Daily Papers

Metric feed-forward 3D reconstruction for panoramic data remains under-explored due to the lack of large-scale panoramic RGB-D training data. We present Realsee3D, a hybrid dataset of 10K indoor scenes (1K real, 9K synthetic) with 299K panoramic viewpoints and precise metric annotations, and Argus, a feed-forward network trained on it for metric panoramic 3D reconstruction. In the sparse unordered capture setting of Realsee3D, a poorly chosen coordinate anchor can cause global pose drift. Argus addresses this with a learned covisibility module that selects the geometrically optimal reference view to anchor the metric world frame. To further improve multi-task learning, we decompose the bidirectional pixel-to-world mapping into interpretable sub-steps with per-step supervision and cross-coordinate joint constraints, reinforcing geometric consistency across prediction branches. On the Realsee3D benchmark, Argus achieves state-of-the-art metric performance in camera pose estimation, depth estimation, and point cloud reconstruction. Project page: https://argus-paper.realsee.ai.

We present Generative Logic (GL), a deterministic architecture that begins from user-supplied axiomatic definitions -- written in a minimalist Mathematical Programming Language (MPL) -- and systematically explores their deductive neighborhood. Definitions are compiled into a distributed grid of simple Logic Blocks (LBs) that exchange messages; any time several expressions unify under an inference rule, a new fact is emitted with full provenance to its sources, yielding replayable, auditable proof graphs. A prototype software implementation instantiates the workflow on first-order Peano arithmetic. Starting only from the Peano axioms, GL enumerates candidate implications, applies normalization and type filters, and automatically reconstructs machine-checkable proofs of foundational arithmetic laws including associativity and commutativity of addition, associativity and commutativity of multiplication, and distributivity. Generated proofs export to navigable HTML so that every inference step can be inspected independently. We outline a hardware-software co-design path toward massively parallel realizations and describe prospective integration with probabilistic models (e.g., Large Language Models (LLMs)) for autoformalization and conjecture seeding. The Python and MPL code to reproduce the Peano experiments, along with the full HTML proof graphs, are available in the project's GitHub repository at https://github.com/Generative-Logic/GL/tree/35a111ea9ba53afe051703d6050be0c3923e9724 and are permanently archived at https://doi.org/10.5281/zenodo.16408441. We invite community feedback and collaboration.

An open-source C++ framework for discovering fast matrix multiplication schemes using the flip graph approach is presented. The framework supports multiple coefficient rings -- binary (Z_2), modular ternary (Z_3) and integer ternary (Z_T = {-1,0,1}) -- and implements both fixed-dimension and meta-dimensional search operators. Using efficient bit-level encoding of coefficient vectors and OpenMP parallelism, the tools enable large-scale exploration on commodity hardware. The study covers 680 schemes ranging from (2 times 2 times 2) to (16 times 16 times 16), with 276 schemes now in Z_T coefficients and 117 in integer coefficients. With this framework, the multiplicative complexity (rank) is improved for 79 matrix multiplication schemes. Notably, a new 4 times 4 times 10 scheme requiring only 115 multiplications is discovered, achieving ωapprox 2.80478 and beating Strassen's exponent for this specific size. Additionally, 93 schemes are rediscovered in ternary coefficients that were previously known only over rationals or integers, and 68 schemes in integer coefficients that previously required fractions. All tools and discovered schemes are made publicly available to enable reproducible research.

Fine-tuning pre-trained models has emerged as a powerful technique in numerous domains, owing to its ability to leverage enormous pre-existing knowledge and achieve remarkable performance on downstream tasks. However, updating the parameters of entire networks is computationally intensive. Although state-of-the-art parameter-efficient transfer learning (PETL) methods significantly reduce the trainable parameters and storage demand, almost all of them still need to back-propagate the gradients through large pre-trained networks. This memory-extensive characteristic extremely limits the applicability of PETL methods in real-world scenarios. To this end, we propose a new memory-efficient PETL strategy, dubbed Universal Parallel Tuning (UniPT). Specifically, we facilitate the transfer process via a lightweight learnable parallel network, which consists of two modules: 1) A parallel interaction module that decouples the inherently sequential connections and processes the intermediate activations detachedly of the pre-trained network. 2) A confidence aggregation module that learns optimal strategies adaptively for integrating cross-layer features. We evaluate UniPT with different backbones (e.g., VSEinfty, CLIP4Clip, Clip-ViL, and MDETR) on five challenging vision-and-language tasks (i.e., image-text retrieval, video-text retrieval, visual question answering, compositional question answering, and visual grounding). Extensive ablations on ten datasets have validated that our UniPT can not only dramatically reduce memory consumption and outperform the best memory-efficient competitor, but also achieve higher performance than existing PETL methods in a low-memory scenario on different architectures. Our code is publicly available at: https://github.com/Paranioar/UniPT.

In the propositional modal (and algebraic) treatment of two-variable first-order logic equality is modelled by a `diagonal' constant, interpreted in square products of universal frames as the identity (also known as the `diagonal') relation. Here we study the decision problem of products of two arbitrary modal logics equipped with such a diagonal. As the presence or absence of equality in two-variable first-order logic does not influence the complexity of its satisfiability problem, one might expect that adding a diagonal to product logics in general is similarly harmless. We show that this is far from being the case, and there can be quite a big jump in complexity, even from decidable to the highly undecidable. Our undecidable logics can also be viewed as new fragments of first- order logic where adding equality changes a decidable fragment to undecidable. We prove our results by a novel application of counter machine problems. While our formalism apparently cannot force reliable counter machine computations directly, the presence of a unique diagonal in the models makes it possible to encode both lossy and insertion-error computations, for the same sequence of instructions. We show that, given such a pair of faulty computations, it is then possible to reconstruct a reliable run from them.

Optics and lenses are abstract categorical gadgets that model systems with bidirectional data flow. In this paper we observe that the denotational definition of optics - identifying two optics as equivalent by observing their behaviour from the outside - is not suitable for operational, software oriented approaches where optics are not merely observed, but built with their internal setups in mind. We identify operational differences between denotationally isomorphic categories of cartesian optics and lenses: their different composition rule and corresponding space-time tradeoffs, positioning them at two opposite ends of a spectrum. With these motivations we lift the existing categorical constructions and their relationships to the 2-categorical level, showing that the relevant operational concerns become visible. We define the 2-category 2-Optic(C) whose 2-cells explicitly track optics' internal configuration. We show that the 1-category Optic(C) arises by locally quotienting out the connected components of this 2-category. We show that the embedding of lenses into cartesian optics gets weakened from a functor to an oplax functor whose oplaxator now detects the different composition rule. We determine the difficulties in showing this functor forms a part of an adjunction in any of the standard 2-categories. We establish a conjecture that the well-known isomorphism between cartesian lenses and optics arises out of the lax 2-adjunction between their double-categorical counterparts. In addition to presenting new research, this paper is also meant to be an accessible introduction to the topic.

Chain-of-thought (CoT) outputs let us read a model's step-by-step reasoning. Since any long, serial reasoning process must pass through this textual trace, the quality of the CoT is a direct window into what the model is thinking. This visibility could help us spot unsafe or misaligned behavior (monitorability), but only if the CoT is transparent about its internal reasoning (faithfulness). Fully measuring faithfulness is difficult, so researchers often focus on examining the CoT in cases where the model changes its answer after adding a cue to the input. This proxy finds some instances of unfaithfulness but loses information when the model maintains its answer, and does not investigate aspects of reasoning not tied to the cue. We extend these results to a more holistic sense of monitorability by introducing verbosity: whether the CoT lists every factor needed to solve the task. We combine faithfulness and verbosity into a single monitorability score that shows how well the CoT serves as the model's external `working memory', a property that many safety schemes based on CoT monitoring depend on. We evaluate instruction-tuned and reasoning models on BBH, GPQA, and MMLU. Our results show that models can appear faithful yet remain hard to monitor when they leave out key factors, and that monitorability differs sharply across model families. We release our evaluation code using the Inspect library to support reproducible future work.

Despite significant advancements, current large language models (LLMs) and vision-language models (LVLMs) continue to struggle with complex, multi-step, cross-modal common sense reasoning tasks, often exhibiting a lack of "deliberative thinking." They tend to rely on superficial associations rather than deep, chained inference, particularly when integrating visual information with abstract concepts. To address this, we propose the Coherent Multimodal Reasoning Framework (CMRF), a novel approach that enhances LVLMs' common sense reasoning capabilities through an iterative, self-evaluating inference mechanism. CMRF mimics human problem-solving by decomposing complex queries, generating step-by-step inferences, and self-correcting errors. Our framework integrates three key modules: a Reasoning Decomposition Unit (RDU) for breaking down problems into sub-questions, a Contextual Inference Engine (CIE) for contextual inference, and a Coherence Assessment Module (CAM) for evaluating logical consistency and confidence. Coupled with an Adaptive Iterative Refinement strategy, CMRF systematically refines its reasoning paths. Built upon LLaVA-1.6-34B and trained on a novel Multimodal Daily Activity Reasoning (MDAR) dataset, CMRF achieves state-of-the-art performance among open-source LVLMs on challenging benchmarks like VCR, A-OKVQA, and DailyLife-MRC. It attains an average accuracy of 69.4%, surpassing the best open-source baseline by +2.4 percentage points, with particular strength in complex reasoning scenarios. Extensive ablation studies and human evaluations confirm the critical contributions of each module and the effectiveness of iterative refinement in fostering more coherent and accurate reasoning.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as mathematical models of contextuality in classical and quantum settings. Each information structure can be regarded as a ringed site with trivial topology; the structure ring is generated by the observables themselves and its multiplication corresponds to joint measurement. We extend Baudot and Bennequin's definition of information cohomology to this setting, as a derived functor in the category of modules over the structure ring, and show explicitly that the bar construction gives a projective resolution in that category, recovering in this way the cochain complexes previously considered in the literature. Finally, we study the particular case of a one-parameter family of coefficients made of functions of probability distributions. The only 1-cocycles are Shannon entropy or Tsallis alpha-entropy, depending on the value of the parameter.

Let V be a highest weight module over a Kac-Moody algebra g, and let conv V denote the convex hull of its weights. We determine the combinatorial isomorphism type of conv V, i.e. we completely classify the faces and their inclusions. In the special case where g is semisimple, this brings closure to a question studied by Cellini-Marietti [IMRN 2015] for the adjoint representation, and by Khare [J. Algebra 2016; Trans. Amer. Math. Soc. 2017] for most modules. The determination of faces of finite-dimensional modules up to the Weyl group action and some of their inclusions also appears in previous work of Satake [Ann. of Math. 1960], Borel-Tits [IHES Publ. Math. 1965], Vinberg [Izv. Akad. Nauk 1990], and Casselman [Austral. Math. Soc. 1997]. For any subset of the simple roots, we introduce a remarkable convex cone which we call the universal Weyl polyhedron, which controls the convex hulls of all modules parabolically induced from the corresponding Levi factor. Namely, the combinatorial isomorphism type of the cone stores the classification of faces for all such highest weight modules, as well as how faces degenerate as the highest weight gets increasingly singular. To our knowledge, this cone is new in finite and infinite type. We further answer a question of Michel Brion, by showing that the localization of conv V along a face is always the convex hull of the weights of a parabolically induced module. Finally, as we determine the inclusion relations between faces representation-theoretically from the set of weights, without recourse to convexity, we answer a similar question for highest weight modules over symmetrizable quantum groups.

Recently, remarkable progress has been made in Unified Multimodal Models (UMMs), which integrate vision-language generation and understanding capabilities within a single framework. However, a significant gap exists where a model's strong visual understanding often fails to transfer to its visual generation. A model might correctly understand an image based on user instructions, yet be unable to generate a faithful image from text prompts. This phenomenon directly raises a compelling question: Can a model achieve self-improvement by using its understanding module to reward its generation module? To bridge this gap and achieve self-improvement, we introduce SRUM, a self-rewarding post-training framework that can be directly applied to existing UMMs of various designs. SRUM creates a feedback loop where the model's own understanding module acts as an internal ``evaluator'', providing corrective signals to improve its generation module, without requiring additional human-labeled data. To ensure this feedback is comprehensive, we designed a global-local dual reward system. To tackle the inherent structural complexity of images, this system offers multi-scale guidance: a global reward ensures the correctness of the overall visual semantics and layout, while a local reward refines fine-grained, object-level fidelity. SRUM leads to powerful capabilities and shows strong generalization, boosting performance on T2I-CompBench from 82.18 to 88.37 and on T2I-ReasonBench from 43.82 to 46.75. Overall, our work establishes a powerful new paradigm for enabling a UMMs' understanding module to guide and enhance its own generation via self-rewarding.

Qualitative research faces a critical reliability challenge: traditional inter-rater agreement methods require multiple human coders, are time-intensive, and often yield moderate consistency. We present a multi-perspective validation framework for LLM-based thematic analysis that combines ensemble validation with dual reliability metrics: Cohen's Kappa (κ) for inter-rater agreement and cosine similarity for semantic consistency. Our framework enables configurable analysis parameters (1-6 seeds, temperature 0.0-2.0), supports custom prompt structures with variable substitution, and provides consensus theme extraction across any JSON format. As proof-of-concept, we evaluate three leading LLMs (Gemini 2.5 Pro, GPT-4o, Claude 3.5 Sonnet) on a psychedelic art therapy interview transcript, conducting six independent runs per model. Results demonstrate Gemini achieves highest reliability (κ= 0.907, cosine=95.3%), followed by GPT-4o (κ= 0.853, cosine=92.6%) and Claude (κ= 0.842, cosine=92.1%). All three models achieve a high agreement (κ> 0.80), validating the multi-run ensemble approach. The framework successfully extracts consensus themes across runs, with Gemini identifying 6 consensus themes (50-83% consistency), GPT-4o identifying 5 themes, and Claude 4 themes. Our open-source implementation provides researchers with transparent reliability metrics, flexible configuration, and structure-agnostic consensus extraction, establishing methodological foundations for reliable AI-assisted qualitative research.

