Large Language Model Reasoning

Post-training techniques combined with inference-time scaling significantly enhance the reasoning and alignment capabilities of large language models (LLMs). However, a fundamental tension arises: inference-time methods benefit from diverse sampling from a relatively flattened probability distribution, whereas reinforcement learning (RL)-based post-training inherently sharpens these distributions. To address this, we propose Exploration-Driven Optimization (EDO), which extends reward-biasing style exploration objectives to iterative post-training and integrates them into standard RL objectives, encouraging greater diversity in sampled solutions while facilitating more effective inference-time computation. We incorporate EDO into iterative Direct Preference Optimization (iDPO) and Group Relative Policy Optimization (GRPO), resulting in two variants: ED-iDPO and ED-GRPO. Extensive experiments demonstrate that both ED-iDPO and ED-GRPO exhibit greater solution diversity and improved reasoning abilities, particularly when combined with test-time computation techniques like self-consistency. Across three in-distribution reasoning benchmarks, EDO achieves a 1.0-1.3% improvement over the strongest baselines, and delivers an additional 1.5% average gain on five out-of-distribution tasks. Beyond accuracy, EDO preserves model entropy and stabilizes RL training dynamics, highlighting its effectiveness in preventing over-optimization collapse. Taken together, these results establish EDO as a practical framework for balancing exploration and exploitation in LLM reasoning, especially in settings that rely on test-time scaling.

While extremely powerful and versatile at various tasks, the thinking capabilities of large language models (LLMs) are often put under scrutiny as they sometimes fail to solve problems that humans can systematically solve. However, recent literature focuses on breaking LLM reasoning with increasingly complex problems, and whether an LLM is robust in simple logical reasoning remains underexplored. This paper proposes Absurd World, a benchmarking framework, to test LLMs against altered realism, where scenarios are logically coherent, and humans can easily solve the tasks. Absurd World breaks a real-world model into symbols, actions, sequences, and events, which are automatically altered to create absurd worlds where the logic to solve the tasks remains the same. It evaluates a large collection of models with simple and advanced prompting techniques, and proves that it is an effective tool to determine LLMs' ability to think logically, ignoring the patterns learned from the real world. One can use this framework to extensively test an LLM against a real-world problem to verify whether the LLM's reasoning capability is robust against variations of the task.

When should a language model answer directly, sample and vote, or engage in multi-agent debate? Recent work shows voting often explains much of the gain attributed to debate, while selective-debate systems activate deliberation only on uncertain examples. We ask: under a matched ceiling on generated tokens (960 per example), how much per-example routing headroom exists, and how much is recoverable from cheap pre-deliberation signals? We evaluate greedy decoding, three-sample voting, and a two-agent critique-revise debate on MuSiQue and GSM8K using Llama 3.1 8B Instruct and Ministral 3 8B Instruct. On MuSiQue, an oracle selecting the correct protocol per example gains +14.0 and +13.7 pp over the best fixed one. The best fixed protocol is model- and dataset-dependent: each (model, dataset) cell has a different winner. This headroom is hard to recover from cheap ex-ante signals. A vote-entropy threshold is the only controller that directionally beats the best fixed protocol on both models (+1.3 and +1.7 pp), though individual paired-bootstrap CIs include zero. A joint analysis (meta-analysis +1.6 pp, p=0.125; Bayesian P(both>0)=0.59) is directionally consistent but not significant. Learned controllers (LR, GBT) do not outperform the threshold. The key finding is structural: vote entropy predicts where debate is safe, not where debate is needed. High entropy sharply reduces debate backfire, but 66% of debate-helpful examples (31/47) occur when voting is unanimous but wrong. A single-prompt self-critique probe on Llama flips the answer in 127/127 unanimous cases, yielding zero mutual information with the debate-helpful label; we cannot rule out a prompt-compliance artifact, but either interpretation disqualifies the probe as a router. Recovering the remaining headroom requires behavioral probes that avoid format-compliance confounds at the 8B scale.

