NeurIPS 2026 论文列表

Universal Transformers (UTs) show strong performance on abstract reasoning tasks such as ARC-AGI, yet the specific sources of their performance gains remain underexplored. We conduct systematic ablations over UT variants and find that performance improvements on abstract reasoning are driven primarily by (i) the recurrent inductive bias induced by parameter sharing across depth and (ii) strong nonlinearity inside the Transformer block, rather than by elaborate architectural heuristics. Motivated by this finding, we propose the Universal Reasoning Model (URM). First, we propose ConvSwiGLU, which augments the feed-forward block with a channel-wise short convolution to effectively enhance nonlinearity of UT. Second, we adopt Truncated Backpropagation Through Loops (TBPTL) to eliminate noise from early loop when training with many loops, by freezing the gradients of early loops. Our approach substantially improves abstract reasoning performance, achieving 57.5% pass@1 on ARC-AGI 1 and 16.0% pass@1 on ARC-AGI 2. More importantly, we pretrain a 8-billion-parameter large language model based on the URM architecture from scratch, and the results show that URM still substantially outperforms the baseline across all reasoning tasks.

Knowledge Graph Question Answering (KGQA) increasingly requires multi-turn interaction with knowledge graphs (KGs) to derive final answers. Such interactive capabilities often rely on proprietary large-scale LLMs, which hinders cost-efficient and local deployment. Reinforcement learning offers a scalable alternative for endowing smaller open-source LLMs with multi-turn interaction ability, as it enables models to improve from self-explored interaction trajectories rather than relying on expensive expert demonstrations. However, KGQA presents a distinctive challenge for RL: unlike tasks where exploration can proceed in a relatively unconstrained textual space, KG reasoning is governed by a sparse graph topology. Free-form policy rollouts frequently generate relation sequences that cannot be executed on the graph, making reward signals sparse and unstable. We propose ICOR, an Interactive Combinatorial Reinforcement Learning framework that grounds policy exploration in the combinatorial structure of KGs. ICOR first retrieves a query-specific set of candidate relations and then restricts policy rollouts to relation-path compositions within this graph-derived space. This design increases the likelihood that sampled trajectories are executable and thus informative for policy optimization. Building on this constrained rollout space, ICOR applies GRPO with a staged feedback mechanism that guides learning from structural validity to answer-consistent reasoning. Experiments on multiple KGQA datasets demonstrate the effectiveness of ICOR.

Modern LLM APIs often reveal only top-$K$ logit scores and censor the remaining vocabulary. We study the per-position distribution-recovery limits of this access model. For censoring threshold $\tau$, the compatible teacher distributions form an identified set whose total-variation diameter is exactly $U_K=(V{-}K)\exp(\tau)/(Z_A+(V{-}K)\exp(\tau)),$ where $Z_A$ is the observed partition function. For KL recovery, we give a computable binary-endpoint lower bound and an asymptotically matching small-ambiguity upper bound, with an extension to reference-aware attackers. Experiments on a Qwen3 math-reasoning teacher reveal a layered extraction hierarchy: on-task top-$K$ distillation recovers 12% of private capability, full-logit distillation recovers 56% despite 99% KL closure, and generation-based extraction recovers 96%. Top-$K$ censoring therefore limits per-position distribution recovery but does not by itself prevent capability extraction, separating fidelity from transfer in prompt-only logit distillation.

Self-evolution offers a scalable path to stronger reasoning: a pretrained language model improves itself with only minimal external supervision. Yet existing methods either depend on extensively curated or teacher-generated training data, or, when the generator runs unsupervised, reward it by a difficulty heuristic that need not improve the solver. We introduce **INFUSER**, an iterative co-training framework with two co-evolving roles: a *Generator* that drafts questions and reference golden answers from a pool of unstructured, automatically collected documents, and a *Solver* that improves by training on them. The solver is trained with standard correctness rewards against the generator-provided answers, while the generator is rewarded by an *optimizer-aware influence score* that measures whether each proposed question would actually improve the solver on the target distribution. Because this continuous, noisy influence score is poorly served by standard GRPO, we propose **DuGRPO**, a dual-normalized variant of GRPO, for generator training. Together, these turn the document pool into an *adaptive curriculum* that favors questions useful to the current solver, not just hard ones. On Qwen3-8B-Base, INFUSER outperforms strong self-evolution baselines with over 20% relative improvement on Olympiad and SuperGPQA benchmarks, and an 8B INFUSER co-evolving generator outperforms a frozen 32B thinking generator on math and coding. Ablations confirm each design choice is necessary. Code is available at