Recent advancements in multimodal large language models (MLLMs) have demonstrated exceptional performance in multimodal perception and understanding. However, leading open-source MLLMs exhibit significant limitations in complex and structured reasoning, particularly in tasks requiring deep reasoning for decision-making and problem-solving. In this work, we present Corvid, an MLLM with enhanced chain-of-thought (CoT) reasoning capabilities. Architecturally, Corvid incorporates a hybrid vision encoder for informative visual representation and a meticulously designed connector (GateMixer) to facilitate cross-modal alignment. To enhance Corvid's CoT reasoning capabilities, we introduce MCoT-Instruct-287K, a high-quality multimodal CoT instruction-following dataset, refined and standardized from diverse public reasoning sources. Leveraging this dataset, we fine-tune Corvid with a two-stage CoT-formatted training approach to progressively enhance its step-by-step reasoning abilities. Furthermore, we propose an effective inference-time scaling strategy that enables Corvid to mitigate over-reasoning and under-reasoning through self-verification. Extensive experiments demonstrate that Corvid outperforms existing o1-like MLLMs and state-of-the-art MLLMs with similar parameter scales, with notable strengths in mathematical reasoning and science problem-solving. Project page: https://mm-vl.github.io/corvid.

We define the bicategory of Graph Convolutional Neural Networks GCNN_n for an arbitrary graph with n nodes. We show it can be factored through the already existing categorical constructions for deep learning called Para and Lens with the base category set to the CoKleisli category of the product comonad. We prove that there exists an injective-on-objects, faithful 2-functor GCNN_n to Para(CoKl(R^{n times n} times -)). We show that this construction allows us to treat the adjacency matrix of a GCNN as a global parameter instead of a a local, layer-wise one. This gives us a high-level categorical characterisation of a particular kind of inductive bias GCNNs possess. Lastly, we hypothesize about possible generalisations of GCNNs to general message-passing graph neural networks, connections to equivariant learning, and the (lack of) functoriality of activation functions.

Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps, mimicking human logic and reducing errors. However, complex tasks with vast solution spaces and vague constraints often exceed the capacity of a single reasoning chain. Inspired by Minimal Free Resolution (MFR) in commutative algebra and algebraic geometry, we propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths. SoT captures deeper logical dependencies, enabling more robust and structured problem-solving. MFR decomposes a module into a sequence of free modules with minimal rank, providing a structured analytical approach to complex systems. This method introduces the concepts of "Module", "Betti numbers","Freeness", "Mapping", "Exactness" and "Minimality", enabling the systematic decomposition of the original complex problem into logically complete minimal subproblems while preserving key problem features and reducing reasoning length. We tested SoT across diverse datasets (e.g., GSM8K, MATH) and models (e.g., GPT-4o-mini, Qwen2.5), achieving inference accuracy that matches or surpasses mainstream CoTs standards. Additionally, by aligning the sampling process with algebraic constraints, our approach enhances the scalability of inference time in LLMs, ensuring both transparent reasoning and high performance. Our code will be publicly available at https://github.com/dlMARiA/Syzygy-of-thoughts.

Chain-of-Thought (CoT) reasoning has proven effective in enhancing large language models by encouraging step-by-step intermediate reasoning, and recent advances have extended this paradigm to Multimodal Large Language Models (MLLMs). In the medical domain, where diagnostic decisions depend on nuanced visual cues and sequential reasoning, CoT aligns naturally with clinical thinking processes. However, Current benchmarks for medical image understanding generally focus on the final answer while ignoring the reasoning path. An opaque process lacks reliable bases for judgment, making it difficult to assist doctors in diagnosis. To address this gap, we introduce a new M3CoTBench benchmark specifically designed to evaluate the correctness, efficiency, impact, and consistency of CoT reasoning in medical image understanding. M3CoTBench features 1) a diverse, multi-level difficulty dataset covering 24 examination types, 2) 13 varying-difficulty tasks, 3) a suite of CoT-specific evaluation metrics (correctness, efficiency, impact, and consistency) tailored to clinical reasoning, and 4) a performance analysis of multiple MLLMs. M3CoTBench systematically evaluates CoT reasoning across diverse medical imaging tasks, revealing current limitations of MLLMs in generating reliable and clinically interpretable reasoning, and aims to foster the development of transparent, trustworthy, and diagnostically accurate AI systems for healthcare. Project page at https://juntaojianggavin.github.io/projects/M3CoTBench/.

In recent years, integrating multimodal understanding and generation into a single unified model has emerged as a promising paradigm. While this approach achieves strong results in text-to-image (T2I) generation, it still struggles with precise image editing. We attribute this limitation to an imbalanced division of responsibilities. The understanding module primarily functions as a translator that encodes user instructions into semantic conditions, while the generation module must simultaneously act as designer and painter, inferring the original layout, identifying the target editing region, and rendering the new content. This imbalance is counterintuitive because the understanding module is typically trained with several times more data on complex reasoning tasks than the generation module. To address this issue, we introduce Draw-In-Mind (DIM), a dataset comprising two complementary subsets: (i) DIM-T2I, containing 14M long-context image-text pairs to enhance complex instruction comprehension; and (ii) DIM-Edit, consisting of 233K chain-of-thought imaginations generated by GPT-4o, serving as explicit design blueprints for image edits. We connect a frozen Qwen2.5-VL-3B with a trainable SANA1.5-1.6B via a lightweight two-layer MLP, and train it on the proposed DIM dataset, resulting in DIM-4.6B-T2I/Edit. Despite its modest parameter scale, DIM-4.6B-Edit achieves SOTA or competitive performance on the ImgEdit and GEdit-Bench benchmarks, outperforming much larger models such as UniWorld-V1 and Step1X-Edit. These findings demonstrate that explicitly assigning the design responsibility to the understanding module provides significant benefits for image editing. Our dataset and models will be available at https://github.com/showlab/DIM.

Large language models (LLMs) deployed for logical reasoning in knowledge-intensive domains exhibit a subtle but critical failure: coherence can be vacuously achieved through systematic abstention. A model that withholds commitment to either entailment or refutation satisfies negation consistency while providing no utility. We introduce Coherence Under Commitment (CUC), a dual-query evaluation paradigm that jointly measures consistency and decisiveness. CUC contributes three innovations: (1) a commitment score c(φ) = p(φ) + p(lnotφ) quantifying probability mass allocated to decisive outcomes; (2) a deterministic elicitation protocol via normalized YES/NO log probabilities, eliminating sampling variance; and (3) a 3-way decision framework (True/False/Uncertain) operationalizing the coherence-commitment trade-off into metrics. Experiments on four open-weight LLMs (1B-3B) across 204 FOLIO examples expose a sharp frontier. Qwen2.5-3B achieves near-zero contradiction (E[v_{neg}]{=}0.025) but only 7.4% coverage, while TinyLlama-1.1B reaches 79.4% coverage with violations on every example. Coherence-only evaluation would rank the abstaining model first; CUC exposes this as vacuous, and the frontier generalizes to LogiQA~v2 (ρ{=}0.97). We argue that evaluation must report both coherence and non-vacuous commitment and release a toolkit for standardized assessment.

We present GSM-MC, a multiple-choice (MC) dataset constructed by collecting answers and incorrect predictions on GSM8K from 60 open-source models. Through extensive experiments, we show that LLMs' performance on the MC version of this popular benchmark is strongly correlated with their performance on the original version and is quite robust to distractor choices and option orders, while the evaluation time is reduced by a factor of up to 30. Following similar procedures, we introduce MATH-MC, constructed from MATH, and PythonIO, a new program reasoning MC dataset constructed from HumanEval and MBPP. Experimental results indicate that LLMs' performance on these MC benchmarks leaves much room for improvement. Our data and code are available at https://github.com/Geralt-Targaryen/MC-Evaluation.

A common assumption holds that enough observational and interventional data, given to a strong enough predictor, suffices. We report a failure mode that contradicts it. Across hundreds of structural causal models, on identified quantities a strong predictor and a Bayesian baseline both succeed, but on unidentified quantities (the couplings between counterfactual worlds) the predictor collapses to a point, on 28% of models to one no valid model can produce, while the truth is an admissible interval more data never narrows. The gap is structural: prediction cannot represent uncertainty over counterfactual couplings. We cast a world model as a single positive semidefinite coupling kernel K(T,T') over admissible worlds, whose diagonal is the ordinary posterior (what a predictor recovers) and whose off-diagonal is the cross-world coupling it cannot, which every counterfactual reads. The paper is the theory of that off-diagonal. It is real: two states with identical posteriors differ on a cross-world query, and the off-diagonal is the coupling that fixes counterfactuals. It can be bounded: positive semidefiniteness is partial-identifying information the marginals lack, and enforcing it bounds counterfactuals in polynomial time where the exact response-type program is intractable. Logical structure sharpens it: ontology axioms tighten the bound by up to a third, propagating to couplings they never touch. It can be acquired: targeted scars, constraints learned from encountered infeasibilities, close the gap several times faster than untargeted ones. Its full reconstruction is approximate counting of the admissible worlds, tractable below the Sly-Sun threshold and inapproximable above; we do not claim to beat the worst case.

In order to avoid well-know paradoxes associated with self-referential definitions, higher-order dependent type theories stratify the theory using a countably infinite hierarchy of universes (also known as sorts), Type_0 : Type_1 : cdots . Such type systems are called cumulative if for any type A we have that A : Type_{i} implies A : Type_{i+1}. The predicative calculus of inductive constructions (pCIC) which forms the basis of the Coq proof assistant, is one such system. In this paper we present and establish the soundness of the predicative calculus of cumulative inductive constructions (pCuIC) which extends the cumulativity relation to inductive types.

The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to embed computational effects, evaluation strategies, and control flow operations. The first instalment modelled sequential higher-order computation with global store, input/output, probabilities, and non-determinism, and embedded both the call-by-name and call-by-value lambda-calculus, as well as Moggi's computational metalanguage and Levy's call-by-push-value. The present paper extends the calculus from sequential to branching and looping control flow. This allows the faithful embedding of a minimal but complete imperative language, including conditionals, exception handling, and iteration, as well as constants and algebraic data types. The calculus is defined through a simple operational semantics, extending the (simplified) Krivine machine for the lambda-calculus with multiple operand stacks to model effects and a continuation stack to model sequential, branching, and looping computation. It features a confluent reduction relation and a system of simple types that guarantees termination of the machine and strong normalization of reduction (in the absence of iteration). These properties carry over to the embedded imperative language, providing a unified functional-imperative model of computation that supports simple types, a direct and intuitive operational semantics, and a confluent reduction semantics.

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as process reward models (PRMs) or self-consistency operate as opaque boxes and do not provide checkable evidence for their judgments, possibly limiting their effectiveness. To address this issue, we draw inspiration from the idea that "the gold standard for supporting a mathematical claim is to provide a proof". We propose a retrospective, step-aware formal verification framework Safe. Rather than assigning arbitrary scores, we strive to articulate mathematical claims in formal mathematical language Lean 4 at each reasoning step and provide formal proofs to identify hallucinations. We evaluate our framework Safe across multiple language models and various mathematical datasets, demonstrating a significant performance improvement while offering interpretable and verifiable evidence. We also propose FormalStep as a benchmark for step correctness theorem proving with 30,809 formal statements. To the best of our knowledge, our work represents the first endeavor to utilize formal mathematical language Lean 4 for verifying natural language content generated by LLMs, aligning with the reason why formal mathematical languages were created in the first place: to provide a robust foundation for hallucination-prone human-written proofs.

Recent works have shown that Large Language Models (LLMs) could empower traditional neuro-symbolic models via programming capabilities to translate language into module descriptions, thus achieving strong visual reasoning results while maintaining the model's transparency and efficiency. However, these models usually exhaustively generate the entire code snippet given each new instance of a task, which is extremely ineffective. We propose generative neuro-symbolic visual reasoning by growing and reusing modules. Specifically, our model consists of three unique stages, module initialization, module generation, and module execution. First, given a vision-language task, we adopt LLMs to examine whether we could reuse and grow over established modules to handle this new task. If not, we initialize a new module needed by the task and specify the inputs and outputs of this new module. After that, the new module is created by querying LLMs to generate corresponding code snippets that match the requirements. In order to get a better sense of the new module's ability, we treat few-shot training examples as test cases to see if our new module could pass these cases. If yes, the new module is added to the module library for future reuse. Finally, we evaluate the performance of our model on the testing set by executing the parsed programs with the newly made visual modules to get the results. We find the proposed model possesses several advantages. First, it performs competitively on standard tasks like visual question answering and referring expression comprehension; Second, the modules learned from one task can be seamlessly transferred to new tasks; Last but not least, it is able to adapt to new visual reasoning tasks by observing a few training examples and reusing modules.

We present Turn, a compiled, actor-based programming language -- statically typed for schema inference, dynamically typed at the value level -- for agentic software: programs that reason and act autonomously by delegating inference to large language models (LLMs). Existing approaches augment general-purpose languages with frameworks, encoding critical invariants (bounded context, typed inference output, credential isolation, durable state) as application-level conventions rather than language guarantees. Turn introduces five language-level constructs that address this gap. Cognitive Type Safety makes LLM inference a typed primitive: the compiler generates a JSON Schema from a struct definition and the VM validates model output before binding. The confidence operator enables deterministic control flow gated on model certainty. Turn's actor-based process model, derived from Erlang, gives each agent an isolated context window, persistent memory, and mailbox. A capability-based identity system returns opaque, unforgeable handles from the VM host, ensuring raw credentials never enter agent memory. Finally, compile-time schema absorption (use schema::<protocol>) synthesizes typed API bindings from external specifications at compile time; the openapi adapter is shipped with graphql, fhir, and mcp in active development. We describe the language design, type rules, schema semantics, and a Rust-based bytecode VM, and evaluate Turn against representative agentic workloads. Turn is open source at https://github.com/ekizito96/Turn.

According to the Test-Time Scaling, the integration of External Slow-Thinking with the Verify mechanism has been demonstrated to enhance multi-round reasoning in large language models (LLMs). However, in the multimodal (MM) domain, there is still a lack of a strong MM-Verifier. In this paper, we introduce MM-Verifier and MM-Reasoner to enhance multimodal reasoning through longer inference and more robust verification. First, we propose a two-step MM verification data synthesis method, which combines a simulation-based tree search with verification and uses rejection sampling to generate high-quality Chain-of-Thought (COT) data. This data is then used to fine-tune the verification model, MM-Verifier. Additionally, we present a more efficient method for synthesizing MMCOT data, bridging the gap between text-based and multimodal reasoning. The synthesized data is used to fine-tune MM-Reasoner. Our MM-Verifier outperforms all larger models on the MathCheck, MathVista, and MathVerse benchmarks. Moreover, MM-Reasoner demonstrates strong effectiveness and scalability, with performance improving as data size increases. Finally, our approach achieves strong performance when combining MM-Reasoner and MM-Verifier, reaching an accuracy of 65.3 on MathVista, surpassing GPT-4o (63.8) with 12 rollouts.