Although large language models rely on chain-of-thought for complex reasoning, the overthinking phenomenon severely degrades inference efficiency. Existing reinforcement learning methods compress reasoning chains by designing elaborate reward functions, which renders high-quality samples extremely sparse in the exploration space and creates a sampling bottleneck for the prior policy. Inspired by cognitive science, we theoretically prove that a posterior distribution guided by reference answers achieves higher expected utility than the prior distribution, thus capable of breaking through the sampling bottleneck of high-quality samples. However, the posterior distribution is unavailable during inference. To this end, we formalize efficient reasoning as a variational inference problem and introduce an efficiency-aware evidence lower bound as the theoretical foundation. Based on this, we propose the VPG-EA framework. It adopts a parameter-shared dual-stream architecture to instantiate both the posterior distribution and the prior policy; after filtering out pseudo-efficient paths via cross-view evaluation, it unidirectionally transfers the posterior's efficient patterns to the prior policy through variational distillation. Experiments on DeepSeek-R1-Distill-Qwen-1.5B and 7B scales demonstrate that VPG-EA improves the comprehensive efficiency metric epsilon cubed by 8.73% and 12.37% over the strongest baselines on each model size, respectively.

Large language models (LLMs) have achieved remarkable progress in mathematical reasoning, but this ability is not equally accessible across languages. Especially low-resource languages exhibit much lower reasoning performance. To address this, we propose Crosslingual On-Policy Self-Distillation (COPSD), which transfers a model's own high-resource reasoning behavior to low-resource languages. COPSD uses the same model as student and teacher: the student sees only the low-resource problem, while the teacher receives privileged crosslingual context, including the problem translation and reference solution in English. Training minimizes full-distribution token-level divergence on the student's own rollouts, providing dense supervision while avoiding the sparsity and instability of outcome-only reinforcement learning (RL). Experiments on 17 low-resource African languages show that COPSD consistently improves low-resource mathematical reasoning across model sizes and substantially outperforms Group Relative Policy Optimization (GRPO). Further analyses show that COPSD improves answer-format adherence, strengthens test-time scaling, and generalizes to harder multilingual reasoning benchmarks, with especially large gains for lower-resource languages. We make our code and data available at: https://github.com/cisnlp/COPSD.

Reasoning LLMs produce thousands of chain-of-thought tokens whose KV cache must reside in scarce GPU HBM. The dominant response -- permanently evicting low-importance tokens -- is catastrophic for reasoning: accuracy collapses to 0-2.5% when half the cache is removed. We ask a different question: must every token live in HBM, or can some live elsewhere? We introduce a semantics-aware memory hierarchy that sorts tokens into four tiers -- HBM, DDR, compressed, and evicted -- using cumulative attention scoring. Low-importance tokens are moved to CPU memory rather than destroyed; before each attention step they are prefetched back at full precision, contributing exactly the same terms as if they had never left the GPU. We formalize this as zero-approximation-error offloading and derive our central finding: accuracy depends solely on how many tokens are permanently discarded (the eviction ratio), not on how many remain in HBM. A controlled 3x3 grid over HBM and eviction ratios confirms this across three model scales (7B-32B) and four benchmarks. With only 3% eviction, the hierarchy retains 91% of full-cache accuracy on GSM8K and 71% on MATH-500 (n=200); at 14B scale it matches the uncompressed baseline (90% vs. 86%) while halving HBM occupancy. A head-to-head reproduction of R-KV -- the current SOTA eviction method -- on our setup achieves only 0-32% at comparable budgets. A system prototype with real GPU-CPU data movement shows that the price of this preservation is modest -- 5-7% transfer overhead -- and scaling analysis projects 2-48 GB HBM savings at production batch sizes.

The Chain-of-Thought (CoT) paradigm, while enhancing the interpretability of Large Language Models (LLMs), is constrained by the inefficiencies and expressive limits of natural language. Latent Chain-of-Thought (latent CoT) reasoning, which operates in a continuous latent space, offers a promising alternative but faces challenges from structural complexities in existing multi-step or multi-model paradigms, such as error propagation and coordination overhead. In this paper, we introduce One-Model One-Step, a novel compression framework for Latent Reasoning with Rule-Based Priors(RuPLaR) to address this challenge. Our method trains an LLM to autonomously generate latent reasoning tokens in a single training stage, guided by rule-based prior probability distributions, thereby eliminating cascaded processes and inter-model dependencies. To ensure reasoning quality, we design a joint training objective that enforces answer consistency via cross-entropy, aligns soft tokens with rule-based priors via KL divergence (the Soft Thinking constraint), and adds a problem-thought semantic alignment constraint in the representation space. Extensive experiments show that our compression framework not only improves accuracy by 11.1% over existing latent CoT methods but also achieves this with minimal token usage, underscoring its effectiveness and extensibility. Code: https://github.com/xiaocen-luo/RuPLaR.

