search diversity via entropy; when diversity drops, it intervenes by dynamically annealing the resampling distribution to preserve exploration. The second, an enhancement called Look-ahead Modulation (LaM), adds a predictive guide to evaluate a state's potential based on its successors. On several challenging math benchmarks, ePF significantly outperforms strong baselines and achieves up to a 50 % relative improvement in task reward. Together, these methods improve PF's resilience by balancing the exploration of diverse solution spaces with the exploitation of high-reward regions, ultimately leading to higher-quality solutions.

Large language models (LLMs) tend to generate lexically, semantically, and stylistically homogenous texts. This poses a risk of knowledge collapse, where homogenous LLMs mediate a shrinking in the range of accessible information over time. Existing works on homogenization are limited by a focus on closed-ended multiple-choice setups or fuzzy semantic features, and do not look at trends across time and cultural contexts. To overcome this, we present a new methodology to measure epistemic diversity, i.e., variation in real-world claims in LLM outputs, which we use to perform a broad empirical study of LLM knowledge collapse. We test 27 LLMs, 155 topics covering 12 countries, and 200 prompt variations sourced from real user chats. For the topics in our study, we show that while newer models tend to generate more diverse claims, nearly all models are less epistemically diverse than a basic web search. We find that model size has a negative impact on epistemic diversity, while retrieval-augmented generation (RAG) has a positive impact, though the improvement from RAG varies by the cultural context. Finally, compared to a traditional knowledge source (Wikipedia), we find that country-specific claims reflect the English language more than the local one, highlighting a gap in epistemic representation

As LLMs become increasingly prevalent, it is interesting to consider how ``creative'' these models can be. From cognitive science, creativity consists of at least two key characteristics: convergent thinking (purposefulness to achieve a given goal) and divergent thinking (adaptability to new environments or constraints) runco2003critical. In this work, we introduce a framework for quantifying LLM creativity that incorporates the two characteristics. This is achieved by (1) Denial Prompting pushes LLMs to come up with more creative solutions to a given problem by incrementally imposing new constraints on the previous solution, compelling LLMs to adopt new strategies, and (2) defining and computing the NeoGauge metric which examines both convergent and divergent thinking in the generated creative responses by LLMs. We apply the proposed framework on Codeforces problems, a natural data source for collecting human coding solutions. We quantify NeoGauge for various proprietary and open-source models and find that even the most creative model, GPT-4, still falls short of demonstrating human-like creativity. We also experiment with advanced reasoning strategies (MCTS, self-correction, etc.) and observe no significant improvement in creativity. As a by-product of our analysis, we release NeoCoder dataset for reproducing our results on future models.

The development and evaluation of Large Language Models (LLMs) has primarily focused on their task-solving capabilities, with recent models even surpassing human performance in some areas. However, this focus often neglects whether machine-generated language matches the human level of diversity, in terms of vocabulary choice, syntactic construction, and expression of meaning, raising questions about whether the fundamentals of language generation have been fully addressed. This paper emphasizes the importance of examining the preservation of human linguistic richness by language models, given the concerning surge in online content produced or aided by LLMs. We propose a comprehensive framework for evaluating LLMs from various linguistic diversity perspectives including lexical, syntactic, and semantic dimensions. Using this framework, we benchmark several state-of-the-art LLMs across all diversity dimensions, and conduct an in-depth case study for syntactic diversity. Finally, we analyze how different development and deployment choices impact the linguistic diversity of LLM outputs.