Large Multimodal Models (LMMs) are increasingly applied to scientific research, yet it remains unclear whether they can reliably understand and reason over the multimodal complexity of papers. A central challenge lies in detecting and resolving inconsistencies across text, figures, tables, and equations, issues that are often subtle, domain-specific, and ultimately undermine clarity, reproducibility, and trust. Existing benchmarks overlook this issue, either isolating single modalities or relying on synthetic errors that fail to capture real-world complexity. We introduce PRISMM-Bench (Peer-Review-sourced Inconsistency Set for Multimodal Models), the first benchmark grounded in real reviewer-flagged inconsistencies in scientific papers. Through a multi-stage pipeline of review mining, LLM-assisted filtering and human verification, we curate 262 inconsistencies from 242 papers. Based on this set, we design three tasks, namely inconsistency identification, remedy and pair matching, which assess a model's capacity to detect, correct, and reason over inconsistencies across different modalities. Furthermore, to address the notorious problem of choice-only shortcuts in multiple-choice evaluation, where models exploit answer patterns without truly understanding the question, we further introduce structured JSON-based answer representations that minimize linguistic biases by reducing reliance on superficial stylistic cues. We benchmark 21 leading LMMs, including large open-weight models (GLM-4.5V 106B, InternVL3 78B) and proprietary models (Gemini 2.5 Pro, GPT-5 with high reasoning). Results reveal strikingly low performance (26.1-54.2%), underscoring the challenge of multimodal scientific reasoning and motivating progress towards trustworthy scientific assistants.

Any-to-any generative models aim to enable seamless interpretation and generation across multiple modalities within a unified framework, yet their ability to preserve relationships across modalities remains uncertain. Do unified models truly achieve cross-modal coherence, or is this coherence merely perceived? To explore this, we introduce ACON, a dataset of 1,000 images (500 newly contributed) paired with captions, editing instructions, and Q&A pairs to evaluate cross-modal transfers rigorously. Using three consistency criteria-cyclic consistency, forward equivariance, and conjugated equivariance-our experiments reveal that any-to-any models do not consistently demonstrate greater cross-modal consistency than specialized models in pointwise evaluations such as cyclic consistency. However, equivariance evaluations uncover weak but observable consistency through structured analyses of the intermediate latent space enabled by multiple editing operations. We release our code and data at https://github.com/JiwanChung/ACON.

This paper explores the intersection of identity, individuality, and reality through competing frameworks, including classical metaphysics, quantum mechanics, and computational theories. Traditional metaphysical notions of fixed identity are challenged by advancements in cloning, teletransportation, and digital replication, which reveal the fluid and relational nature of individuality. Quantum mechanics further complicates these notions, emphasizing the indistinguishability and contextuality of fundamental particles. Computational approaches, such as the Ruliad and Constructor Theory, offer expansive views of emergent realities but often lack practical constraints for observer relevance. Algorithmic idealism is introduced as a unifying framework, proposing that reality is an emergent construct governed by computational rules prioritizing coherence, sufficiency, and observer-dependent experiences. By redefining identity as an informational construct and reality as a process shaped by algorithmic transitions, algorithmic idealism resolves foundational paradoxes and offers a superior lens for understanding existence in an increasingly digital and interconnected world. The framework bridges gaps between competing theories, providing a coherent and pragmatic model for addressing ethical, metaphysical, and technological challenges.

Chain-of-thought (CoT) reasoning has been proposed as a transparency mechanism for large language models in safety-critical deployments, yet its effectiveness depends on faithfulness (whether models accurately verbalize the factors that actually influence their outputs), a property that prior evaluations have examined in only two proprietary models, finding acknowledgment rates as low as 25% for Claude 3.7 Sonnet and 39% for DeepSeek-R1. To extend this evaluation across the open-weight ecosystem, this study tests 12 open-weight reasoning models spanning 9 architectural families (7B-685B parameters) on 498 multiple-choice questions from MMLU and GPQA Diamond, injecting six categories of reasoning hints (sycophancy, consistency, visual pattern, metadata, grader hacking, and unethical information) and measuring the rate at which models acknowledge hint influence in their CoT when hints successfully alter answers. Across 41,832 inference runs, overall faithfulness rates range from 39.7% (Seed-1.6-Flash) to 89.9% (DeepSeek-V3.2-Speciale) across model families, with consistency hints (35.5%) and sycophancy hints (53.9%) exhibiting the lowest acknowledgment rates. Training methodology and model family predict faithfulness more strongly than parameter count, and keyword-based analysis reveals a striking gap between thinking-token acknowledgment (approximately 87.5%) and answer-text acknowledgment (approximately 28.6%), suggesting that models internally recognize hint influence but systematically suppress this acknowledgment in their outputs. These findings carry direct implications for the viability of CoT monitoring as a safety mechanism and suggest that faithfulness is not a fixed property of reasoning models but varies systematically with architecture, training method, and the nature of the influencing cue.

Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet they often rely on single-paradigm reasoning that limits their effectiveness across diverse tasks. In this paper, we introduce Chain-of-Reasoning (CoR), a novel unified framework that integrates multiple reasoning paradigms--Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR)--to enable synergistic collaboration. CoR generates multiple potential answers using different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy that allows models to progressively master these paradigms, culminating in the development of CoR-Math-7B. Experimental results demonstrate that CoR-Math-7B significantly outperforms current SOTA models, achieving up to a 41.0% absolute improvement over GPT-4 in theorem proving tasks and a 7.9% improvement over RL-based methods in arithmetic tasks. These results showcase the enhanced mathematical comprehensive ability of our model, achieving significant performance gains on specific tasks and enabling zero-shot generalization across tasks.

Compositional visual reasoning methods, which translate a complex query into a structured composition of feasible visual tasks, have exhibited a strong potential in complicated multi-modal tasks. Empowered by recent advances in large language models (LLMs), this multi-modal challenge has been brought to a new stage by treating LLMs as few-shot/zero-shot planners, i.e., vision-language (VL) programming. Such methods, despite their numerous merits, suffer from challenges due to LLM planning mistakes or inaccuracy of visual execution modules, lagging behind the non-compositional models. In this work, we devise a "plug-and-play" method, ExoViP, to correct errors in both the planning and execution stages through introspective verification. We employ verification modules as "exoskeletons" to enhance current VL programming schemes. Specifically, our proposed verification module utilizes a mixture of three sub-verifiers to validate predictions after each reasoning step, subsequently calibrating the visual module predictions and refining the reasoning trace planned by LLMs. Experimental results on two representative VL programming methods showcase consistent improvements on five compositional reasoning tasks on standard benchmarks. In light of this, we believe that ExoViP can foster better performance and generalization on open-domain multi-modal challenges.

Recent advancements in Large Multimodal Models (LMMs) have shown promising results in mathematical reasoning within visual contexts, with models approaching human-level performance on existing benchmarks such as MathVista. However, we observe significant limitations in the diversity of questions and breadth of subjects covered by these benchmarks. To address this issue, we present the MATH-Vision (MATH-V) dataset, a meticulously curated collection of 3,040 high-quality mathematical problems with visual contexts sourced from real math competitions. Spanning 16 distinct mathematical disciplines and graded across 5 levels of difficulty, our dataset provides a comprehensive and diverse set of challenges for evaluating the mathematical reasoning abilities of LMMs. Through extensive experimentation, we unveil a notable performance gap between current LMMs and human performance on MATH-V, underscoring the imperative for further advancements in LMMs. Moreover, our detailed categorization allows for a thorough error analysis of LMMs, offering valuable insights to guide future research and development. The project is available at https://mathvision-cuhk.github.io

Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the relativity of causal knowledge, which posits structural causal models (SCMs) are inherently imperfect, subjective representations embedded within networks of relationships. By leveraging category theory, we arrange SCMs into a functor category and show that their observational and interventional probability measures naturally form convex structures. This result allows us to encode non-intervened SCMs with convex spaces of probability measures. Next, using sheaf theory, we construct the network sheaf and cosheaf of causal knowledge. These structures enable the transfer of causal knowledge across the network while incorporating interventional consistency and the perspective of the subjects, ultimately leading to the formal, mathematical definition of relative causal knowledge.

For any {rm E}-rigid presentation e, we construct an orthogonal projection functor to {rm rep}(e^perp) left adjoint to the natural embedding. We establish a bijection between presentations in {rm rep}(e^perp) and presentations compatible with e. For quivers with potentials, we show that {rm rep}(e^perp) forms a module category of another quiver with potential. We derive mutation formulas for the delta-vectors of positive and negative complements and the dimension vectors of simple modules in {rm rep}(e^perp), enabling an algorithm to find the projected quiver with potential. Additionally, we introduce a modified projection for quivers with potentials that preserves general presentations. For applications to cluster algebras, we establish a connection to the stabilization functors.

Comparative settings (e.g. pairwise choice, listwise ranking) have been adopted by a wide range of subjective studies for image quality assessment (IQA), as it inherently standardizes the evaluation criteria across different observers and offer more clear-cut responses. In this work, we extend the edge of emerging large multi-modality models (LMMs) to further advance visual quality comparison into open-ended settings, that 1) can respond to open-range questions on quality comparison; 2) can provide detailed reasonings beyond direct answers. To this end, we propose the Co-Instruct. To train this first-of-its-kind open-source open-ended visual quality comparer, we collect the Co-Instruct-562K dataset, from two sources: (a) LMM-merged single image quality description, (b) GPT-4V "teacher" responses on unlabeled data. Furthermore, to better evaluate this setting, we propose the MICBench, the first benchmark on multi-image comparison for LMMs. We demonstrate that Co-Instruct not only achieves 30% higher superior accuracy than state-of-the-art open-source LMMs, but also outperforms GPT-4V (its teacher), on both existing related benchmarks and the proposed MICBench. Our model is published at https://huggingface.co/q-future/co-instruct.

Schema-guided reasoning pipelines ask LLMs to produce explicit intermediate structures -- rubrics, checklists, verification queries -- before committing to a final decision. But do these structures causally determine the output, or merely accompany it? We introduce a causal evaluation protocol that makes this directly measurable: by selecting tasks where a deterministic function maps intermediate structures to decisions, every controlled edit implies a unique correct output. Across eight models and three benchmarks, models appear self-consistent with their own intermediate structures but fail to update predictions after intervention in up to 60% of cases -- revealing that apparent faithfulness is fragile once the intermediate structure changes. When derivation of the final decision from the structure is delegated to an external tool, this fragility largely disappears; however, prompts which ask to prioritize the intermediate structure over the original input do not materially close the gap. Overall, intermediate structures in schema-guided pipelines function as influential context rather than stable causal mediators.

Neurosymbolic approaches integrating large language models with formal reasoning have recently achieved human-level performance on mathematics competition problems in algebra, geometry and number theory. In comparison, combinatorics remains a challenging domain, characterized by a lack of appropriate benchmarks and theorem libraries. To address this gap, we introduce CombiBench, a comprehensive benchmark comprising 100 combinatorial problems, each formalized in Lean~4 and paired with its corresponding informal statement. The problem set covers a wide spectrum of difficulty levels, ranging from middle school to IMO and university level, and span over ten combinatorial topics. CombiBench is suitable for testing IMO solving capabilities since it includes all IMO combinatorial problems since 2000 (except IMO 2004 P3 as its statement contain an images). Furthermore, we provide a comprehensive and standardized evaluation framework, dubbed Fine-Eval (for Fill-in-the-blank in Lean Evaluation), for formal mathematics. It accommodates not only proof-based problems but also, for the first time, the evaluation of fill-in-the-blank questions. Using Fine-Eval as the evaluation method and Kimina Lean Server as the backend, we benchmark several LLMs on CombiBench and observe that their capabilities for formally solving combinatorial problems remain limited. Among all models tested (none of which has been trained for this particular task), Kimina-Prover attains the best results, solving 7 problems (out of 100) under both ``with solution'' and ``without solution'' scenarios. We open source the benchmark dataset alongside with the code of the proposed evaluation method at https://github.com/MoonshotAI/CombiBench/.

Transfer learning has recently become the dominant paradigm of machine learning. Pre-trained models fine-tuned for downstream tasks achieve better performance with fewer labelled examples. Nonetheless, it remains unclear how to develop models that specialise towards multiple tasks without incurring negative interference and that generalise systematically to non-identically distributed tasks. Modular deep learning has emerged as a promising solution to these challenges. In this framework, units of computation are often implemented as autonomous parameter-efficient modules. Information is conditionally routed to a subset of modules and subsequently aggregated. These properties enable positive transfer and systematic generalisation by separating computation from routing and updating modules locally. We offer a survey of modular architectures, providing a unified view over several threads of research that evolved independently in the scientific literature. Moreover, we explore various additional purposes of modularity, including scaling language models, causal inference, programme induction, and planning in reinforcement learning. Finally, we report various concrete applications where modularity has been successfully deployed such as cross-lingual and cross-modal knowledge transfer. Related talks and projects to this survey, are available at https://www.modulardeeplearning.com/.

Multimodal large language models (MLLMs) have shown promising capabilities in reasoning tasks, yet still struggle with complex problems requiring explicit self-reflection and self-correction, especially compared to their unimodal text-based counterparts. Existing reflection methods are simplistic and struggle to generate meaningful and instructive feedback, as the reasoning ability and knowledge limits of pre-trained models are largely fixed during initial training. To overcome these challenges, we propose Multimodal Self-Reflection enhanced reasoning with Group Relative Policy Optimization (SRPO), a two-stage reflection-aware reinforcement learning (RL) framework explicitly designed to enhance multimodal LLM reasoning. In the first stage, we construct a high-quality, reflection-focused dataset under the guidance of an advanced MLLM, which generates reflections based on initial responses to help the policy model learn both reasoning and self-reflection. In the second stage, we introduce a novel reward mechanism within the GRPO framework that encourages concise and cognitively meaningful reflection while avoiding redundancy. Extensive experiments across multiple multimodal reasoning benchmarks, including MathVista, MathVision, MathVerse, and MMMU-Pro, using Qwen-2.5-VL-7B and Qwen-2.5-VL-32B demonstrate that SRPO significantly outperforms state-of-the-art models, achieving notable improvements in both reasoning accuracy and reflection quality.