Recent work shows that large language models (LLMs) encode behavioural traits ("personas") as linear directions in activation space, often called "persona vectors". Prior work has used such directions as static handles for behavioural steering. Building on this, we treat them as dynamic signals instead: probes we can monitor and intervene on as reasoning unfolds. We use the term polylogue to denote the time series of alignments between persona vectors and hidden activations over the course of generation. Experiments across four open-weight models show that polylogue features predict correctness on MMLU-Pro competitively with low-dimensional activation baselines, while remaining interpretable through their associated persona directions. They also suggest concrete steering targets, namely which latent directions to modulate at different stages of a response. We instantiate this as a simple paragraph-conditioned intervention that improves accuracy on three of four models, pointing to stage-aware latent steering as a promising direction for reasoning-time control. Together, this positions the polylogue as an interpretable tool for reasoning-time monitoring and intervention.

Despite surpassing human performance across mathematics, coding, and other knowledge-intensive tasks, large language models (LLMs) continue to struggle with causal reasoning. A core obstacle is the target data itself: causal systems are complex and often expressed in non-executable forms, while ground-truth answers to causal queries are inherently scarce. We introduce CauSim, a framework that turns causal reasoning from a scarce-label problem into a scalable supervised one. CauSim constructs increasingly complex causal simulators: executable structural causal models (SCMs), incrementally built by LLMs, that scale to globally complex systems while maintaining verifiable answers to causal queries. CauSim operates across representations by formalizing non-executable causal knowledge into code, enabling data augmentation, and translating executable SCMs into natural language, enabling supervision in previously difficult-to-supervise representations. We structure our research into two parts: (1) how to construct increasingly complex causal simulators, and (2) a systematic study of what CauSim enables, demonstrating generalization across representations, consistent gains from curriculum scaling and data volume, LLM self-improvement through self-generated simulators, and data augmentation via formalization of existing domain knowledge.

Large Language Models (LLMs) are increasingly deployed as autonomous agents that execute tool-augmented, multi-step tasks, where latency is a critical factor for real-world applications. Yet an overlooked threat is Reasoning-Level Denial-of-Service (R-DoS), in which an attacker preserves task correctness but degrades availability by inflating an agent's reasoning depth or tool-use budget. We introduce OTora, the first unified, two-stage red-teaming framework for instantiating R-DoS attacks. Stage I optimizes an adversarial trigger that induces targeted tool invocations using insertion-aware scoring and dynamic target co-evolution, supporting both black-box and white-box settings. Stage II generates agent-aware reasoning payloads via an ICL-guided genetic search that amplifies overthinking while maintaining correct task outcomes. Across WebShop, Email, and OS agents built on multiple backbone models such as LLaMA-70B and GPT-OSS-120B, OTora achieves up to 10 times increases in reasoning tokens and order-of-magnitude latency slowdowns, all while preserving near-baseline task accuracy. Finally, we discuss mitigation strategies for detecting and constraining abnormal reasoning and latency spikes. The code is available at https://github.com/llm2409/OTora.

Reasoning-centric large language models (LLMs) achieve strong performance by generating intermediate reasoning trajectories, but often incur excessive token usage and high inference-time decoding cost. We observe that, when solving the same problems, larger reasoning models can often produce more concise traces, whereas smaller reasoning models tend to generate longer and more redundant trajectories. This is especially problematic in real-world deployment, where memory, latency, and serving-cost constraints often favor smaller models. Our observations suggest that reasoning compression can be transferred from large models to small ones rather than enforced through explicit length constraints. Based on this insight, we propose Mixed-Policy Distillation (MPD), a reasoning compression framework that transfers concise reasoning behavior from a larger-sized teacher to a smaller student by distilling teacher-compressed student trajectories. Unlike on-policy distillation, which aligns the student with teacher distributions over verbose student trajectories, or off-policy distillation, which relies on teacher-generated trajectories and may suffer from distribution mismatch, MPD combines the strengths of both. Given a student-sampled trajectory, the teacher rewrites it into a more concise reasoning trace, and the student is trained via KL-based alignment on the compressed trajectory. This preserves student-policy exploration while injecting teacher-guided compression. Experiments on Qwen3-1.7B show that MPD reduces token usage by up to 27.1% while improving performance across multiple reasoning benchmarks, demonstrating an effective approach to efficient small-model reasoning.