While reinforcement learning (RL) successfully enhances reasoning in large language models, its role in fostering compositional generalization (the ability to synthesize novel skills from known components) is often conflated with mere length generalization. To this end, we study what RL post-training teaches models about skill composition and how the composition structure affects the skill trasnfer. We focus on the \countdown{} task (given $n$ numbers and a target, form an expression that evaluates to the target) and analyze model solutions using expression trees, where each subtree corresponds to a reusable subtask and thus can be viewed as a ``skill.'' Tracking tree shapes and their success rates over training, we find: (i) out-of-distribution (OOD) generalization to larger $n$ and to unseen tree shapes, indicating compositional reuse of subtasks; (ii) the order of skill acquisition depends upon the composition structure---models master shallow balanced trees (workload is balanced between subtasks) before deep unbalanced ones, with persistent fragility on right-heavy structures for a fixed composition depth. Our diagnostic reveals what is learned, in what order, and where generalization fails, clarifying how RL-only post-training induces OOD generalization beyond what standard metrics such as pass@k reveal. To study the implication of our findings for more real-world tasks, we present a preliminary study on formal theorem proving.

Recent works have demonstrated that transformers can be trained to recover sparse, binary cryptographic secrets in the Learning With Errors (LWE) problem, a foundational problem that underlies many post-quantum cryptographic schemes. However, as architectures have evolved to efficient encoder-only models, the mechanism by which these models recover the cryptographic secret has become more opaque. In this paper, we present the first layer-wise and embedding-level mechanistic interpretability analysis of encoder-only transformers trained on LWE samples. We reveal a surprising phenomenon: despite achieving near-zero exact prediction accuracy on the training objective, the models successfully recover the secret by bypassing the standard predictive pathways. We use dimensionality reduction, causal intervention, and linear probing and find that the secret is implicitly present in the positional embedding. Building on this mechanistic understanding, we introduce an architectural intervention that applies $L_1$ sparsity regularization directly to the positional embeddings. This modification forces the model to explicitly isolate the latent secret, transforming the computationally expensive post-hoc secret recovery process into a direct, human-interpretable parameter inspection. Our findings provide fundamental insights into how transformers allocate representational capacity when faced with high-noise, structured combinatorial problems.

Open-vocabulary indoor scene synthesis aims to generate plausible layouts from arbitrary user instructions while ensuring physical feasibility and semantic consistency. Existing methods directly infer spatial relations between objects from instructions and solve for layouts based on predefined rules, achieving progress in physical feasibility. However, they often struggle to precisely align with complex instructions due to insufficient comprehension of spatial relations and limited capability to translate them into layouts. In this paper, we propose a Hierarchical Reasoning and Reflection agent framework (HierRR), which leverages a relational hierarchy to enable multi-granularity spatial relation comprehension and attributable layout reasoning, improving semantic consistency while maintaining physical feasibility. Specifically, HierRR introduces the spatial transformation chain‑of‑thought reasoning module that explicitly models the mapping from spatial relations to executable geometric placements, mitigating semantic drift during reasoning. Furthermore, the semantic- and vision-guided reflection module is employed to iteratively refine spatial relations and layout reasoning from local to global along the hierarchy, effectively bridging the gap between language instructions and geometric layouts. Extensive comparative experiments and ablation studies demonstrate that HierRR generates more plausible and semantically consistent indoor scene layouts than existing methods, while generalizing effectively to complex scenes with numerous objects and diverse spatial constraints.

Recent think-answer approaches in VLMs, such as Qwen3-VL-Thinking, boost reasoning performance by leveraging intermediate thinking steps before the final answer, but their high computational cost limits real-world deployment. To distill such capabilities into compact think-answer VLMs, a primary objective is to improve the student's ability to utilize visual evidence throughout its reasoning trace. To this end, we introduce a novel think-answer distillation framework that encourages the student to anchor its thinking on visual information by masking the student's salient reasoning prefixes. To compensate for such masked textual cues, the student is encouraged to rely more on visual evidence as an alternative source of information during distillation. Our masking strategies include: 1) $\textit{token-wise salient reasoning-prefix masking}$, which masks high-influence reasoning prefixes selectively for each next-token prediction, and 2) $\textit{self-paced masking budget scheduling}$, which gradually increases the masking scale according to distillation difficulty, {measured by discrepancy between teacher--student distributions. In the distillation phase, the student is guided by our salient reasoning-prefix mask, which blocks both future tokens and salient reasoning cues, in place of the standard causal mask used for auto-regressive language modeling. Experimental results show that our approach outperforms recent open-source VLMs, VLM distillation, and self-distillation methods on multimodal reasoning benchmarks, while further analyses confirm enhanced visual utilization along the student thinking process.