Enhancing the intelligibility and interpretability of machine learning is a crucial task in responding to the demand for Explicability as an AI principle, and in promoting the better social implementation of AI. The aim of our research is to contribute to this improvement by reformulating machine learning models through the lens of category theory, thereby developing a semantic framework for structuring and understanding AI systems. Our categorical modeling in this paper clarifies and formalizes the structural interplay between residuals and parameters in supervised learning. The present paper focuses on the multiple linear regression model, which represents the most basic form of supervised learning. By defining two concrete categories corresponding to parameters and data, along with an adjoint pair of functors between them, we introduce our categorical formulation of supervised learning. We show that the essential structure of this framework is captured by what we call the Gauss-Markov Adjunction. Within this setting, the dual flow of information can be explicitly described as a correspondence between variations in parameters and residuals. The ordinary least squares estimator for the parameters and the minimum residual are related via the preservation of limits by the right adjoint functor. Furthermore, we position this formulation as an instance of extended denotational semantics for supervised learning, and propose applying a semantic perspective developed in theoretical computer science as a formal foundation for Explicability in AI.

Convolution is a broadly useful operation with applications including signal processing, machine learning, probability, optics, polynomial multiplication, and efficient parsing. Usually, however, this operation is understood and implemented in more specialized forms, hiding commonalities and limiting usefulness. This paper formulates convolution in the common algebraic framework of semirings and semimodules and populates that framework with various representation types. One of those types is the grand abstract template and itself generalizes to the free semimodule monad. Other representations serve varied uses and performance trade-offs, with implementations calculated from simple and regular specifications. Of particular interest is Brzozowski's method for regular expression matching. Uncovering the method's essence frees it from syntactic manipulations, while generalizing from boolean to weighted membership (such as multisets and probability distributions) and from sets to n-ary relations. The classic trie data structure then provides an elegant and efficient alternative to syntax. Pleasantly, polynomial arithmetic requires no additional implementation effort, works correctly with a variety of representations, and handles multivariate polynomials and power series with ease. Image convolution also falls out as a special case.

The capability of Unified Multimodal Models (UMMs) to apply world knowledge across diverse tasks remains a critical, unresolved challenge. Existing benchmarks fall short, offering only siloed, single-task evaluations with limited diagnostic power. To bridge this gap, we propose AEGIS (i.e., Assessing Editing, Generation, Interpretation-Understanding for Super-intelligence), a comprehensive multi-task benchmark covering visual understanding, generation, editing, and interleaved generation. AEGIS comprises 1,050 challenging, manually-annotated questions spanning 21 topics (including STEM, humanities, daily life, etc.) and 6 reasoning types. To concretely evaluate the performance of UMMs in world knowledge scope without ambiguous metrics, we further propose Deterministic Checklist-based Evaluation (DCE), a protocol that replaces ambiguous prompt-based scoring with atomic ``Y/N'' judgments, to enhance evaluation reliability. Our extensive experiments reveal that most UMMs exhibit severe world knowledge deficits and that performance degrades significantly with complex reasoning. Additionally, simple plug-in reasoning modules can partially mitigate these vulnerabilities, highlighting a promising direction for future research. These results highlight the importance of world-knowledge-based reasoning as a critical frontier for UMMs.

The evaluation of Large Language Models (LLMs) on mathematical reasoning has largely focused on elementary problems, competition-style questions, or formal theorem proving, leaving graduate-level and computational mathematics relatively underexplored. We introduce CompMath-MCQ, a new benchmark dataset for assessing LLMs on advanced mathematical reasoning in a multiple-choice setting. The dataset consists of 1{,}500 originally authored questions by professors of graduate-level courses, covering topics including Linear Algebra, Numerical Optimization, Vector Calculus, Probability, and Python-based scientific computing. Three option choices are provided for each question, with exactly one of them being correct. To ensure the absence of data leakage, all questions are newly created and not sourced from existing materials. The validity of questions is verified through a procedure based on cross-LLM disagreement, followed by manual expert review. By adopting a multiple-choice format, our dataset enables objective, reproducible, and bias-free evaluation through lm_eval library. Baseline results with state-of-the-art LLMs indicate that advanced computational mathematical reasoning remains a significant challenge. We release CompMath-MCQ at the following link: https://github.com/biancaraimondi/CompMath-MCQ.git

Large Language Models (LLMs) present an intriguing avenue for exploration in the field of formal theorem proving. Nevertheless, their full potential, particularly concerning the mitigation of hallucinations and refinement through prover error messages, remains an area that has yet to be thoroughly investigated. To enhance the effectiveness of LLMs in the field, we introduce the Lyra, a new framework that employs two distinct correction mechanisms: Tool Correction (TC) and Conjecture Correction (CC). To implement Tool Correction in the post-processing of formal proofs, we leverage prior knowledge to utilize predefined prover tools (e.g., Sledgehammer) for guiding the replacement of incorrect tools. Tool Correction significantly contributes to mitigating hallucinations, thereby improving the overall accuracy of the proof. In addition, we introduce Conjecture Correction, an error feedback mechanism designed to interact with prover to refine formal proof conjectures with prover error messages. Compared to the previous refinement framework, the proposed Conjecture Correction refines generation with instruction but does not collect paired (generation, error & refinement) prompts. Our method has achieved state-of-the-art (SOTA) performance on both miniF2F validation (48.0% -> 55.3%) and test (45.5% -> 51.2%). We also present 3 IMO problems solved by Lyra. We believe Tool Correction (post-process for hallucination mitigation) and Conjecture Correction (subgoal adjustment from interaction with environment) could provide a promising avenue for future research in this field.

Extracting causal relationships from observed correlations is a growing area in probabilistic reasoning, originating with the seminal work of Pearl and others from the early 1990s. This paper develops a new, categorically oriented view based on a clear distinction between syntax (string diagrams) and semantics (stochastic matrices), connected via interpretations as structure-preserving functors. A key notion in the identification of causal effects is that of an intervention, whereby a variable is forcefully set to a particular value independent of any prior propensities. We represent the effect of such an intervention as an endofunctor which performs `string diagram surgery' within the syntactic category of string diagrams. This diagram surgery in turn yields a new, interventional distribution via the interpretation functor. While in general there is no way to compute interventional distributions purely from observed data, we show that this is possible in certain special cases using a calculational tool called comb disintegration. We demonstrate the use of this technique on a well-known toy example, where we predict the causal effect of smoking on cancer in the presence of a confounding common cause. After developing this specific example, we show this technique provides simple sufficient conditions for computing interventions which apply to a wide variety of situations considered in the causal inference literature.

Empirical evaluation serves as the primary compass guiding research progress in foundation models. Despite a large body of work focused on training frontier vision-language models (VLMs), approaches to their evaluation remain nascent. To guide their maturation, we propose three desiderata that evaluations should satisfy: (1) faithfulness to the modality and application, (2) discriminability between models of varying quality, and (3) efficiency in compute. Through this lens, we identify critical failure modes that violate faithfulness and discriminability, misrepresenting model capabilities: (i) multiple-choice formats reward guessing, poorly reflect downstream use cases, and saturate early as models improve; (ii) blindly solvable questions, which can be answered without images, constitute up to 70% of some evaluations; and (iii) mislabeled or ambiguous samples compromise up to 42% of examples in certain datasets. Regarding efficiency, the computational burden of evaluating frontier models has become prohibitive: by some accounts, nearly 20% of development compute is devoted to evaluation alone. Rather than discarding existing benchmarks, we curate them via transformation and filtering to maximize fidelity and discriminability. We find that converting multiple-choice questions to generative tasks reveals sharp capability drops of up to 35%. In addition, filtering blindly solvable and mislabeled samples improves discriminative power while simultaneously reducing computational cost. We release DatBench-Full, a cleaned evaluation suite of 33 datasets spanning nine VLM capabilities, and DatBench, a discriminative subset that achieves 13x average speedup (up to 50x) while closely matching the discriminative power of the original datasets. Our work outlines a path toward evaluation practices that are both rigorous and sustainable as VLMs continue to scale.

We present FIMO, an innovative dataset comprising formal mathematical problem statements sourced from the International Mathematical Olympiad (IMO) Shortlisted Problems. Designed to facilitate advanced automated theorem proving at the IMO level, FIMO is currently tailored for the Lean formal language. It comprises 149 formal problem statements, accompanied by both informal problem descriptions and their corresponding LaTeX-based informal proofs. Through initial experiments involving GPT-4, our findings underscore the existing limitations in current methodologies, indicating a substantial journey ahead before achieving satisfactory IMO-level automated theorem proving outcomes.

Multi-modal Chain-of-Thought (MCoT) requires models to leverage knowledge from both textual and visual modalities for step-by-step reasoning, which gains increasing attention. Nevertheless, the current MCoT benchmark still faces some challenges: (1) absence of visual modal reasoning, (2) single-step visual modal reasoning, and (3) Domain missing, thereby hindering the development of MCoT. Motivated by this, we introduce a novel benchmark (M^3CoT) to address the above challenges, advancing the multi-domain, multi-step, and multi-modal CoT. Additionally, we conduct a thorough evaluation involving abundant MCoT approaches on Vision Large Language Models (VLLMs). In addition, we highlight that the current VLLMs still struggle to correctly reason in M^3CoT and there remains a large gap between existing VLLMs and human performance in M^3CoT, despite their superior results on previous MCoT benchmarks. To our knowledge, we take the first meaningful step toward the multi-domain, multi-step, and multi-modal scenario in MCoT. We hope that M^3CoT can serve as a valuable resource, providing a pioneering foundation in multi-domain, multi-step, multi-modal chain-of-thought research.

Recent work on chain-of-thought (CoT) faithfulness reports single aggregate numbers (e.g., DeepSeek-R1 acknowledges hints 39% of the time), implying that faithfulness is an objective, measurable property of a model. This paper demonstrates that it is not. Three classifiers (a regex-only detector, a two-stage regex-plus-LLM pipeline, and an independent Claude Sonnet 4 judge) are applied to 10,276 influenced reasoning traces from 12 open-weight models spanning 9 families and 7B to 1T parameters. On identical data, these classifiers produce overall faithfulness rates of 74.4%, 82.6%, and 69.7%, respectively, with non-overlapping 95% confidence intervals. Per-model gaps range from 2.6 to 30.6 percentage points; all are statistically significant (McNemar's test, p < 0.001). The disagreements are systematic, not random: inter-classifier agreement measured by Cohen's kappa ranges from 0.06 ("slight") for sycophancy hints to 0.42 ("moderate") for grader hints, and the asymmetry is pronounced: for sycophancy, 883 cases are classified as faithful by the pipeline but unfaithful by the Sonnet judge, while only 2 go the other direction. Classifier choice can also reverse model rankings: Qwen3.5-27B ranks 1st under the pipeline but 7th under the Sonnet judge; OLMo-3.1-32B moves in the opposite direction, from 9th to 3rd. The root cause is that different classifiers operationalize related faithfulness constructs at different levels of stringency (lexical mention versus epistemic dependence), and these constructs yield divergent measurements on the same behavior. These results demonstrate that published faithfulness numbers cannot be meaningfully compared across studies that use different classifiers, and that future evaluations should report sensitivity ranges across multiple classification methodologies rather than single point estimates.

In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the specialized nature of Coq syntax and semantics poses unique challenges for Large Language Models (LLMs). Addressing this gap, we present a comprehensive dataset specifically designed to enhance LLMs' proficiency in interpreting and generating Coq code. This dataset, derived from a collection of over 10,000 Coq source files, encompasses a wide array of propositions, proofs, and definitions, enriched with metadata including source references and licensing information. Our primary aim is to facilitate the development of LLMs capable of generating syntactically correct and semantically meaningful Coq constructs, thereby advancing the frontier of automated theorem proving. Initial experiments with this dataset have showcased its significant potential; models trained on this data exhibited enhanced accuracy in Coq code generation. Notably, a particular experiment revealed that a fine-tuned LLM was capable of generating 141 valid proofs for a basic lemma, highlighting the dataset's utility in facilitating the discovery of diverse and valid proof strategies. This paper discusses the dataset's composition, the methodology behind its creation, and the implications of our findings for the future of machine learning in formal verification. The dataset is accessible for further research and exploration: https://huggingface.co/datasets/florath/coq-facts-props-proofs-gen0-v1

We develop a framework, in the style of Adler, for interpreting the notion of "witnessing" that has appeared (usually as a variant of Kim's Lemma) in different areas of neostability theory as a binary relation between abstract independence relations. This involves extending the relativisations of Kim-independence and Conant-independence due to Mutchnik to arbitrary independence relations. After developing this framework, we show that several results from simplicity, NTP_2, NSOP_1, and beyond follow as instances of general theorems for abstract independence relations. In particular, we prove the equivalence between witnessing and symmetry and the implications from this notion to chain local character and the weak independence theorem, and recover some partial converses. Finally, we use this framework to prove a dichotomy between NSOP_1 and Kruckman and Ramsey's BTP that applies to most known NSOP_4 examples in the literature.

Scientific user facilities, such as synchrotron beamlines, are equipped with a wide array of hardware and software tools that require a codebase for human-computer-interaction. This often necessitates developers to be involved to establish connection between users/researchers and the complex instrumentation. The advent of generative AI presents an opportunity to bridge this knowledge gap, enabling seamless communication and efficient experimental workflows. Here we present a modular architecture for the Virtual Scientific Companion (VISION) by assembling multiple AI-enabled cognitive blocks that each scaffolds large language models (LLMs) for a specialized task. With VISION, we performed LLM-based operation on the beamline workstation with low latency and demonstrated the first voice-controlled experiment at an X-ray scattering beamline. The modular and scalable architecture allows for easy adaptation to new instrument and capabilities. Development on natural language-based scientific experimentation is a building block for an impending future where a science exocortex -- a synthetic extension to the cognition of scientists -- may radically transform scientific practice and discovery.