Traditional simulation methods reproduce occurred emergency instances through presetting to assist people in risk assessment and emergency decision-making. However, due to the lack of randomness and diversity, existing simulation systems struggle to fully explore the potential risk as emergency instances are scarce. In contrast, Large Models (LMs) can dynamically adjust generation strategies to introduce controllable randomness, while also possessing extensive prior knowledge and cross-domain knowledge transfer capabilities. Inspired by it, we propose the LMs-driven World Line Divergence System (WLDS), which enables diversified visualization and deduction of emergency instances in different domains. WLDS leverages LMs to deduce emergency instances in various development directions, and introduces the factual calibration and logical calibration mechanism to ensure factual accuracy and logical rigor during the deduction process. The interactive module can independently select deduction directions to avoid potential hallucinations that are difficult for the system to identify. Furthermore, by introducing the visualization module, WLDS forms simulation and deduction that combine text and images, which enhances interpretability. Extensive experiments conducted on the proposed Emergency Instances Deduction (EID) benchmark dataset demonstrate that WLDS achieves high-precision and high-fidelity simulation and deduction of emergency instances in multiple specific domains. Relevant experiments further demonstrate that WLDS can generate more emergency instances deduction data for users and provide support for better decision-making in similar emergency instances in the future.

The effectiveness of Reinforcement Learning (RL) in Large Language Models (LLMs) depends on the nature and diversity of the data used before and during RL. In particular, reasoning problems can often be approached in multiple ways that rely on different forms of reasoning, and exposure to only a limited range of such approaches in the training data may limit the effectiveness of RL. Motivated by this, we investigate using diverse self-generated data during mid-training as an intermediate step before RL training. Specifically, we adopt a bootstrapped data-generation framework guided by George Polya's problem-solving approaches for generating multiple variants of correct answers for each question in the training data, and then perform fine-tuning. We first provide a theoretical perspective on how mid-training on such data improves RL and explain how policy-gradient updates can incentivize combining multiple approaches. We then empirically demonstrate that RL-trained models initialized with our mid-training data achieve consistent improvements across various mathematical reasoning benchmarks and other OOD tasks like code generation and narrative reasoning. Overall, our investigative study shows that a language model learning multiple problem-solving approaches, through self-generated data helps subsequent RL.

Recent advances in large language models (LLMs) have demonstrated remarkable reasoning capabilities, largely stimulated by Reinforcement Learning with Verifiable Rewards (RLVR). However, existing RL algorithms face a fundamental limitation: their exploration remains largely constrained by the inherent capability boundary of the policy model. Although recent methods introduce external expert demonstrations to extend this boundary, they typically rely on complete trajectory-level guidance, which is sample-inefficient, information-sparse, and may confine exploration to a static guidance space. Inspired by the potential of multi-agent systems, we propose $\textbf{AIPO}$, an enhanced reinforcement learning framework that improves LLM reasoning through active multi-agent interaction during exploration. Specifically, AIPO enables the policy model to proactively consult three functional collaborative agents, $\textit{Verify Agent}$, $\textit{Knowledge Agent}$, and $\textit{Reasoning Agent}$, when encountering reasoning bottlenecks, thereby receiving fine-grained and targeted guidance to actively expand its capability boundary during training. We further introduce a tailored importance sampling coefficient together with a clipping strategy to mitigate the off-policy bias and gradient vanishing issues that arise when learning from agent-provided feedback. After training, the policy model performs reasoning independently without relying on collaborative agents. Extensive experiments on diverse reasoning benchmarks, including AIME, MATH500, GPQA-Diamond, and LiveCodeBench, show that AIPO consistently improves reasoning performance, generalizes robustly across different policy models and RLVR algorithms, and effectively expands the reasoning capability boundary of the policy model.