Deep ensembles (DE) have been successful in improving model performance by learning diverse members via the stochasticity of random initialization. While recent works have attempted to promote further diversity in DE via hyperparameters or regularizing loss functions, these methods primarily still rely on a stochastic approach to explore the hypothesis space. In this work, we present Multi-Symmetry Ensembles (MSE), a framework for constructing diverse ensembles by capturing the multiplicity of hypotheses along symmetry axes, which explore the hypothesis space beyond stochastic perturbations of model weights and hyperparameters. We leverage recent advances in contrastive representation learning to create models that separately capture opposing hypotheses of invariant and equivariant functional classes and present a simple ensembling approach to efficiently combine appropriate hypotheses for a given task. We show that MSE effectively captures the multiplicity of conflicting hypotheses that is often required in large, diverse datasets like ImageNet. As a result of their inherent diversity, MSE improves classification performance, uncertainty quantification, and generalization across a series of transfer tasks.

In the Reinforcement Learning (RL) framework, the learning is guided through a reward signal. This means that in situations of sparse rewards the agent has to focus on exploration, in order to discover which action, or set of actions leads to the reward. RL agents usually struggle with this. Exploration is the focus of Quality-Diversity (QD) methods. In this thesis, we approach the problem of sparse rewards with these algorithms, and in particular with Novelty Search (NS). This is a method that only focuses on the diversity of the possible policies behaviors. The first part of the thesis focuses on learning a representation of the space in which the diversity of the policies is evaluated. In this regard, we propose the TAXONS algorithm, a method that learns a low-dimensional representation of the search space through an AutoEncoder. While effective, TAXONS still requires information on when to capture the observation used to learn said space. For this, we study multiple ways, and in particular the signature transform, to encode information about the whole trajectory of observations. The thesis continues with the introduction of the SERENE algorithm, a method that can efficiently focus on the interesting parts of the search space. This method separates the exploration of the search space from the exploitation of the reward through a two-alternating-steps approach. The exploration is performed through NS. Any discovered reward is then locally exploited through emitters. The third and final contribution combines TAXONS and SERENE into a single approach: STAX. Throughout this thesis, we introduce methods that lower the amount of prior information needed in sparse rewards settings. These contributions are a promising step towards the development of methods that can autonomously explore and find high-performance policies in a variety of sparse rewards settings.

Post-training alignment often reduces LLM diversity, leading to a phenomenon known as mode collapse. Unlike prior work that attributes this effect to algorithmic limitations, we identify a fundamental, pervasive data-level driver: typicality bias in preference data, whereby annotators systematically favor familiar text as a result of well-established findings in cognitive psychology. We formalize this bias theoretically, verify it on preference datasets empirically, and show that it plays a central role in mode collapse. Motivated by this analysis, we introduce Verbalized Sampling, a simple, training-free prompting strategy to circumvent mode collapse. VS prompts the model to verbalize a probability distribution over a set of responses (e.g., ``Generate 5 jokes about coffee and their corresponding probabilities''). Comprehensive experiments show that VS significantly improves performance across creative writing (poems, stories, jokes), dialogue simulation, open-ended QA, and synthetic data generation, without sacrificing factual accuracy and safety. For instance, in creative writing, VS increases diversity by 1.6-2.1x over direct prompting. We further observe an emergent trend that more capable models benefit more from VS. In sum, our work provides a new data-centric perspective on mode collapse and a practical inference-time remedy that helps unlock pre-trained generative diversity.

Evaluating modern machine learning models has become prohibitively expensive. Benchmarks such as LMMs-Eval and HELM demand thousands of GPU hours per model. Costly evaluation reduces inclusivity, slows the cycle of innovation, and worsens environmental impact. The typical approach follows two steps. First, select an anchor subset of data. Second, train a mapping from the accuracy on this subset to the final test result. The drawback is that anchor selection depends on clustering, which can be complex and sensitive to design choices. We argue that promoting diversity among samples is not essential; what matters is to select samples that maximise diversity in model responses. Our method, Diversifying Sample Condensation (DISCO), selects the top-k samples with the greatest model disagreements. This uses greedy, sample-wise statistics rather than global clustering. The approach is conceptually simpler. From a theoretical view, inter-model disagreement provides an information-theoretically optimal rule for such greedy selection. DISCO shows empirical gains over prior methods, achieving state-of-the-art results in performance prediction across MMLU, Hellaswag, Winogrande, and ARC. Code is available here: https://github.com/arubique/disco-public.