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to solve complex problems by generating intermediate reasoning steps. While much attention has been paid to the length and content of these reasoning chains, far less is known about their internal geometry. We study the *geometry* of CoT trajectories in the hidden state space of transformer models, formalizing each reasoning chain as a discrete curve in $\mathbb{R}^d$ and characterizing it through spectral, positional, and kinematic geometric functionals. We introduce the effective dimension $d_\rho$ as a measure of trajectory complexity and show theoretically that trajectories with flatter eigenvalue spectra correspond to harder tasks, as they explore more of the hidden dimensions. Lastly, we explore how kinematic features of the trajectory, mean position, positional dispersion, initial hidden states, mean velocity, mean speed, and speed dispersion, can be used to predict solution correctness before generation is complete, and may inform future early-stopping strategies. Experimentally, on mathematical reasoning problems from the MATH500 dataset, $d_\rho$ achieves 0.93 AUC in distinguishing easy from hard problems, while kinematic features show promise for predicting correctness from only the first 20% of generated tokens. These correctness signatures transfer across questions of varying difficulty, establishing that the *shape* of a model's internal reasoning trajectory is a principled window into both task hardness and solution quality.

Large language models solve complex problems by generating lengthy chains of explicit reasoning tokens. While effective, this makes reasoning expensive, length-sensitive, and constrained to (discrete) natural language. While latent reasoning offers a continuous alternative, determining useful structures for intermediate latent states is an open challenge. In this paper, we formulate latent reasoning as a geometric path-approximation problem within the model’s pretrained token-embedding space. We introduce Geometric Latent Reasoning (GLR), which uses a lightweight transition head to predict iterative direction updates in embedding space. Using textual chain-of-thought traces as anchors, GLR learns to approximate discrete reasoning trajectories while permitting continuous deviations from exact token embeddings. Evaluations on mathematical reasoning benchmarks using Qwen3 models reveal an emergent phenomenon: geometric latent reasoning induces substantially shorter generations without an explicit length objective. By replacing early explicit reasoning with continuous latent steps, models often reach correct answers using substantially fewer total generation steps. These findings suggest that continuous trajectories act as compact intermediate reasoning states, exposing a new tradeoff between latent computation budget, output length, and accuracy.

Geospatial reasoning requires solving image-grounded problems over complex object relationships and scene structures. However, developing this capability is hindered by the cost of annotating a vast and combinatorial question space. We propose GeoX, a self-play framework that acquires spatial logic through executable programs and verifiable rewards in the absence of large-scale human-curated data. Given a satellite or aerial image, our framework employs a single multimodal policy to alternate between proposing spatial problems with executable programs and solving them under three reasoning modes of abduction, deduction, and induction, using a segmentation tool and standard computational libraries. Program execution turns each program into a reward that jointly optimizes the two roles via reinforcement learning. GeoX consistently improves its base VLMs by up to 5.5 points on average, matching or exceeding conventional baselines trained on millions of curated samples. Alongside the framework, we release a benchmark for geospatial reasoning curated from self-play generations.

Several educational domains rely heavily on diagrams and visual cues, yet most existing tutoring datasets are limited to text-only interactions. This limits the development of AI tutors that can teach in visually grounded ways used by human instructors. Thus, we introduce GeoDial, a multimodal tutoring dataset of over 1.3K teacher-student dialogs in the domain of geometry collected from experienced math teachers, where instructional turns are explicitly grounded in diagram highlights. We propose a scalable annotation protocol that integrates dialog acts, visual highlighting, and feedback, enabling fine-grained supervision of both language and visual tutoring behavior. To illustrate the challenges posed by this setting, we fine-tune several vision–language models on GeoDial and evaluate their ability to generate tutoring utterances and diagram highlights. While supervised fine-tuning substantially improves the quality of generated dialog, it struggles to produce accurate diagram highlights, revealing a key limitation of current methods and highlighting the need for approaches that more effectively integrate visual reasoning with pedagogical interaction.