While recent advancements in inference-time learning have improved LLM reasoning on Text-to-SQL tasks, current solutions still struggle to perform well on the most challenging tasks in the Bird-Bench (BIRD) benchmark. This is due to inadequate solution space exploration, which is necessary to uncover promising candidate queries that can be further refined to produce the correct output. To address this challenge, we introduce CA-SQL, a novel Text-to-SQL pipeline that utilizes the estimated difficulty of a task to dynamically scale the breadth of the exploration for generating solution candidates. In addition, we use a custom prompt seeding method, based on principles of evolutionary search, to further elicit exploratory behavior from the base LLM and a novel voting method to select the best candidate solution at the end of the search. Experiments demonstrate that our solution achieves a state-of-the-art score of 51.72% on the "challenging" tier of BIRD development set problems, using only GPT-4o-mini, out-performing other in-context learning approaches, even those that leverage larger models. Overall, our method attains a competitive 61.06% execution accuracy and 68.77% Soft F1 score on the BIRD development dataset.

Recent efforts to improve the reasoning abilities of Large Language Models (LLMs) have focused on integrating formal logic solvers within neurosymbolic frameworks. A key challenge is that formal solvers lack commonsense world knowledge, preventing them from making reasoning steps that humans find obvious. Prior methods address this by using LLMs to supply missing commonsense assumptions, but these approaches implicitly assume universal agreement on such commonsense facts. In reality, commonsense beliefs vary across individuals. We propose a probabilistic framework for abductive commonsense reasoning that explicitly models this variation, aiming to determine whether most people would judge a statement as true or false. We introduce Probabilistic Abductive CommonSense (PACS), a novel algorithm that uses an LLM and a formal solver to sample proofs as observations of individuals' distinct commonsense beliefs, and aggregates conclusions across these samples. Empirically, PACS outperforms chain-of-thought reasoning, prior neurosymbolic methods, and search-based approaches across multiple benchmarks.

Robot swarms promise scalable assistance in complex and hazardous environments. Task planning lies at the core of human-swarm collaboration, translating the operator's intent into coordinated swarm actions and helping determine when validation or intervention is required during execution. In long-horizon missions under dynamic scenarios, however, reliable task planning becomes difficult to maintain: emerging events and changing conditions demand continual adaptation, and sustained operator oversight imposes substantial cognitive burden. Existing LLM-based planning tools can support plan generation, yet they remain susceptible to invalid task orderings and infeasible robot actions, resulting in frequent manual adjustment. Here we introduce a neuro-symbolic framework for long-horizon human-swarm collaboration that tightly melds verifiable task planning with context-grounded LLM reasoning. We formalize mission goals and operational rules as temporal logic formulas and admissible task orderings as task automata. Conditioned on these formal constraints and live perceptual context, LLMs generate executable subtask sequences that satisfy mission rules and remain grounded in the current scene. An uncertainty-aware scheduler then assigns subtasks across the heterogeneous swarm to maximize parallelisms while remaining resilient to disruptions. An event-triggered interaction protocol further limits operator involvement to sparse, high-level confirmation and guidance. Deployment on a heterogeneous robotic fleet yields similar results while remaining robust to hardware-specific actuation and communication uncertainties. Together, these results support a formal and scalable paradigm for reliable and low-overhead human-swarm collaboration in dynamic environments

Language model (LM) "reasoning", commonly described as Chain-of-Thought or test-time scaling, often improves benchmark performance, but the dynamics underlying this process remain poorly understood. We study these dynamics through the lens of uncertainty quantification by treating the "reasoning" traces, the intermediate token sequences generated by LMs, as evolving model states. We summarize each trace by an uncertainty trace profile: a small set of features describing the shape of the uncertainty signal over its trace, such as its slope and linearity. We find that across five LMs evaluated on GSM8K and ProntoQA, these profiles predict whether a trace yields a correct final answer with AUROC up to 0.807, improving markedly on recent related work. We reach AUROC 0.801 using only the first few hundred tokens of full traces, suggesting that errors can be detected early in the generation. A detailed comparison of correct and incorrect traces further reveals qualitatively distinct uncertainty profiles, with correct traces showing a steeper and less linear decline in uncertainty. Together, the results suggest that our method, grounded in decision-making under uncertainty, provides a principled lens for studying the generative process underlying LM "reasoning".