Learning neural subset selection tasks, such as compound selection in AI-aided drug discovery, have become increasingly pivotal across diverse applications. The existing methodologies in the field primarily concentrate on constructing models that capture the relationship between utility function values and subsets within their respective supersets. However, these approaches tend to overlook the valuable information contained within the superset when utilizing neural networks to model set functions. In this work, we address this oversight by adopting a probabilistic perspective. Our theoretical findings demonstrate that when the target value is conditioned on both the input set and subset, it is essential to incorporate an invariant sufficient statistic of the superset into the subset of interest for effective learning. This ensures that the output value remains invariant to permutations of the subset and its corresponding superset, enabling identification of the specific superset from which the subset originated. Motivated by these insights, we propose a simple yet effective information aggregation module designed to merge the representations of subsets and supersets from a permutation invariance perspective. Comprehensive empirical evaluations across diverse tasks and datasets validate the enhanced efficacy of our approach over conventional methods, underscoring the practicality and potency of our proposed strategies in real-world contexts.

Recent advances such as LLaVA and Mini-GPT4 have successfully integrated visual information into LLMs, yielding inspiring outcomes and giving rise to a new generation of multi-modal LLMs, or MLLMs. Nevertheless, these methods struggle with hallucinations and the mutual interference between tasks. To tackle these problems, we propose an efficient and accurate approach to adapt to downstream tasks by utilizing LLM as a bridge to connect multiple expert models, namely u-LLaVA. Firstly, we incorporate the modality alignment module and multi-task modules into LLM. Then, we reorganize or rebuild multi-type public datasets to enable efficient modality alignment and instruction following. Finally, task-specific information is extracted from the trained LLM and provided to different modules for solving downstream tasks. The overall framework is simple, effective, and achieves state-of-the-art performance across multiple benchmarks. We also release our model, the generated data, and the code base publicly available.

While Chain-of-Thought (CoT) prompting advances LLM reasoning, challenges persist in consistency, accuracy, and self-correction, especially for complex or ethically sensitive tasks. Existing single-dimensional reflection methods offer insufficient improvements. We propose MyGO Poly-Reflective Chain-of-Thought (PR-CoT), a novel methodology employing structured multi-perspective reflection. After initial CoT, PR-CoT guides the LLM to self-assess its reasoning across multiple predefined angles: logical consistency, information completeness, biases/ethics, and alternative solutions. Implemented purely via prompt engineering, this process refines the initial CoT into a more robust and accurate final answer without model retraining. Experiments across arithmetic, commonsense, ethical decision-making, and logical puzzles, using GPT-three point five and GPT-four models, demonstrate PR-CoT's superior performance. It significantly outperforms traditional CoT and existing reflection methods in logical consistency and error correction, with notable gains in nuanced domains like ethical decision-making. Ablation studies, human evaluations, and qualitative analyses further validate the contribution of each reflection perspective and the overall efficacy of our poly-reflective paradigm in fostering more reliable LLM reasoning.

We extend the simply-typed guarded lambda-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming and reasoning about infinite stochastic processes like Markov chains. We demonstrate the logic sound by interpreting its judgements in the topos of trees and by using probabilistic couplings for the semantics of relational assertions over distributions on discrete types. The program logic is designed to support syntax-directed proofs in the style of relational refinement types, but retains the expressiveness of higher-order logic extended with discrete distributions, and the ability to reason relationally about expressions that have different types or syntactic structure. In addition, our proof system leverages a well-known theorem from the coupling literature to justify better proof rules for relational reasoning about probabilistic expressions. We illustrate these benefits with a broad range of examples that were beyond the scope of previous systems, including shift couplings and lump couplings between random walks.

We consider three monads on Top, the category of topological spaces, which formalize topological aspects of probability and possibility in categorical terms. The first one is the Hoare hyperspace monad H, which assigns to every space its space of closed subsets equipped with the lower Vietoris topology. The second is the monad V of continuous valuations, also known as the extended probabilistic powerdomain. We construct both monads in a unified way in terms of double dualization. This reveals a close analogy between them, and allows us to prove that the operation of taking the support of a continuous valuation is a morphism of monads from V to H. In particular, this implies that every H-algebra (topological complete semilattice) is also a V-algebra. Third, we show that V can be restricted to a submonad of tau-smooth probability measures on Top. By composing these two morphisms of monads, we obtain that taking the support of a tau-smooth probability measure is also a morphism of monads.

Vision-language models (VLMs) lag behind text-only language models on mathematical reasoning when the same problems are presented as images rather than text. We empirically characterize this as a modality gap: the same question in text form yields markedly higher accuracy than its visually typeset counterpart, due to compounded failures in reading dense formulas, layout, and mixed symbolic-diagrammatic context. First, we introduce VisTIRA (Vision and Tool-Integrated Reasoning Agent), a tool-integrated reasoning framework that enables structured problem solving by iteratively decomposing a given math problem (as an image) into natural language rationales and executable Python steps to determine the final answer. Second, we build a framework to measure and improve visual math reasoning: a LaTeX-based pipeline that converts chain-of-thought math corpora (e.g., NuminaMath) into challenging image counterparts, and a large set of synthetic tool-use trajectories derived from a real-world, homework-style image dataset (called SnapAsk) for fine-tuning VLMs. Our experiments show that tool-integrated supervision improves image-based reasoning, and OCR grounding can further narrow the gap for smaller models, although its benefit diminishes at scale. These findings highlight that modality gap severity inversely correlates with model size, and that structured reasoning and OCR-based grounding are complementary strategies for advancing visual mathematical reasoning.

Large reasoning models (e.g., R1, o3) have demonstrated remarkable mathematical problem-solving abilities. However, the high reported accuracy of these advanced models on popular datasets, reliance on purely numerical evaluation and potential benchmark leakage, often masks their true reasoning shortcomings. To address this, we propose leveraging the inherent rigor and methodological complexity of mathematical proofs as a diagnostic tool to expose these hidden failures. Specifically, we introduce the RFMDataset (Reveal Failure Modes), a collection of 200 diverse mathematical proof problems, and thoroughly evaluate advanced models' performance on it. Our in-depth analysis of their failures uncovers 10 fine-grained error types, which shows fundamental limitations in current large reasoning models: 1) large reasoning models grapple profoundly with mathematical proofs, with some generating entirely correct proofs for less than 20% of problems and failing even on basic ones; 2) models exhibit a diverse spectrum of reasoning failures, prominently demonstrating the lack of guarantees for the correctness and rigor of single-step reasoning; and 3) models show hallucination and incompleteness during the reasoning process. Our findings reveal that models' self-reflection is insufficient to resolve the current logical dilemmas, necessitating formalized and fine-grained logical training.

Multimodal large language models (MLLMs) that integrate visual and textual reasoning leverage chain-of-thought (CoT) prompting to tackle complex visual tasks, yet continue to exhibit visual hallucinations and an over-reliance on textual priors. We present a systematic diagnosis of state-of-the-art vision-language models using a three-stage evaluation framework, uncovering key failure modes. To address these, we propose an agent-based architecture that combines LLM reasoning with lightweight visual modules, enabling fine-grained analysis and iterative refinement of reasoning chains. Our results highlight future visual reasoning models should focus on integrating a broader set of specialized tools for analyzing visual content. Our system achieves significant gains (+10.3 on MMMU, +6.0 on MathVista over a 7B baseline), matching or surpassing much larger models. We will release our framework and evaluation suite to facilitate future research.

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

Multimodal Mathematical Reasoning (MMR) has recently attracted increasing attention for its capability to solve mathematical problems involving both textual and visual modalities. However, current models still face significant challenges in real-world visual math tasks, often misinterpreting diagrams, failing to align mathematical symbols with visual evidence, or producing inconsistent reasoning steps. Moreover, existing evaluations mainly focus on checking final answers rather than verifying the correctness or executability of each intermediate step. A growing body of recent research addresses these issues by integrating structured perception, explicit alignment, and verifiable reasoning within unified frameworks. To establish a clear roadmap for understanding and comparing different MMR approaches, we systematically review them around four fundamental questions: (1) What to extract from multimodal inputs, (2) How to represent and align textual and visual information, (3) How to perform the reasoning, and (4) How to evaluate the correctness of the overall reasoning process. Finally, we discuss open challenges and share our thoughts on future research directions.

Answering questions with Chain-of-Thought (CoT) has significantly enhanced the reasoning capabilities of Large Language Models (LLMs), yet its impact on Large Multimodal Models (LMMs) still lacks a systematic assessment and in-depth investigation. In this paper, we introduce MME-CoT, a specialized benchmark evaluating the CoT reasoning performance of LMMs, spanning six domains: math, science, OCR, logic, space-time, and general scenes. As the first comprehensive study in this area, we propose a thorough evaluation suite incorporating three novel metrics that assess the reasoning quality, robustness, and efficiency at a fine-grained level. Leveraging curated high-quality data and a unique evaluation strategy, we conduct an in-depth analysis of state-of-the-art LMMs, uncovering several key insights: 1) Models with reflection mechanism demonstrate a superior CoT quality, with Kimi k1.5 outperforming GPT-4o and demonstrating the highest quality results; 2) CoT prompting often degrades LMM performance on perception-heavy tasks, suggesting a potentially harmful overthinking behavior; and 3) Although the CoT quality is high, LMMs with reflection exhibit significant inefficiency in both normal response and self-correction phases. We hope MME-CoT serves as a foundation for advancing multimodal reasoning in LMMs. Project Page: https://mmecot.github.io/

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (IVL) together with a real-valued logic. Our IVL provides a programming-language-style for expressing verification conditions whose validity implies the correctness of a program under investigation. As our focus is on verifying quantitative properties such as bounds on expected outcomes, expected run-times, or termination probabilities, off-the-shelf IVLs based on Boolean first-order logic do not suffice. Instead, a paradigm shift from the standard Boolean to a real-valued domain is required. Our IVL features quantitative generalizations of standard verification constructs such as assume- and assert-statements. Verification conditions are generated by a weakest-precondition-style semantics, based on our real-valued logic. We show that our verification infrastructure supports natural encodings of numerous verification techniques from the literature. With our SMT-based implementation, we automatically verify a variety of benchmarks. To the best of our knowledge, this establishes the first deductive verification infrastructure for expectation-based reasoning about probabilistic programs.

Recent advances in Vision Language Models (VLMs) have driven significant progress in visual reasoning. However, open-source VLMs still lag behind proprietary systems, largely due to the lack of high-quality reasoning data. Existing datasets offer limited coverage of challenging domains such as STEM diagrams and visual puzzles, and lack consistent, long-form Chain-of-Thought (CoT) annotations essential for eliciting strong reasoning capabilities. To bridge this gap, we introduce MMFineReason, a large-scale multimodal reasoning dataset comprising 1.8M samples and 5.1B solution tokens, featuring high-quality reasoning annotations distilled from Qwen3-VL-235B-A22B-Thinking. The dataset is established via a systematic three-stage pipeline: (1) large-scale data collection and standardization, (2) CoT rationale generation, and (3) comprehensive selection based on reasoning quality and difficulty awareness. The resulting dataset spans STEM problems, visual puzzles, games, and complex diagrams, with each sample annotated with visually grounded reasoning traces. We fine-tune Qwen3-VL-Instruct on MMFineReason to develop MMFineReason-2B/4B/8B versions. Our models establish new state-of-the-art results for their size class. Notably, MMFineReason-4B succesfully surpasses Qwen3-VL-8B-Thinking, and MMFineReason-8B even outperforms Qwen3-VL-30B-A3B-Thinking while approaching Qwen3-VL-32B-Thinking, demonstrating remarkable parameter efficiency. Crucially, we uncover a "less is more" phenomenon via our difficulty-aware filtering strategy: a subset of just 7\% (123K samples) achieves performance comparable to the full dataset. Notably, we reveal a synergistic effect where reasoning-oriented data composition simultaneously boosts general capabilities.

We study the matrix models pi:C(S_N^+)to M_N(C(X)) which are flat, in the sense that the standard generators of C(S_N^+) are mapped to rank 1 projections. Our first result is a generalization of the Pauli matrix construction at N=4, using finite groups and 2-cocycles. Our second result is the construction of a universal representation of C(S_N^+), inspired from the Sinkhorn algorithm, that we conjecture to be inner faithful.

This article presents a theoretical framework for adapting the Common Model of Cognition to large generative network models within the field of artificial intelligence. This can be accomplished by restructuring modules within the Common Model into shadow production systems that are peripheral to a central production system, which handles higher-level reasoning based on the shadow productions' output. Implementing this novel structure within the Common Model allows for a seamless connection between cognitive architectures and generative neural networks.

This paper reformulates a classical result in probability theory from the 1930s in modern categorical terms: de Finetti's representation theorem is redescribed as limit statement for a chain of finite spaces in the Kleisli category of the Giry monad. This new limit is used to identify among exchangeable coalgebras the final one.

Large language models (LLMs) often struggle with maintaining accuracy across a sequence of intermediate reasoning steps in mathematical reasoning, leading to error propagation that undermines the final result. The current methodology to mitigate this issue primarily involves using a verifier model to assess the correctness of generated solution candidates, focusing either on the overall reasoning path or on an incomplete reasoning path. By rethinking this approach, we argue that assessing potentials of incomplete reasoning paths could be more advantageous as it guides towards correct final answers, transforming the task into a planning problem. Our proposed verifier, the Outcome-supervision Value Model (OVM), employs outcome supervision for training, offering an efficient and intuitive method for planning by prioritizing steps that lead to accurate conclusions over mere per-step correctness. Furthermore, the OVM eschews the need for labor-intensive annotations on step-level correctness, enhancing its scalability. Our experiments on two multi-step mathematical reasoning datasets, GSM8K and Game of 24, demonstrate the superior performance of the OVM model. Notably, in GSM8K, our OVM-7B model achieves state-of-the-art results among LLMs up to 13B parameters; especially it does not utilize GPT-4 or code execution. These findings offer a novel perspective on the role of outcome supervision in training verifiers for multi-step reasoning tasks and provide theoretical justification for its advantage in value estimation for planning.