Multimodal Chain-of-Thought (CoT) reasoning has significantly advanced large models, yet forcing continuous visual evidence into discrete text or fixed tool calls inevitably sacrifices fine-grained detail. Recent paradigms attempt to reason directly within a continuous latent space; however, supervising latent slots in isolation fails to account for their collective geometry, resulting in a fragmented latent space that lacks structural guidance. To ensure structural integrity across training stages, we propose GeLVR(Geometry-Consistent Latent Visual Reasoning), a framework that establishes geometric consistency as a governing principle: the relational structure is explicitly aligned during SFT and actively preserved throughout RL, anchoring both stages to a common geometric scaffold. To operationalize this paradigm during the reward-driven phase, we further introduce GePO (Geometry-preserving Policy Optimization), a policy-optimization algorithm tailored for the hybrid discrete-continuous action spaces of latent reasoning. GePO employs a spherical von Mises-Fisher (vMF) policy to respect the decoder's inherent geometry and integrates the geometry-preserving regularizer directly into the RL objective. This ensures that reward optimization and structural integrity advance jointly rather than in tension. Extensive experiments across multiple visual reasoning benchmarks demonstrate that GeLVR consistently outperforms state-of-the-art baselines, particularly in high-resolution and fine-grained perception tasks. Comprehensive ablations further validate the necessity of each geometry-consistent component in establishing stable and coherent latent reasoning. Code is available in the supplementary materials.

Open-source native GUI agents still lag behind closed-source systems on long-horizon tasks. One reason is the direct reuse of generic post-training pipelines that ignore GUI-specific failure modes: standard supervised fine-tuning (SFT) with long chain-of-thought (CoT) reasoning often degrades grounding, and stronger offline optimization in RL does not necessarily translate to better online performance. This offline-to-online mismatch arises in part from \emph{partial verifiability}: multiple actions may validly advance a task, but supervision typically marks only one demonstrated action as correct, creating reward ambiguity. We present \textbf{GUI-Libra}, a data-efficient post-training recipe for reliable reasoning-and-acting in native GUI agents. GUI-Libra combines a construction and filtering pipeline for a curated 81K GUI reasoning dataset, \emph{action-aware supervised fine-tuning} that mixes reasoning-then-action and direct-action supervision with action-aware token reweighting, and KL-constrained RL with success-adaptive scaling to improve offline-to-online predictability under ambiguous rewards. Across web and mobile benchmarks, GUI-Libra consistently improves both step-wise accuracy and end-to-end task completion. GUI-Libra-4B and GUI-Libra-8B improve their base models by +15.6\% and +12.2\% on AndroidWorld, +4.0\% and +8.7\% on Online-Mind2Web, and +12.5\% and +11.3\% on WebArena-Lite-v2. These results show that careful reasoning data curation and tailored post-training can substantially improve long-horizon task solving without costly online data collection. We release our dataset, code, and models to support future research.

Knowledge distillation from large reasoning models (LRMs) often uses raw teacher trajectories as supervision. However, this practice creates a mismatch between the goal of distillation and the nature of teacher trajectories. Advanced LRMs typically improve their reasoning capabilities through reward-driven post-training, such as RLHF. This training optimizes them as strong solvers, rather than as teachers that produce reasoning processes smaller models can easily learn. Since smaller models have different "cognitive capacities" compared to their larger teachers, directly imitating raw teacher trajectories can sometimes be ineffective and often requires a substantial number of high-quality samples. To bridge this mismatch, we propose **C**ognition-**A**ligned **R**easoning **D**istillation (**CARD**), an RL-based framework that transforms solver trajectories into teaching trajectories aligned with the student’s cognition. Avoiding expensive resampling, our framework directly transforms existing trajectories. We optimize CARD with two reward signals: (1) a Distribution Alignment Reward that matches the student’s predictive distribution, and (2) a Logical Coherence Reward that reduces misleading failed reasoning steps. Comprehensive evaluations across multiple student models and settings demonstrate that CARD outperforms distillation from raw teacher trajectories in in-domain settings while achieving substantial gains in out-of-distribution performance.