Recent Text-to-Speech (TTS) systems trained on reading or acted corpora have achieved near human-level naturalness. The diversity of human speech, however, often goes beyond the coverage of these corpora. We believe the ability to handle such diversity is crucial for AI systems to achieve human-level communication. Our work explores the use of more abundant real-world data for building speech synthesizers. We train TTS systems using real-world speech from YouTube and podcasts. We observe the mismatch between training and inference alignments in mel-spectrogram based autoregressive models, leading to unintelligible synthesis, and demonstrate that learned discrete codes within multiple code groups effectively resolves this issue. We introduce our MQTTS system whose architecture is designed for multiple code generation and monotonic alignment, along with the use of a clean silence prompt to improve synthesis quality. We conduct ablation analyses to identify the efficacy of our methods. We show that MQTTS outperforms existing TTS systems in several objective and subjective measures.

The emerging field of Diverse Intelligence seeks to identify, formalize, and understand commonalities in behavioral competencies across a wide range of implementations. Especially interesting are simple systems that provide unexpected examples of memory, decision-making, or problem-solving in substrates that at first glance do not appear to be complex enough to implement such capabilities. We seek to develop tools to help understand the minimal requirements for such capabilities, and to learn to recognize and predict basal forms of intelligence in unconventional substrates. Here, we apply novel analyses to the behavior of classical sorting algorithms, short pieces of code which have been studied for many decades. To study these sorting algorithms as a model of biological morphogenesis and its competencies, we break two formerly-ubiquitous assumptions: top-down control (instead, showing how each element within a array of numbers can exert minimal agency and implement sorting policies from the bottom up), and fully reliable hardware (instead, allowing some of the elements to be "damaged" and fail to execute the algorithm). We quantitatively characterize sorting activity as the traversal of a problem space, showing that arrays of autonomous elements sort themselves more reliably and robustly than traditional implementations in the presence of errors. Moreover, we find the ability to temporarily reduce progress in order to navigate around a defect, and unexpected clustering behavior among the elements in chimeric arrays whose elements follow one of two different algorithms. The discovery of emergent problem-solving capacities in simple, familiar algorithms contributes a new perspective to the field of Diverse Intelligence, showing how basal forms of intelligence can emerge in simple systems without being explicitly encoded in their underlying mechanics.

The proliferation of pretrained models, as a result of advancements in pretraining techniques, has led to the emergence of a vast zoo of publicly available models. Effectively utilizing these resources to obtain models with robust out-of-distribution generalization capabilities for downstream tasks has become a crucial area of research. Previous research has primarily focused on identifying the most powerful models within the model zoo, neglecting to fully leverage the diverse inductive biases contained within. This paper argues that the knowledge contained in weaker models is valuable and presents a method for leveraging the diversity within the model zoo to improve out-of-distribution generalization capabilities. Specifically, we investigate the behaviors of various pretrained models across different domains of downstream tasks by characterizing the variations in their encoded representations in terms of two dimensions: diversity shift and correlation shift. This characterization enables us to propose a new algorithm for integrating diverse pretrained models, not limited to the strongest models, in order to achieve enhanced out-of-distribution generalization performance. Our proposed method demonstrates state-of-the-art empirical results on a variety of datasets, thus validating the benefits of utilizing diverse knowledge.

Data diversity is crucial for the instruction tuning of large language models. Existing studies have explored various diversity-aware data selection methods to construct high-quality datasets and enhance model performance. However, the fundamental problem of precisely defining and measuring data diversity remains underexplored, limiting clear guidance for data engineering. To address this, we systematically analyze 11 existing diversity measurement methods by evaluating their correlation with model performance through extensive fine-tuning experiments. Our results indicate that a reliable diversity measure should properly account for both inter-sample differences and the information distribution in the sample space. Building on this, we propose NovelSum, a new diversity metric based on sample-level "novelty." Experiments on both simulated and real-world data show that NovelSum accurately captures diversity variations and achieves a 0.97 correlation with instruction-tuned model performance, highlighting its value in guiding data engineering practices. With NovelSum as an optimization objective, we further develop a greedy, diversity-oriented data selection strategy that outperforms existing approaches, validating both the effectiveness and practical significance of our metric.