Natural language image-caption datasets, widely used for training Large Multimodal Models, mainly focus on natural scenarios and overlook the intricate details of mathematical figures that are critical for problem-solving, hindering the advancement of current LMMs in multimodal mathematical reasoning. To this end, we propose leveraging code as supervision for cross-modal alignment, since code inherently encodes all information needed to generate corresponding figures, establishing a precise connection between the two modalities. Specifically, we co-develop our image-to-code model and dataset with model-in-the-loop approach, resulting in an image-to-code model, FigCodifier and ImgCode-8.6M dataset, the largest image-code dataset to date. Furthermore, we utilize FigCodifier to synthesize novel mathematical figures and then construct MM-MathInstruct-3M, a high-quality multimodal math instruction fine-tuning dataset. Finally, we present MathCoder-VL, trained with ImgCode-8.6M for cross-modal alignment and subsequently fine-tuned on MM-MathInstruct-3M for multimodal math problem solving. Our model achieves a new open-source SOTA across all six metrics. Notably, it surpasses GPT-4o and Claude 3.5 Sonnet in the geometry problem-solving subset of MathVista, achieving improvements of 8.9% and 9.2%. The dataset and models will be released at https://github.com/mathllm/MathCoder.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear structural equation model for a fixed mixed graph G=(V, D,B) is parameterized by a rational function with parameters for each vertex and edge in G. This rational parametrization naturally allows for the study of these models from an algebraic and combinatorial point of view. Indeed, this point of view has led to a collection of results in the literature, mainly focusing on questions related to identifiability and determining relationships between covariances (i.e., finding polynomials in the Gaussian vanishing ideal). So far, a large proportion of these results has focused on the case when D, the directed part of the mixed graph G, is acyclic. This is due to the fact that in the acyclic case, the parametrization becomes polynomial and there is a description of the entries of the covariance matrices in terms of a finite sum. We move beyond the acyclic case and give a closed form expression for the entries of the covariance matrices in terms of the one-connections in a graph obtained from D through some small operations. This closed form expression then allows us to show that if G is simple, then the parametrization map is generically finite-to-one. Finally, having a closed form expression for the covariance matrices allows for the development of an algorithm for systematically exploring possible polynomials in the Gaussian vanishing ideal.

Observability into the decision making of modern AI systems may be required to safely deploy increasingly capable agents. Monitoring the chain-of-thought (CoT) of today's reasoning models has proven effective for detecting misbehavior. However, this "monitorability" may be fragile under different training procedures, data sources, or even continued system scaling. To measure and track monitorability, we propose three evaluation archetypes (intervention, process, and outcome-property) and a new monitorability metric, and introduce a broad evaluation suite. We demonstrate that these evaluations can catch simple model organisms trained to have obfuscated CoTs, and that CoT monitoring is more effective than action-only monitoring in practical settings. We compare the monitorability of various frontier models and find that most models are fairly, but not perfectly, monitorable. We also evaluate how monitorability scales with inference-time compute, reinforcement learning optimization, and pre-training model size. We find that longer CoTs are generally more monitorable and that RL optimization does not materially decrease monitorability even at the current frontier scale. Notably, we find that for a model at a low reasoning effort, we could instead deploy a smaller model at a higher reasoning effort (thereby matching capabilities) and obtain a higher monitorability, albeit at a higher overall inference compute cost. We further investigate agent-monitor scaling trends and find that scaling a weak monitor's test-time compute when monitoring a strong agent increases monitorability. Giving the weak monitor access to CoT not only improves monitorability, but it steepens the monitor's test-time compute to monitorability scaling trend. Finally, we show we can improve monitorability by asking models follow-up questions and giving their follow-up CoT to the monitor.

We prove that the homotopy limits and homotopy colimits of chain complexes can be computed by the cobar and bar constructions. We also show that the totalizations of double complexes compute the homotopy limits and homotopy colimits of simplicial and cosimplicial chain complexes.

Training expert LLMs in domains with scarce data is difficult, often relying on multiple-choice questions (MCQs). However, standard outcome-based reinforcement learning (RL) on MCQs is risky. While it may improve accuracy, we observe it often degrades reasoning quality such as logical consistency. Existing solutions to supervise reasoning, such as large-scale Process Reward Models (PRMs), are prohibitively expensive. To address this, we propose CLARity, a cost-effective RL framework that enhances reasoning quality using only a small, general-purpose LLM. CLARity integrates a consistency-aware reward mechanism with a 2-stage refine-then-monitor training pipeline to enhance reasoning consistency, and a dynamic data reformulation strategy to to better exploit limited data. Experiments demonstrate that CLARity improves response consistency by 16.5% and accuracy by 7.5% over baselines. Human evaluations further confirm holistic improvements in coherence and professionalism. Thus, CLARity offers a generalizable solution that enables smaller models to effectively guide expert models by reasoning consistency.Our code is open sourced at: https://github.com/Infinite-set/CLARity

Chain-of-Thought (CoT) reasoning has been extensively explored in large models to tackle complex understanding tasks. However, it still remains an open question whether such strategies can be applied to verifying and reinforcing image generation scenarios. In this paper, we provide the first comprehensive investigation of the potential of CoT reasoning to enhance autoregressive image generation. We focus on three techniques: scaling test-time computation for verification, aligning model preferences with Direct Preference Optimization (DPO), and integrating these techniques for complementary effects. Our results demonstrate that these approaches can be effectively adapted and combined to significantly improve image generation performance. Furthermore, given the pivotal role of reward models in our findings, we propose the Potential Assessment Reward Model (PARM) and PARM++, specialized for autoregressive image generation. PARM adaptively assesses each generation step through a potential assessment approach, merging the strengths of existing reward models, and PARM++ further introduces a reflection mechanism to self-correct the generated unsatisfactory image. Using our investigated reasoning strategies, we enhance a baseline model, Show-o, to achieve superior results, with a significant +24% improvement on the GenEval benchmark, surpassing Stable Diffusion 3 by +15%. We hope our study provides unique insights and paves a new path for integrating CoT reasoning with autoregressive image generation. Code and models are released at https://github.com/ZiyuGuo99/Image-Generation-CoT

We introduce Probabilistic Dependent Type Systems (PDTS) via a functional language based on a subsystem of intuitionistic type theory including dependent sums and products, which is expanded to include stochastic functions. We provide a sampling-based semantics for the language based on non-deterministic beta reduction. Further, we derive a probabilistic logic from the PDTS introduced as a direct result of the Curry-Howard isomorphism. The probabilistic logic derived is shown to provide a universal representation for finite discrete distributions.

The remarkable progress of Multi-modal Large Language Models (MLLMs) has garnered unparalleled attention, due to their superior performance in visual contexts. However, their capabilities in visual math problem-solving remain insufficiently evaluated and understood. We investigate current benchmarks to incorporate excessive visual content within textual questions, which potentially assist MLLMs in deducing answers without truly interpreting the input diagrams. To this end, we introduce MathVerse, an all-around visual math benchmark designed for an equitable and in-depth evaluation of MLLMs. We meticulously collect 2,612 high-quality, multi-subject math problems with diagrams from publicly available sources. Each problem is then transformed by human annotators into six distinct versions, each offering varying degrees of information content in multi-modality, contributing to 15K test samples in total. This approach allows MathVerse to comprehensively assess whether and how much MLLMs can truly understand the visual diagrams for mathematical reasoning. In addition, we propose a Chain-of-Thought (CoT) evaluation strategy for a fine-grained assessment of the output answers. Rather than naively judging True or False, we employ GPT-4(V) to adaptively extract crucial reasoning steps, and then score each step with detailed error analysis, which can reveal the intermediate CoT reasoning quality by MLLMs. We hope the MathVerse benchmark may provide unique insights to guide the future development of MLLMs. Project page: https://mathverse-cuhk.github.io

As large language models (LLMs) reach high scores on established mathematical benchmarks, such as GSM8K and MATH, the research community has turned to International Mathematical Olympiad (IMO) problems to push the evaluation frontier. However, existing Olympiad-level benchmarks suffer from practical constraints that introduce grading noise and potential bias, such as heterogeneous answer formats requiring model-based judges and a reliance on potentially flawed solutions. We introduce RIMO, a two-track benchmark designed to preserve peak Olympiad difficulty while eliminating this evaluation noise. The first track, RIMO-N, rewrites 335 IMO problems to admit a single, unique integer answer, allowing for deterministic correctness checking. The second track, RIMO-P, features 456 proof problems with expert-checked solutions, which are decomposed into a sequence of sub-problems to evaluate the step-by-step reasoning process via an automated grading system. Our benchmarking of ten frontier LLMs, including GPT-4o and Gemini 2.5 Flash, reveals that while these systems excel on older benchmarks, their performance drops sharply on RIMO. These results highlight a substantial gap between current LLM capabilities and actual Olympiad-level reasoning. By providing a challenging yet easy-to-evaluate suite, RIMO offers a high-resolution yardstick for future research, presenting a clear target for closing the profound reasoning gap our findings expose.

Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as high-level tactics. However, human experts have to construct proofs manually by entering tactics into the proof assistant. In this paper, we study the problem of using machine learning to automate the interaction with proof assistants. We construct CoqGym, a large-scale dataset and learning environment containing 71K human-written proofs from 123 projects developed with the Coq proof assistant. We develop ASTactic, a deep learning-based model that generates tactics as programs in the form of abstract syntax trees (ASTs). Experiments show that ASTactic trained on CoqGym can generate effective tactics and can be used to prove new theorems not previously provable by automated methods. Code is available at https://github.com/princeton-vl/CoqGym.

Large Reasoning Models (LRMs) exhibit strong performance, yet often produce rationales that sound plausible but fail to reflect their true decision process, undermining reliability and trust. We introduce a formal framework for reasoning faithfulness, defined by two testable conditions: stance consistency (a coherent stance linking reasoning to answer) and causal influence (the stated reasoning causally drives the answer under output-level interventions), explicitly decoupled from accuracy. To operationalize this, we present RFEval, a benchmark of 7,186 instances across seven tasks that probes faithfulness via controlled, output-level counterfactual interventions. Evaluating twelve open-source LRMs, we find unfaithfulness in 49.7% of outputs, predominantly from stance inconsistency. Failures are concentrated in brittle, convergent domains such as math and code, and correlate more with post-training regimes than with scale: within-family ablations indicate that adding current RL-style objectives on top of supervised fine-tuning can reduce reasoning faithfulness, even when accuracy is maintained. Crucially, accuracy is neither a sufficient nor a reliable proxy for faithfulness: once controlling for model and task, the accuracy-faithfulness link is weak and statistically insignificant. Our work establishes a rigorous methodology for auditing LRM reliability and shows that trustworthy AI requires optimizing not only for correct outcomes but also for the structural integrity of the reasoning process. Our code and dataset can be found at project page: https://aidaslab.github.io/RFEval/}{https://aidaslab.github.io/RFEval/

In this paper, we introduce BMMR, a large-scale bilingual, multimodal, multi-disciplinary reasoning dataset for the community to develop and evaluate large multimodal models (LMMs). BMMR comprises 110k college-level questions spanning 300 UNESCO-defined subjects, spanning diverse formats-multiple-choice, fill-in-the-blank, and open-ended QA-and sourced from both print and digital media such as books, exams, and quizzes. All data are curated and filtered via a human-in-the-loop and scalable framework, and each instance is paired with a high-quality reasoning path. The dataset is organized into two parts: BMMR-Eval that comprises 20,458 high-quality instances to comprehensively assess LMMs' knowledge and reasoning across multiple disciplines in both Chinese and English; and BMMR-Train that contains 88,991 instances to support further research and development, extending the current focus on mathematical reasoning to diverse disciplines and domains. In addition, we propose the process-based multi-discipline verifier (i.e., BMMR-Verifier) for accurate and fine-grained evaluation of reasoning paths. Extensive experiments on 24 models reveal that (i) even SOTA models (e.g., o3 and Gemini-2.5-Pro) leave substantial headroom on BMMR-Eval; (ii) reasoning models exhibit discipline bias and outperform LMMs only on specific subjects; (iii) open-source models still trail their proprietary counterparts; and (iv) fine-tuning on BMMR-Train narrows this gap. Additionally, we conduct reasoning-chain analyses using BMMR-Verifier and other in-depth studies, uncovering the challenges LMMs currently face in multidisciplinary reasoning. We will release the data, and we hope our work can offer insights and contributions to the community.

Scientific studies of consciousness rely on objects whose existence is assumed to be independent of any consciousness. On the contrary, we assume consciousness to be fundamental, and that one of the main features of consciousness is characterized as being other-dependent. We set up a framework which naturally subsumes this feature by defining a compact closed category where morphisms represent conscious processes. These morphisms are a composition of a set of generators, each being specified by their relations with other generators, and therefore co-dependent. The framework is general enough and fits well into a compositional model of consciousness. Interestingly, we also show how our proposal may become a step towards avoiding the hard problem of consciousness, and thereby address the combination problem of conscious experiences.

Large language models (LLMs) continue to struggle with mathematical reasoning, and common post-training pipelines often reduce each generated solution to a binary outcome: correct or incorrect. This perspective is limiting in practice, as failures in chain-of-thought (CoT) reasoning are frequently structured; solutions may appear convincing while containing subtle logical, algebraic, or numerical flaws. Meanwhile, reinforcement learning from human feedback (RLHF) variants that rely on large reward models or LLM-as-a-judge signals are often expensive, difficult to scale, and unstable to iterate. We propose a lightweight and pragmatic post-training pipeline that targets such structured errors under realistic compute budgets. Starting from supervised fine-tuning (SFT) on MetaMathQA-style CoT data, we introduce a compact MathVerifier that decomposes a candidate solution into a six-dimensional error profile and aggregates it into interpretable wrongness and absurdity scores. These verifier signals serve two roles: (i) mining hard negatives that are near-correct yet structurally flawed, and (ii) defining per-sample importance weights that emphasize the most informative preference pairs. We integrate both into an offline Direct Preference Optimization (DPO) objective via a verifier-guided weighted formulation. Experiments on a 1.5B-parameter Qwen2.5 model show that verifier-guided, weighted DPO yields more targeted improvements than vanilla SFT and unweighted DPO, particularly on problems where solutions are numerically close to correct but logically inconsistent, while avoiding the overhead of training large reward models or relying on external judges.

Although Large Language Models (LLMs) and Large Multimodal Models (LMMs) exhibit impressive skills in various domains, their ability for mathematical reasoning within visual contexts has not been formally examined. Equipping LLMs and LMMs with this capability is vital for general-purpose AI assistants and showcases promising potential in education, data analysis, and scientific discovery. To bridge this gap, we present MathVista, a benchmark designed to amalgamate challenges from diverse mathematical and visual tasks. We first taxonomize the key task types, reasoning skills, and visual contexts from the literature to guide our selection from 28 existing math-focused and visual question answering datasets. Then, we construct three new datasets, IQTest, FunctionQA, and PaperQA, to accommodate for missing types of visual contexts. The problems featured often require deep visual understanding beyond OCR or image captioning, and compositional reasoning with rich domain-specific tools, thus posing a notable challenge to existing models. We conduct a comprehensive evaluation of 11 prominent open-source and proprietary foundation models (LLMs, LLMs augmented with tools, and LMMs), and early experiments with GPT-4V. The best-performing model, Multimodal Bard, achieves only 58% of human performance (34.8% vs 60.3%), indicating ample room for further improvement. Given this significant gap, MathVista fuels future research in the development of general-purpose AI agents capable of tackling mathematically intensive and visually rich real-world tasks. Preliminary tests show that MathVista also presents challenges to GPT-4V, underscoring the benchmark's importance. The project is available at https://mathvista.github.io/.