Tool-integrated reasoning (TIR) is difficult to scale to small language models due to instability in long-horizon tool interactions and limited model capacity. While reinforcement learning methods like group relative policy optimization provide only sparse outcome-level rewards. Recently, on-policy distillation (OPD) has gained popularity by supplying dense token-level supervision from a teacher on student-generated trajectories. However, our experiments indicate that applying OPD to TIR leads to a critical failure mode: erroneous tool calls tend to cascade across subsequent reasoning steps, progressively amplifying student-teacher divergence and rendering the teacher's token-level supervision increasingly unreliable. To address this, we propose SOD, a step-wise on-policy distillation framework for small language model agents, which adaptively reweights distillation strength at each step based on step-level divergence. Therefore, SOD can attenuate potentially misleading teacher signals in high-divergence regions while preserving dense guidance in well-aligned states. Experiments on challenging math, science, and code benchmarks show that SOD achieves up to 20.86% improvement over the second-best baseline. Notably, our 0.6B student achieves 26.13% on AIME 2025, demonstrating effective transfer of agentic reasoning to lightweight models. Our code is available at https://github.com/YoungZ365/SOD.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a pivotal technique for enhancing the reasoning capabilities of Large Language Models (LLMs). However, the de facto practice of mainstream RL algorithms is to treat all tokens of one response equally and assign the same optimization objective to each token, failing to provide granular guidance for the reasoning process. While in Chain-of-Thought (CoT) reasoning, different tokens usually play distinct roles. Therefore, the current RL algorithms lack an effective mechanism to dynamically balance the exploration-exploitation trade-off during learning. To this end, we propose Hierarchical Token-level Objective Control Policy Optimization (HTPO), a novel RL algorithm that takes the divide-and-conquer idea to hierarchically partition the response tokens into specific functional groups from three aspects (i.e., prompt difficulty, answer correctness, and token entropy). Within each group, according to the contributions to exploration or exploitation, we design specialized optimization objectives to facilitate the effective execution of each token's expected functionality. In this way, HTPO can achieve a more balanced exploration-exploitation trade-off. Extensive experiments on challenging reasoning benchmarks validate the superiority of our HTPO algorithm, which significantly outperforms the strong DAPO baseline (e.g., +8.6% and +6.7% on AIME'24 and AIME'25, respectively). When scaling test-time compute, the HTPO-trained model maintains a consistent performance advantage over the DAPO baseline, and the gap widens as the sampling budget increases, validating that our adaptive token-level control method fosters effective exploration without sacrificing exploitation performance. Code will be at https://github.com/xcyao00/HTPO.

Large reasoning models often reach correct answers through flawed intermediate steps, creating a gap between final accuracy and reasoning reliability. Existing alignment strategies address this with external verifiers or massive sampling, limiting scalability. In this work, we introduce CASPO (Confidence-Aware Step-wise Preference Optimization), a framework that aligns token-level confidence with step-wise logical correctness through iterative Direct Preference Optimization, without training a separate reward model. During inference, we propose Confidence-aware Thought (CaT), which leverages this calibrated confidence to dynamically prune uncertain reasoning branches with negligible O(V) latency. Experiments across ten benchmarks and multiple model families show that CASPO consistently improves reasoning reliability and inference efficiency. CASPO scales to Qwen3-8B-Base and surpasses tree-search baselines on AIME'24 and AIME'25 without using reward-model data. We also release a step-wise dataset with confidence annotations to support fine-grained analysis of reasoning reliability. Code is available at https://github.com/Thecommonirin/CASPO.

Modern reasoning language models generate dense, sequential chain-of-thought traces implicitly assuming that every token contributes and that steps must be consumed in order. We challenge both assumptions through a systematic intervention pipeline--removal, masking, shuffling, and noise injection--applied to model-generated reasoning chains across three models and three benchmarks. Our findings are counterintuitive on three dimensions. Order: Does the sequential order of a reasoning chain matter for answer extraction? No--line-level shuffling reduces accuracy by less than 0.5 pp; word-level shuffling retains 62%-89% accuracy; only token-level shuffling collapses to near zero. Pretrained-only and instruction-tuned variants exhibit near-identical tolerance (78.67% vs. 78.00% under line shuffling), indicating order-independence originates from pretraining rather than reasoning-specific fine-tuning. Dense: Is all the information in a reasoning chain important for answer extraction? No--masking numeric digits collapses accuracy to exactly 0%, while masking alphabetic prose improves accuracy by 4.7 pp. Robustness: Is a reasoning chain that is both order-shuffling and non-dense still robust? Yes--the most aggressively reduced representation (all natural language removed, lines arbitrarily shuffled) still achieves 83% accuracy, and injecting false answers at 3x true-answer frequency leaves accuracy unchanged (83.3%->83.3%), falsifying a frequency-based extraction account. These results establish that answer extraction operates on a sparse, order-insensitive, and structurally robust informational substrate, opening paths toward parallelized and token-efficient reasoning generation.