Reinforcement learning from verifiable rewards (RLVR) has shown strong promise for LLM reasoning, but typical outcome-based RLVR methods remain inefficient on hard problems. Correct final-answer rollouts are rare, and standard sample-level credit assignment fails to leverage partial reasoning progress embedded in unsuccessful attempts. To address this problem, we introduce **SCRL** (**S**ubproblem **C**urriculum **R**einforcement **L**earning), a curriculum reinforcement learning framework built on verifiable subproblems derived from reasoning chains. Given a reference solution, SCRL derives a series of verifiable subproblems and constructs a subproblem curriculum, with the final subproblem fixed as the original problem. This converts partial progress on hard problems into verifiable learning signals. Algorithmically, we propose *subproblem-level normalization*, a training technique based on RLVR that normalizes rewards independently at each subproblem position within the rollout group. By assigning the resulting advantages to the corresponding answer spans, we enable finer-grained credit assignment without external rubrics or reward models. Our theoretical analysis shows that this subproblem curriculum makes hard problems more learnable by lifting them out of gradient dead zones, with larger relative gains as the original problem becomes harder. Across seven mathematical reasoning benchmarks, SCRL outperforms strong curriculum-learning baselines, yielding +4.1 and +1.9 average-point gains compared to GRPO on Qwen3-4B-Base and Qwen3-14B-Base respectively. On three hard benchmarks (AIME24, AIME25, and IMO-Bench), SCRL further yields point gains of +3.7 in pass@$1$ and +4.6 in pass@$64$ on Qwen3-4B-Base, suggesting improved exploration on hard reasoning problems. Further ablations show that the proposed credit assignment is effective and that the gains do not require highly curated subproblems or strong external generators, highlighting SCRL as a practical curriculum framework that enables fine-grained credit assignment for LLM reasoning.

Reasoning across multiple long-form videos requires models to find sparse evidence within each video and link related entities, events, and narratives across streams. Existing long-video benchmarks mainly evaluate single-video understanding, while multi-video benchmarks typically use short clips. We introduce CLoVR-Bench, a comprehensive benchmark for Cross-Long-Video Reasoning with 2,000 expert-annotated QA pairs over 400 long-form videos. Its three-level taxonomy covers Comparative Analysis, Tracking and Retrieval, and Integrated Reasoning, spanning 14 tasks and 36 subtasks that diagnose both intra-video localization and inter-video alignment. Our evaluation of 13 representative MLLMs shows substantial gaps across this hierarchy, with performance degrading from localized comparison to long-range retrieval and integrated cross-video reasoning. We further propose HOLMES, a training-free framework that formulates cross-long-video reasoning as evidence-slot filling over a typed binding graph. HOLMES plans option-discriminating evidence slots, localizes evidence with risk-conditioned policies, records coverage certificates for failed searches, verifies cross-video bindings visually, audits constraints, and returns answers through hard graph-readout gates. Experiments show that HOLMES improves both open-source and closed-source backbones, outperforms adapted long-video baselines, and yields the largest gains on tasks requiring long-range evidence search and cross-video binding. Together, CLoVR-Bench and HOLMES provide a diagnostic testbed and an interpretable baseline for future cross-long-video reasoning.

Looped-in-depth architectures provide an inductive bias toward learning step-by-step procedures for tasks that require compositional reasoning. The effective depth reached by looping determines the quality of the solution. Similar to deep architectures, looped architectures are prone to signal propagation issues as the halting decision is postponed. In this paper, we address these signal propagation issues by using pre-norm layers and residual scaling. Furthermore, we propose ***FPRM***: a Fixed-Point Reasoning Model that uses fixed-point convergence as an end-to-end halting mechanism in a looped architecture. We show that fixed-point halting allows FPRM to adapt its compute to the difficulty of the task. FPRM proves effective on common reasoning benchmarks, namely sudoku, maze, and state tracking.

Large language models can now generate complex, multi-step mathematical proofs, but reliably determining their correctness and localizing early logical errors remains a critical challenge. Existing evaluation approaches largely depend on model-based natural-language judgments, which often overlook local reasoning gaps. While formal theorem provers like Lean offer a path to rigorous verification, using them to evaluate informal text requires solving locality and semantic mismatches: a prover might bypass a local flaw by proving an overly broad target, or validate an auto-formalized statement that drifts from the original mathematical intent. To address this, we introduce FaithSieve, a Lean-assisted framework for fine-grained evaluation of natural-language mathematical proofs. FaithSieve decomposes coarse proof steps into local reasoning units, extracts typed proof obligations, and verifies them through a formal evaluation agent. Formal validation is gated by semantic alignment scoring, so Lean evidence is incorporated only when the formal statement faithfully preserves the context, objects, and logical form of the original claim. We construct two expert-verified datasets, ProofLoc-Olympiad and ProofLoc-University, to benchmark first-error localization. On the 350-problem Olympiad dataset, FaithSieve using a GPT-5.4 backbone achieves 81.43\% exact first-error accuracy, outperforming the direct-judging baseline of 72.29\%. Furthermore, on the 200-problem ProofLoc-University benchmark spanning six advanced domains, FaithSieve reaches 84.5\% exact accuracy, compared to 75.0\% for the direct judge. Our work demonstrates that decomposing proofs into fine-grained units and grounding them with faithful formal evidence significantly improves reliable evaluation of natural-language reasoning.