Large language models (LLMs) can be used to generate text data for training and evaluating other models. However, creating high-quality datasets with LLMs can be challenging. In this work, we explore human-AI partnerships to facilitate high diversity and accuracy in LLM-based text data generation. We first examine two approaches to diversify text generation: 1) logit suppression, which minimizes the generation of languages that have already been frequently generated, and 2) temperature sampling, which flattens the token sampling probability. We found that diversification approaches can increase data diversity but often at the cost of data accuracy (i.e., text and labels being appropriate for the target domain). To address this issue, we examined two human interventions, 1) label replacement (LR), correcting misaligned labels, and 2) out-of-scope filtering (OOSF), removing instances that are out of the user's domain of interest or to which no considered label applies. With oracle studies, we found that LR increases the absolute accuracy of models trained with diversified datasets by 14.4%. Moreover, we found that some models trained with data generated with LR interventions outperformed LLM-based few-shot classification. In contrast, OOSF was not effective in increasing model accuracy, implying the need for future work in human-in-the-loop text data generation.

The Combined Algorithm Selection and Hyperparameters optimization (CASH) problem is one of the fundamental problems in Automated Machine Learning (AutoML). Motivated by the success of ensemble learning, recent AutoML systems build post-hoc ensembles to output the final predictions instead of using the best single learner. However, while most CASH methods focus on searching for a single learner with the best performance, they neglect the diversity among base learners (i.e., they may suggest similar configurations to previously evaluated ones), which is also a crucial consideration when building an ensemble. To tackle this issue and further enhance the ensemble performance, we propose DivBO, a diversity-aware framework to inject explicit search of diversity into the CASH problems. In the framework, we propose to use a diversity surrogate to predict the pair-wise diversity of two unseen configurations. Furthermore, we introduce a temporary pool and a weighted acquisition function to guide the search of both performance and diversity based on Bayesian optimization. Empirical results on 15 public datasets show that DivBO achieves the best average ranks (1.82 and 1.73) on both validation and test errors among 10 compared methods, including post-hoc designs in recent AutoML systems and state-of-the-art baselines for ensemble learning on CASH problems.

Chain-of-thought reasoning, a cognitive process fundamental to human intelligence, has garnered significant attention in the realm of artificial intelligence and natural language processing. However, there still remains a lack of a comprehensive survey for this arena. To this end, we take the first step and present a thorough survey of this research field carefully and widely. We use X-of-Thought to refer to Chain-of-Thought in a broad sense. In detail, we systematically organize the current research according to the taxonomies of methods, including XoT construction, XoT structure variants, and enhanced XoT. Additionally, we describe XoT with frontier applications, covering planning, tool use, and distillation. Furthermore, we address challenges and discuss some future directions, including faithfulness, multi-modal, and theory. We hope this survey serves as a valuable resource for researchers seeking to innovate within the domain of chain-of-thought reasoning.

Ensembling neural networks is an effective way to increase accuracy, and can often match the performance of individual larger models. This observation poses a natural question: given the choice between a deep ensemble and a single neural network with similar accuracy, is one preferable over the other? Recent work suggests that deep ensembles may offer distinct benefits beyond predictive power: namely, uncertainty quantification and robustness to dataset shift. In this work, we demonstrate limitations to these purported benefits, and show that a single (but larger) neural network can replicate these qualities. First, we show that ensemble diversity, by any metric, does not meaningfully contribute to an ensemble's uncertainty quantification on out-of-distribution (OOD) data, but is instead highly correlated with the relative improvement of a single larger model. Second, we show that the OOD performance afforded by ensembles is strongly determined by their in-distribution (InD) performance, and -- in this sense -- is not indicative of any "effective robustness". While deep ensembles are a practical way to achieve improvements to predictive power, uncertainty quantification, and robustness, our results show that these improvements can be replicated by a (larger) single model.