Vision Language Models (VLMs) are increasingly used for tasks like medical report generation and visual question answering. However, fluent diagnostic text does not guarantee safe visual understanding. In clinical practice, interpretation begins with pre-diagnostic sanity checks: verifying that the input is valid to read (correct modality and anatomy, plausible viewpoint and orientation, and no obvious integrity violations). Existing benchmarks largely assume this step is solved, and therefore miss a critical failure mode: a model can produce plausible narratives even when the input is inconsistent or invalid. We introduce MedObvious, a 1,880-task benchmark that isolates input validation as a set-level consistency capability over small multi-panel image sets: the model must identify whether any panel violates expected coherence. MedObvious spans five progressive tiers, from basic orientation/modality mismatches to clinically motivated anatomy/viewpoint verification and triage-style cues, and includes five evaluation formats to test robustness across interfaces. Evaluating 17 different VLMs, we find that sanity checking remains unreliable: several models hallucinate anomalies on normal (negative-control) inputs, performance degrades when scaling to larger image sets, and measured accuracy varies substantially between multiple-choice and open-ended settings. These results show that pre-diagnostic verification remains unsolved for medical VLMs and should be treated as a distinct, safety-critical capability before deployment.

Modularization is a cornerstone of computer science, abstracting complex functions into atomic building blocks. In this paper, we introduce a new level of modularization by abstracting generative models into atomic generative modules. Analogous to fractals in mathematics, our method constructs a new type of generative model by recursively invoking atomic generative modules, resulting in self-similar fractal architectures that we call fractal generative models. As a running example, we instantiate our fractal framework using autoregressive models as the atomic generative modules and examine it on the challenging task of pixel-by-pixel image generation, demonstrating strong performance in both likelihood estimation and generation quality. We hope this work could open a new paradigm in generative modeling and provide a fertile ground for future research. Code is available at https://github.com/LTH14/fractalgen.

We introduce MAmmoTH, a series of open-source large language models (LLMs) specifically tailored for general math problem-solving. The MAmmoTH models are trained on MathInstruct, our meticulously curated instruction tuning dataset. MathInstruct is compiled from 13 math datasets with intermediate rationales, six of which have rationales newly curated by us. It presents a unique hybrid of chain-of-thought (CoT) and program-of-thought (PoT) rationales, and also ensures extensive coverage of diverse fields in math. The hybrid of CoT and PoT not only unleashes the potential of tool use but also allows different thought processes for different math problems. As a result, the MAmmoTH series substantially outperform existing open-source models on nine mathematical reasoning datasets across all scales with an average accuracy gain between 13% and 29%. Remarkably, our MAmmoTH-7B model reaches 35% on MATH (a competition-level dataset), which exceeds the best open-source 7B model (WizardMath) by 25%, and the MAmmoTH-34B model achieves 46% accuracy on MATH, even surpassing GPT-4's CoT result. Our work underscores the importance of diverse problem coverage and the use of hybrid rationales in developing superior math generalist models.

Despite significant progress, multimodal large language models continue to struggle with visual mathematical problem solving. Some recent works recognize that visual perception is a bottleneck in visual mathematical reasoning, but their solutions are limited to improving the extraction and interpretation of visual inputs. Notably, they all ignore the key issue of whether the extracted visual cues are faithfully integrated and properly utilized in subsequent reasoning. Motivated by this, we present CogFlow, a novel cognitive-inspired three-stage framework that incorporates a knowledge internalization stage, explicitly simulating the hierarchical flow of human reasoning: perceptionRightarrowinternalizationRightarrowreasoning. Inline with this hierarchical flow, we holistically enhance all its stages. We devise Synergistic Visual Rewards to boost perception capabilities in parametric and semantic spaces, jointly improving visual information extraction from symbols and diagrams. To guarantee faithful integration of extracted visual cues into subsequent reasoning, we introduce a Knowledge Internalization Reward model in the internalization stage, bridging perception and reasoning. Moreover, we design a Visual-Gated Policy Optimization algorithm to further enforce the reasoning is grounded with the visual knowledge, preventing models seeking shortcuts that appear coherent but are visually ungrounded reasoning chains. Moreover, we contribute a new dataset MathCog for model training, which contains samples with over 120K high-quality perception-reasoning aligned annotations. Comprehensive experiments and analysis on commonly used visual mathematical reasoning benchmarks validate the superiority of the proposed CogFlow.

As Large Language Model (LLM) agents are increasingly tasked with high-stakes autonomous decision-making, the transparency of their reasoning processes has become a critical safety concern. While Chain-of-Thought (CoT) prompting allows agents to generate human-readable reasoning traces, it remains unclear whether these traces are faithful generative drivers of the model's output or merely post-hoc rationalizations. We introduce Project Ariadne, a novel XAI framework that utilizes Structural Causal Models (SCMs) and counterfactual logic to audit the causal integrity of agentic reasoning. Unlike existing interpretability methods that rely on surface-level textual similarity, Project Ariadne performs hard interventions (do-calculus) on intermediate reasoning nodes -- systematically inverting logic, negating premises, and reversing factual claims -- to measure the Causal Sensitivity (φ) of the terminal answer. Our empirical evaluation of state-of-the-art models reveals a persistent Faithfulness Gap. We define and detect a widespread failure mode termed Causal Decoupling, where agents exhibit a violation density (ρ) of up to 0.77 in factual and scientific domains. In these instances, agents arrive at identical conclusions despite contradictory internal logic, proving that their reasoning traces function as "Reasoning Theater" while decision-making is governed by latent parametric priors. Our findings suggest that current agentic architectures are inherently prone to unfaithful explanation, and we propose the Ariadne Score as a new benchmark for aligning stated logic with model action.

While Large Language Models (LLMs) have excelled in textual reasoning, they struggle with mathematical domains like geometry that intrinsically rely on visual aids. Existing approaches to Visual Chain-of-Thought (VCoT) are often limited by rigid external tools or fail to generate the high-fidelity, strategically-timed diagrams necessary for complex problem-solving. To bridge this gap, we introduce MathCanvas, a comprehensive framework designed to endow unified Large Multimodal Models (LMMs) with intrinsic VCoT capabilities for mathematics. Our approach consists of two phases. First, a Visual Manipulation stage pre-trains the model on a novel 15.2M-pair corpus, comprising 10M caption-to-diagram pairs (MathCanvas-Imagen) and 5.2M step-by-step editing trajectories (MathCanvas-Edit), to master diagram generation and editing. Second, a Strategic Visual-Aided Reasoning stage fine-tunes the model on MathCanvas-Instruct, a new 219K-example dataset of interleaved visual-textual reasoning paths, teaching it when and how to leverage visual aids. To facilitate rigorous evaluation, we introduce MathCanvas-Bench, a challenging benchmark with 3K problems that require models to produce interleaved visual-textual solutions. Our model, BAGEL-Canvas, trained under this framework, achieves an 86% relative improvement over strong LMM baselines on MathCanvas-Bench, demonstrating excellent generalization to other public math benchmarks. Our work provides a complete toolkit-framework, datasets, and benchmark-to unlock complex, human-like visual-aided reasoning in LMMs. Project Page: https://mathcanvas.github.io/

We introduce Minary, a computational framework designed as a candidate for the first formally provable autopoietic primitive. Minary represents interacting probabilistic events as multi-dimensional vectors and combines them via linear superposition rather than multiplicative scalar operations, thereby preserving uncertainty and enabling constructive and destructive interference in the range [-1,1]. A fixed set of ``perspectives'' evaluates ``semantic dimensions'' according to hidden competencies, and their interactions drive two discrete-time stochastic processes. We model this system as an iterated random affine map and use the theory of iterated random functions to prove that it converges in distribution to a unique stationary law; we moreover obtain an explicit closed form for the limiting expectation in terms of row, column, and global averages of the competency matrix. We then derive exact formulas for the mean and variance of the normalized consensus conditioned on the activation of a given semantic dimension, revealing how consensus depends on competency structure rather than raw input signals. Finally, we argue that Minary is organizationally closed yet operationally open in the sense of Maturana and Varela, and we discuss implications for building self-maintaining, distributed, and parallelizable computational systems that house a uniquely subjective notion of identity.

Chain-of-thought (CoT) monitoring has been proposed as a promising safety mechanism for detecting misaligned behavior in large language models. However, its reliability remains largely unexplored beyond English and across diverse model families. We present the first large-scale evaluation of CoT monitorability across 13 diverse languages and seven frontier model families, comprising 16 models. Using adversarial-hint evaluations that require explicit intermediate computation, together with analysis of internal answer-token probabilities, we consistently find CoT unfaithfulness across languages and hint types, with an average rate of 95.9\% across 8B--120B parameter models. We find that frontier models systematically engage in strategic manipulation, including answer-switching, post-hoc rationalization, and procedural exploitation of hints, making external monitors struggle to detect deception. We show that frontier models often commit to the misaligned cue in their latent activations within the first 15\% of generation, even when the CoT appears faithful. Surprisingly, these deceptive patterns remain 100\% in low-resource languages, revealing fundamental limitations in current CoT-based oversight. Our results reveal that CoT monitoring is fundamentally fragile under linguistic distribution shift, providing a substantially weaker safety signal than what English-only studies suggest. These findings underscore an urgent need to develop robust CoT monitors and to accelerate research into white-box monitoring techniques, especially to improve CoT monitorability in mid- and low-resource languages. Our code is available https://multilingual-cot-monitoring.github.io/{blue{here}}.

We introduce k-quantifier logics -- logics with access to k-tuples of elements and very general quantification patterns for transitions between k-tuples. The framework is very expressive and encompasses e.g. the k-variable fragments of first-order logic, modal logic, and monotone neighbourhood semantics. We introduce a corresponding notion of bisimulation and prove variants of the classical Ehrenfeucht-Fraisse and Hennessy-Milner theorem. Finally, we show a Lindstrom-style characterisation for k-quantifier logics that satisfy Los' theorem by proving that they are the unique maximally expressive logics that satisfy Los' theorem and are invariant under the associated bisimulation relations.

We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and orthomodular lattices. We prove a determinization lemma showing that lifting to sets or distributions yields a deterministic global dynamic, an ordinal stabilization theorem sending operator transforms to the fixed subspace by stage omega under normal spectral contraction, and a product of Riesz projections theorem for commuting layers. We establish a compositionality law for lifted maps, show closure of Phi packings, and present a quantitative application to sensory depletion that models tissue removal as a projection and derives strict decreases in the attainable fixed point under minimal monotonicity and positivity assumptions. We also state measurable conditions for probabilistic lifts, give explicit non normal and non commuting counterexamples, and provide finite dimensional and stochastic witnesses together with per theorem scope tables and a small reproducible code appendix.

Multimodal reasoning remains a fundamental challenge in artificial intelligence. Despite substantial advances in text-based reasoning, even state-of-the-art models such as GPT-o3 struggle to maintain strong performance in multimodal scenarios. To address this gap, we introduce a caption-assisted reasoning framework that effectively bridges visual and textual modalities. Our approach achieved 1st place in the ICML 2025 AI for Math Workshop \& Challenge 2: SeePhys, highlighting its effectiveness and robustness. Furthermore, we validate its generalization on the MathVerse benchmark for geometric reasoning, demonstrating the versatility of our method. Our code is publicly available at https://github.com/OpenDCAI/SciReasoner.

Modular approaches, which use a different composition of modules for each problem and avoid forgetting by design, have been shown to be a promising direction in continual learning (CL). However, searching through the large, discrete space of possible module compositions is a challenge because evaluating a composition's performance requires a round of neural network training. To address this challenge, we develop a modular CL framework, called PICLE, that accelerates search by using a probabilistic model to cheaply compute the fitness of each composition. The model combines prior knowledge about good module compositions with dataset-specific information. Its use is complemented by splitting up the search space into subsets, such as perceptual and latent subsets. We show that PICLE is the first modular CL algorithm to achieve different types of transfer while scaling to large search spaces. We evaluate it on two benchmark suites designed to capture different desiderata of CL techniques. On these benchmarks, PICLE offers significantly better performance than state-of-the-art CL baselines.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

While existing alignment paradigms have been integral in developing large language models (LLMs), LLMs often learn an averaged human preference and struggle to model diverse preferences across cultures, demographics, and communities. We propose Modular Pluralism, a modular framework based on multi-LLM collaboration for pluralistic alignment: it "plugs into" a base LLM a pool of smaller but specialized community LMs, where models collaborate in distinct modes to flexibility support three modes of pluralism: Overton, steerable, and distributional. Modular Pluralism is uniquely compatible with black-box LLMs and offers the modular control of adding new community LMs for previously underrepresented communities. We evaluate Modular Pluralism with six tasks and four datasets featuring questions/instructions with value-laden and perspective-informed responses. Extensive experiments demonstrate that Modular Pluralism advances the three pluralism objectives across six black-box and open-source LLMs. Further analysis reveals that LLMs are generally faithful to the inputs from smaller community LLMs, allowing seamless patching by adding a new community LM to better cover previously underrepresented communities.

Formal proofs are challenging to write even for experienced experts. Recent progress in Neural Theorem Proving (NTP) shows promise in expediting this process. However, the formal corpora available on the Internet are limited compared to the general text, posing a significant data scarcity challenge for NTP. To address this issue, this work proposes Alchemy, a general framework for data synthesis that constructs formal theorems through symbolic mutation. Specifically, for each candidate theorem in Mathlib, we identify all invocable theorems that can be used to rewrite or apply to it. Subsequently, we mutate the candidate theorem by replacing the corresponding term in the statement with its equivalent form or antecedent. As a result, our method increases the number of theorems in Mathlib by an order of magnitude, from 110k to 6M. Furthermore, we perform continual pretraining and supervised finetuning on this augmented corpus for large language models. Experimental results demonstrate the effectiveness of our approach, achieving a 5% absolute performance improvement on Leandojo benchmark. Additionally, our synthetic data achieve a 2.5% absolute performance gain on the out-of-distribution miniF2F benchmark. To provide further insights, we conduct a comprehensive analysis of synthetic data composition and the training paradigm, offering valuable guidance for developing a strong theorem prover.