Alignment with human preference prevents large language models (LLMs) from generating misleading or toxic content while requiring high-cost human feedback. Assuming resources of human annotation are limited, there are two different ways of allocating considered: more diverse PROMPTS or more diverse RESPONSES to be labeled. Nonetheless, a straightforward comparison between their impact is absent. In this work, we first control the diversity of both sides according to the number of samples for fine-tuning, which can directly reflect their influence. We find that instead of numerous prompts, more responses but fewer prompts better trigger LLMs for human alignment. Additionally, the concept of diversity for prompts can be more complex than responses that are typically quantified by single digits. Consequently, a new formulation of prompt diversity is proposed, further implying a linear correlation with the final performance of LLMs after fine-tuning. We also leverage it on data augmentation and conduct experiments to show its effect on different algorithms.

Compressing long chain-of-thought (CoT) from large language models (LLMs) is an emerging strategy to improve the reasoning efficiency of LLMs. Despite its promising benefits, existing studies equally compress all thoughts within a long CoT, hindering more concise and effective reasoning. To this end, we first investigate the importance of different thoughts by examining their effectiveness and efficiency in contributing to reasoning through automatic long CoT chunking and Monte Carlo rollouts. Building upon the insights, we propose a theoretically bounded metric to jointly measure the effectiveness and efficiency of different thoughts. We then propose LongotimesShort, an efficient reasoning framework that enables two LLMs to collaboratively solve the problem: a long-thought LLM for more effectively generating important thoughts, while a short-thought LLM for efficiently generating remaining thoughts. Specifically, we begin by synthesizing a small amount of cold-start data to fine-tune LLMs for long-thought and short-thought reasoning styles, respectively. Furthermore, we propose a synergizing-oriented multi-turn reinforcement learning, focusing on the model self-evolution and collaboration between long-thought and short-thought LLMs. Experimental results show that our method enables Qwen2.5-7B and Llama3.1-8B to achieve comparable performance compared to DeepSeek-R1-Distill-Qwen-7B and DeepSeek-R1-Distill-Llama-8B, while reducing token length by over 80% across the MATH500, AIME24/25, AMC23, and GPQA Diamond benchmarks. Our data and code are available at https://github.com/yasNing/Long-otimes-Short/.

Post-training of language models, either through reinforcement learning, preference optimization or supervised finetuning, tends to sharpen the output probability distribution and reduce the diversity of generated responses. This is particularly a problem for creative generative tasks where varied responses are desired. In this work we introduce Diverse Preference Optimization (DivPO), an optimization method which learns to generate much more diverse responses than standard pipelines, while maintaining the quality of the generations. In DivPO, preference pairs are selected by first considering a pool of responses, and a measure of diversity among them, and selecting chosen examples as being more rare but high quality, while rejected examples are more common, but low quality. DivPO results in generating 45.6% more diverse persona attributes, and an 74.6% increase in story diversity, while maintaining similar win rates as standard baselines.

Abstract reasoning, the ability to reason from the abstract essence of a problem, serves as a key to generalization in human reasoning. However, eliciting language models to perform reasoning with abstraction remains unexplored. This paper seeks to bridge this gap by introducing a novel structured reasoning format called Abstraction-of-Thought (AoT). The uniqueness of AoT lies in its explicit requirement for varying levels of abstraction within the reasoning process. This approach could elicit language models to first contemplate on the abstract level before incorporating concrete details, which is overlooked by the prevailing step-by-step Chain-of-Thought (CoT) method. To align models with the AoT format, we present AoT Collection, a generic finetuning dataset consisting of 348k high-quality samples with AoT reasoning processes, collected via an automated and scalable pipeline. We finetune a wide range of language models with AoT Collection and conduct extensive evaluations on 23 unseen tasks from the challenging benchmark Big-Bench Hard. Experimental results indicate that models aligned to AoT reasoning format substantially outperform those aligned to CoT in many reasoning tasks.

The effectiveness of Large Language Models (LLMs) is heavily influenced by the reasoning strategies, or styles of thought, employed in their prompts. However, the interplay between these reasoning styles, model architecture, and task type remains poorly understood. To address this, we introduce StyleBench, a comprehensive benchmark for systematically evaluating reasoning styles across diverse tasks and models. We assess five representative reasoning styles, including Chain of Thought (CoT), Tree of Thought (ToT), Algorithm of Thought (AoT), Sketch of Thought (SoT), and Chain-of-Draft (CoD) on five reasoning tasks, using 15 open-source models from major families (LLaMA, Qwen, Mistral, Gemma, GPT-OSS, Phi, and DeepSeek) ranging from 270M to 120B parameters. Our large-scale analysis reveals that no single style is universally optimal. We demonstrate that strategy efficacy is highly contingent on both model scale and task type: search-based methods (AoT, ToT) excel in open-ended problems but require large-scale models, while concise styles (SoT, CoD) achieve radical efficiency gains on well-defined tasks. Furthermore, we identify key behavioral patterns: smaller models frequently fail to follow output instructions and default to guessing, while reasoning robustness emerges as a function of scale. Our findings offer a crucial roadmap for selecting optimal reasoning strategies based on specific constraints, we open source the benchmark in https://github.com/JamesJunyuGuo/Style_Bench.

This paper revisits Ramon Llull's Ars combinatoria - a medieval framework for generating knowledge through symbolic recombination - as a conceptual foundation for building a modern Llull's thinking machine for research ideation. Our approach defines three compositional axes: Theme (e.g., efficiency, adaptivity), Domain (e.g., question answering, machine translation), and Method (e.g., adversarial training, linear attention). These elements represent high-level abstractions common in scientific work - motivations, problem settings, and technical approaches - and serve as building blocks for LLM-driven exploration. We mine elements from human experts or conference papers and show that prompting LLMs with curated combinations produces research ideas that are diverse, relevant, and grounded in current literature. This modern thinking machine offers a lightweight, interpretable tool for augmenting scientific creativity and suggests a path toward collaborative ideation between humans and AI.

Compositional understanding is crucial for human intelligence, yet it remains unclear whether contemporary vision models exhibit it. The dominant machine learning paradigm is built on the premise that scaling data and model sizes will improve out-of-distribution performance, including compositional generalization. We test this premise through controlled experiments that systematically vary data scale, concept diversity, and combination coverage. We find that compositional generalization is driven by data diversity, not mere data scale. Increased combinatorial coverage forces models to discover a linearly factored representational structure, where concepts decompose into additive components. We prove this structure is key to efficiency, enabling perfect generalization from few observed combinations. Evaluating pretrained models (DINO, CLIP), we find above-random yet imperfect performance, suggesting partial presence of this structure. Our work motivates stronger emphasis on constructing diverse datasets for compositional generalization, and considering the importance of representational structure that enables efficient compositional learning. Code available at https://github.com/oshapio/visual-compositional-generalization.

This position paper argues that, in order to understand AI, we cannot rely on our existing vocabulary of human words. Instead, we should strive to develop neologisms: new words that represent precise human concepts that we want to teach machines, or machine concepts that we need to learn. We start from the premise that humans and machines have differing concepts. This means interpretability can be framed as a communication problem: humans must be able to reference and control machine concepts, and communicate human concepts to machines. Creating a shared human-machine language through developing neologisms, we believe, could solve this communication problem. Successful neologisms achieve a useful amount of abstraction: not too detailed, so they're reusable in many contexts, and not too high-level, so they convey precise information. As a proof of concept, we demonstrate how a "length neologism" enables controlling LLM response length, while a "diversity neologism" allows sampling more variable responses. Taken together, we argue that we cannot understand AI using our existing vocabulary, and expanding it through neologisms creates opportunities for both controlling and understanding machines better.