We give a simple, fully correct, and assumption-light replacement for the contested "domain-extension" in Step 9 of a recent windowed-QFT lattice algorithm with complex-Gaussian windows~chen2024quantum. The published Step~9 suffers from a periodicity/support mismatch. We present a pair-shift difference construction that coherently cancels all unknown offsets, produces an exact uniform CRT-coset state over Z_{P}, and then uses the QFT to enforce the intended modular linear relation. The unitary is reversible, uses poly(log M_2) gates, and preserves the algorithm's asymptotics. Project Page: https://github.com/yifanzhang-pro/quantum-lattice.

We propose a new definition of higher-order DisCoCat (categorical compositional distributional) models where the meaning of a word is not a diagram, but a diagram-valued higher-order function. Our models can be seen as a variant of Montague semantics based on a lambda calculus where the primitives act on string diagrams rather than logical formulae. As a special case, we show how to translate from the Lambek calculus into Peirce's system beta for first-order logic. This allows us to give a purely diagrammatic treatment of higher-order and non-linear processes in natural language semantics: adverbs, prepositions, negation and quantifiers. The theoretical definition presented in this article comes with a proof-of-concept implementation in DisCoPy, the Python library for string diagrams.

Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this approach is advanced by stating and proving equivalent conditions for second-order stochastic dominance, a widely used way of comparing probability distributions by their spread. Furthermore, we lay foundation for the theory of comparing statistical experiments within Markov categories by stating and proving the classical Blackwell-Sherman-Stein Theorem. Our version not only offers new insight into the proof, but its abstract nature also makes the result more general, automatically specializing to the standard Blackwell-Sherman-Stein Theorem in measure-theoretic probability as well as a Bayesian version that involves prior-dependent garbling. Along the way, we define and characterize representable Markov categories, within which one can talk about Markov kernels to or from spaces of distributions. We do so by exploring the relation between Markov categories and Kleisli categories of probability monads.

As an efficient alternative to conventional full finetuning, parameter-efficient finetuning (PEFT) is becoming the prevailing method to adapt pretrained language models. In PEFT, a lightweight module is learned on each dataset while the underlying pretrained language model remains unchanged, resulting in multiple compact modules representing diverse skills when applied to various domains and tasks. In this paper, we propose to compose these parameter-efficient modules through linear arithmetic operations in the weight space, thereby integrating different module capabilities. Specifically, we first define addition and negation operators for the module, and then further compose these two basic operators to perform flexible arithmetic. Our approach requires no additional training and enables highly flexible module composition. We apply different arithmetic operations to compose the parameter-efficient modules for (1) distribution generalization, (2) multi-tasking, (3) unlearning, and (4) domain transfer. Additionally, we extend our approach to detoxify Alpaca-LoRA, the latest instruction-tuned large language model based on LLaMA. Empirical results demonstrate that our approach produces new and effective parameter-efficient modules that significantly outperform existing ones across all settings.

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find invariant representations of the data. These are representations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a {\em finite sample} setting, we consider the notion of epsilon-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen SEMs? This larger collection of SEMs is generated through a parameterized family of interventions. Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds probabilistically over a family of linear SEMs without faithfulness assumptions. Our results show bounds that do not scale in ambient dimension when intervention sites are restricted to lie in a constant size subset of in-degree bounded nodes. We also show how to extend our results to a linear indirect observation model that incorporates latent variables.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

Natural-language software requirements are often ambiguous, inconsistent, and underspecified; in safety-critical domains, these defects propagate into formal models that verify the wrong specification and into implementations that ship unsafe behavior. We show that large language models, equipped with an SMT solver, can audit such requirements: translating them into formal logic, detecting ambiguity through stochastic variation in the generated formalization, and exposing inconsistency, vacuousness, and safety violations through solver queries on the resulting specification. We present VERIMED, a neurosymbolic pipeline that operationalizes this idea for medical-device software requirements, and report two findings. First, stochastic variation across independent formalizations is a signal of ambiguity: requirements that admit multiple plausible interpretations produce SMT-inequivalent formalizations, and bidirectional SMT equivalence checking turns this disagreement into a solver-checkable test. Second, the usefulness of symbolic feedback depends on its granularity: in counterexample-guided repair on a hemodialysis question-answering benchmark, concrete SMT counterexamples raise verified accuracy from 55.4% to 98.5%. Over an extensive experimental evaluation on open-source hemodialysis safety requirements, we show that the LLM-based approach in VERIMED successfully reduces ambiguity-sensitive requirements and enables rigorous auditing of software requirements through SMT-based queries.

NVIDIA's CUTLASS library provides a robust and expressive set of methods for describing and manipulating multi-dimensional tensor data on the GPU. These methods are conceptually grounded in the abstract notion of a CuTe layout and a rich algebra of such layouts, including operations such as composition, logical product, and logical division. In this paper, we present a categorical framework for understanding this layout algebra by focusing on a naturally occurring class of tractable layouts. To this end, we define two categories Tuple and Nest whose morphisms give rise to layouts. We define a suite of operations on morphisms in these categories and prove their compatibility with the corresponding layout operations. Moreover, we give a complete characterization of the layouts which arise from our construction. Finally, we provide a Python implementation of our categorical constructions, along with tests that demonstrate alignment with CUTLASS behavior. This implementation can be found at our git repository https://github.com/ColfaxResearch/layout-categories.

Existing open-source multimodal large language models (MLLMs) generally follow a training process involving pre-training and supervised fine-tuning. However, these models suffer from distribution shifts, which limit their multimodal reasoning, particularly in the Chain-of-Thought (CoT) performance. To address this, we introduce a preference optimization (PO) process to enhance the multimodal reasoning capabilities of MLLMs. Specifically, (1) on the data side, we design an automated preference data construction pipeline to create MMPR, a high-quality, large-scale multimodal reasoning preference dataset. and (2) on the model side, we explore integrating PO with MLLMs, developing a simple yet effective method, termed Mixed Preference Optimization (MPO), which boosts multimodal CoT performance. Our approach demonstrates improved performance across multiple benchmarks, particularly in multimodal reasoning tasks. Notably, our model, InternVL2-8B-MPO, achieves an accuracy of 67.0 on MathVista, outperforming InternVL2-8B by 8.7 points and achieving performance comparable to the 10x larger InternVL2-76B. We hope this study could inspire further advancements in MLLMs. Code, data, and model shall be publicly released.

Multi-agent LLM systems share state through memory stores, vector indices, and tool registries. We model such sharing as long-running read-generate-write operations under deterministic-generation semantics -- the regime durable-execution engines enforce by deterministic replay -- and formalize four concurrency anomalies in TLA+: stale-generation, phantom-tool, causal-cascade, and tool-effect reordering, structural analogues of classical isolation anomalies, each with a TLC counter-example. The exclusion lattice over these anomalies is trivial; the contribution is the mechanically verified realizability and strict separation of one maximal chain within it, L_0 subsetneq cdots subsetneq L_4, to our knowledge the first machine-checked consistency hierarchy for such runtimes. A development of 274 Verus obligations (zero assume, zero admit; trust base: two structural axioms and a mutex correspondence) proves the detectors sound and complete against the specifications and each runtime its avoidance set. Three deployed Rust runtimes realize L0-L1 (pessimistic locking, serializable snapshot isolation, default-SI), each verified against stale-generation and refined to its state machine; L2-L4 are exec-mode-verified with dependency-free prevention twins (A3, A6, A2: 0/1000 versus 1000/1000), and L2 is run live across three model families (A3 prevented in all 120 retracted sessions). We reproduce a silent lost update in ByteDance's deer-flow, formalizing its fix as a verified L_0 to L_1 refinement, and exhibit tool-effect reordering in LangGraph's ToolNode on unmodified output, removed by an L3 commit-order sequencer. The verified detector, refinements, and realizability artifacts are the contribution; the phenomena and lattice are classical.

Recent advancements in Chain-of-Thoughts (CoT) and Program-of-Thoughts (PoT) methods have greatly enhanced language models' mathematical reasoning capabilities, facilitating their integration into instruction tuning datasets with LLMs. However, existing methods for large-scale dataset creation require substantial seed data and high computational costs for data synthesis, posing significant challenges for scalability. We introduce InfinityMATH, a scalable instruction tuning dataset for programmatic mathematical reasoning. The construction pipeline emphasizes decoupling numbers from mathematical problems to synthesize number-independent programs, enabling efficient and flexible scaling while minimizing dependency on specific numerical values. Fine-tuning experiments with open-source language and code models, such as Llama2 and CodeLlama, demonstrate the practical benefits of InfinityMATH. These fine-tuned models, showed significant relative improvements on both in-domain and out-of-domain benchmarks, ranging from 184.7% to 514.3% on average. Additionally, these models exhibited high robustness on the GSM8K+ and MATH+ benchmarks, which are enhanced version of test sets with simply the number variations. InfinityMATH ensures that models are more versatile and effective across a broader range of mathematical problems. The data is available at https://huggingface.co/datasets/flagopen/InfinityMATH.

Large Reasoning Models (LRMs) have significantly enhanced their capabilities in complex problem-solving by introducing a thinking draft that enables multi-path Chain-of-Thought explorations before producing final answers. Ensuring the faithfulness of these intermediate reasoning processes is crucial for reliable monitoring, interpretation, and effective control. In this paper, we propose a systematic counterfactual intervention framework to rigorously evaluate thinking draft faithfulness. Our approach focuses on two complementary dimensions: (1) Intra-Draft Faithfulness, which assesses whether individual reasoning steps causally influence subsequent steps and the final draft conclusion through counterfactual step insertions; and (2) Draft-to-Answer Faithfulness, which evaluates whether final answers are logically consistent with and dependent on the thinking draft, by perturbing the draft's concluding logic. We conduct extensive experiments across six state-of-the-art LRMs. Our findings show that current LRMs demonstrate selective faithfulness to intermediate reasoning steps and frequently fail to faithfully align with the draft conclusions. These results underscore the need for more faithful and interpretable reasoning in advanced LRMs.

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest shift/imbalance in covariates (i.e., secondary non-imaging data). Controlling for such nuisance variables is common within standard statistical analysis, but the ideas do not directly apply to overparameterized models. Consequently, recent work has shown how strategies from invariant representation learning provides a meaningful starting point, but the current repertoire of methods is limited to accounting for shifts/imbalances in just a couple of covariates at a time. In this paper, we show how viewing this problem from the perspective of Category theory provides a simple and effective solution that completely avoids elaborate multi-stage training pipelines that would otherwise be needed. We show the effectiveness of this approach via extensive experiments on real datasets. Further, we discuss how this style of formulation offers a unified perspective on at least 5+ distinct problem settings, from self-supervised learning to matching problems in 3D reconstruction.

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s geq 3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [J.-G. Young et al., Phys. Rev. E 96, 032312 (2017)], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analysis of higher-order phenomena based on local structures.

We develop a discipline-agnostic emergence calculus that treats theories as fixed points of idempotent operators acting on descriptions. We show that, once processes are composable but access to the underlying system is mediated by a bounded observational interface, a canonical toolkit of six closure-changing primitives (P1--P6) is unavoidable. The framework unifies order-theoretic closure operators with dynamics-induced endomaps E_{τ,f} built from a Markov kernel, a coarse-graining lens, and a time scale τ. We introduce a computable total-variation idempotence defect for E_{τ,f}; small retention error implies approximate idempotence and yields stable "objects" packaged at the chosen τ within a fixed lens. For directionality, we define an arrow-of-time functional as the path-space KL divergence between forward and time-reversed trajectories and prove it is monotone under coarse-graining (data processing); we also formalize a protocol-trap audit showing that protocol holonomy alone cannot sustain asymmetry without a genuine affinity in the lifted dynamics. Finally, we prove a finite forcing-style counting lemma: relative to a partition-based theory, definable predicate extensions are exponentially rare, giving a clean anti-saturation mechanism for strict ladder climbing.

As Large Reasoning Models (LRMs) are increasingly deployed, auditing their chain-of-thought (CoT) traces for safety becomes critical. Recent work has reported that monitorability--the degree to which CoT faithfully and informatively reflects internal computation--can appear as a "free gift" during the early stages of Reinforcement Learning with Verifiable Rewards (RLVR). We make this observation concrete through a systematic evaluation across model families and training domains. Our results show that this effect is not universal: monitorability improvements are strongly data-dependent. In particular, we demonstrate the critical role of data diversity and instruction-following data during RLVR training. We further show that monitorability is orthogonal to capability--improvements in reasoning performance do not imply increased transparency. Through mechanistic analysis, we attribute monitorability gains primarily to response distribution sharpening (entropy reduction) and increased attention to the prompt, rather than stronger causal reliance on reasoning traces. We also reveal how monitorability dynamics vary with controlled training and evaluation difficulty. Together, these findings provide a holistic view of how monitorability emerges under RLVR, clarifying when gains are likely to occur and when they are not.

This report overviews our ongoing work in enriching chain-of-thoughts datasets requiring arithmetical reasoning with the integration of non-parametric components, such as a calculator. We conduct an analysis of prominent relevant datasets such as GSM8K, Ape210K, AQuA-RAT, and MathQA and propose a machine-processable HTML-like format specifically tailored for working with semi-structured chains. By converting the datasets into this unified format, we enable the effective integration of large language models and symbolic systems, empowering them to tackle arithmetical reasoning tasks more efficiently.

We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal structure, mutually compatible (i.e. a bimonoidal structure). If the underlying monoidal category is cartesian monoidal, a bimonoidal structure is given uniquely by a commutative strength. However, if the underlying monoidal category is not cartesian monoidal, a strength is not enough to guarantee all the desired properties of joints and marginals. A bimonoidal structure is then the correct requirement for the more general case. We explain the theory and the operational interpretation, with the help of the graphical calculus for monoidal categories. We give a definition of stochastic independence based on the bimonoidal structure, compatible with the intuition and with other approaches in the literature for cartesian monoidal categories. We then show as an example that the Kantorovich monad on the category of complete metric spaces is a bimonoidal monad for a non-cartesian monoidal structure.