The rise of Large Language Models (LLMs) has accentuated the need for diverse, high-quality pre-training data. Synthetic data emerges as a viable solution to the challenges of data scarcity and inaccessibility. While previous literature has focused predominantly on the quality and quantity of real data, our work enables the measurement of diversity in synthetic data and explores its impact on LLM performance. We study the downstream effects of synthetic data diversity during both the pre-training and fine-tuning stages by introducing a new diversity metric, LLM cluster-agent, designed to evaluate the diversity of synthetic datasets. Through a series of controlled experiments with models of 350M and 1.4B parameters, we demonstrate that the proposed cluster-based LLM scoring of diversity correlates positively with both pre-training and supervised fine-tuning performance. Our findings also reveal that synthetic data diversity in pre-training affects supervised fine-tuning more significantly than pre-training itself, even for smaller models. We hope this study advances our understanding of the optimal use of synthetic data in LLM training and opens new avenues for efficient data generation processes.

We study the task of long-form opinion text generation, which faces at least two distinct challenges. First, existing neural generation models fall short of coherence, thus requiring efficient content planning. Second, diverse types of information are needed to guide the generator to cover both subjective and objective content. To this end, we propose DYPLOC, a generation framework that conducts dynamic planning of content while generating the output based on a novel design of mixed language models. To enrich the generation with diverse content, we further propose to use large pre-trained models to predict relevant concepts and to generate claims. We experiment with two challenging tasks on newly collected datasets: (1) argument generation with Reddit ChangeMyView, and (2) writing articles using New York Times' Opinion section. Automatic evaluation shows that our model significantly outperforms competitive comparisons. Human judges further confirm that our generations are more coherent with richer content.

What data should a vision-language model be trained on? To answer this question, many data curation efforts center on the quality of a dataset. However, most of these existing methods are (i) offline, i.e. they produce a static dataset from a set of predetermined filtering criteria, and (ii) concept-agnostic, i.e. they use model-based filters which induce additional data biases. In this work, we go beyond such offline, concept-agnostic methods and advocate for more flexible, task-adaptive online concept-based curation. Our first contribution is DataConcept, a collection of 128M web-crawled image-text pairs annotated with fine-grained details about their concept composition. Building on DataConcept, we introduce Concept-Aware Batch Sampling (CABS), a simple yet effective batch sampling framework that flexibly constructs batches on-the-fly based on specific target distributions. We propose two variants: (i) Diversity Maximization (CABS-DM) to curate batches with a broad coverage of available concepts, and (ii) Frequency Maximization (CABS-FM) to curate batches with high object multiplicity. Through extensive evaluations across 28 benchmarks, we demonstrate that our CABS method significantly benefits CLIP/SigLIP model classes and yields highly performant models. Overall, CABS represents a strong open-source alternative to proprietary online data curation algorithms, enabling practitioners to define custom concept distributions that optimize for specific downstream tasks.

Current vision systems are trained on huge datasets, and these datasets come with costs: curation is expensive, they inherit human biases, and there are concerns over privacy and usage rights. To counter these costs, interest has surged in learning from cheaper data sources, such as unlabeled images. In this paper we go a step further and ask if we can do away with real image datasets entirely, instead learning from noise processes. We investigate a suite of image generation models that produce images from simple random processes. These are then used as training data for a visual representation learner with a contrastive loss. We study two types of noise processes, statistical image models and deep generative models under different random initializations. Our findings show that it is important for the noise to capture certain structural properties of real data but that good performance can be achieved even with processes that are far from realistic. We also find that diversity is a key property to learn good representations. Datasets, models, and code are available at https://mbaradad.github.io/learning_with_noise.