Training a family of large language models (LLMs), either from scratch or via iterative compression, is prohibitively expensive and inefficient, requiring separate training runs for each model in the family. In this paper, we introduce Star Elastic, a novel LLM post-training method that adds N nested submodels to a given parent reasoning model using the compute of one run (N-fold savings) via a single post-training job. Beyond reducing training costs, Star Elastic also addresses a fundamental limitation of efficient reasoning: the rigidity of static architectures, which forces the allocation of constant resources regardless of token difficulty. By unlocking elastic budget control, Star Elastic enables a novel inference scheme that uses different submodels for each reasoning phase (thinking and answering). Star Elastic supports (1) nesting along the SSM, embedding channel, MoE, and FFN axes, (2) learning nested submodels via an end-to-end trainable router, and (3) curriculum-based knowledge distillation. Building on the Nemotron Elastic framework, we apply Star Elastic to the NVIDIA Nemotron Nano models, with a particular focus on hybrid Mixture-of-Experts (MoE) architectures: from Nemotron Nano v3 (30B/3.6A), we generate 23B (2.8A) and 12B (2.0A) variants with 160B training tokens. All nested models match or outperform independently trained baselines of comparable size and achieve a 360x reduction versus pretraining from scratch and a 7x reduction over state-of-the-art compression. Crucially, elastic budget control advances the accuracy-latency Pareto frontier, achieving up to 16% higher accuracy and 1.9x lower latency via dynamic per-phase model selection. We further extend Star Elastic to quantized regimes via Quantization-Aware Distillation (QAD), producing nested NVFP4 and FP8 elastic checkpoints that preserve zero-shot slicing while delivering smaller deployment footprints.

Reinforcement learning (RL) has achieved remarkable success in LLM reasoning, but whether it can also improve direct recall of parametric knowledge remains an open question. We study this question in a controlled zero-shot, one-hop, closed-book QA setting with no chain-of-thought, training only on binary correctness rewards and applying fact-level train-test deduplication to ensure gains reflect improved recall rather than reasoning or memorization. Across three model families and multiple factual QA benchmarks, RL yields ~27% average relative gains, surpassing both training- and inference-time baselines alike. Mechanistically, RL primarily redistributes probability mass over existing knowledge rather than acquiring new facts, moving correct answers from the low-probability tail into reliable greedy generations. Our data-attribution study reveals that the hardest examples are the most informative: those whose answers never appear in 128 pre-RL samples (only ~18% of training data) drive ~83% of the gain, since rare correct rollouts still emerge during training and get reinforced. Together, these findings broaden the role of RL beyond reasoning, repositioning it as a tool for unlocking rather than acquiring latent parametric knowledge.

Reinforcement learning with verifiable rewards (RLVR) has become a highly effective method for improving the reasoning abilities of Large Language Models (LLMs). Recent research shows that Negative Sample Reinforcement (NSR) -- which focuses on penalizing incorrect steps rather than simply rewarding correct ones -- can match or even exceed the performance of more complex frameworks like PPO and GRPO across the entire Pass@k spectrum. However, current NSR techniques usually apply a fixed penalty throughout the training process and treat every incorrect response with the same weight. To address these limitations, we propose two extensions to the NSR framework: Adaptive Negative Sample Reinforcement. Rather than using a fixed update rule, A-NSR uses time-dependent scheduling functions. In the initial training phases, the system focuses heavily on correcting errors to stabilize the model. As training continues, it shifts toward more subtle and controlled updates. We also introduce Confidence-Weighted Negative Reinforcement, which operates on the principle that different mistakes carry different levels of importance. CW-NSR assigns specific penalty weights based on the model's normalized sequence likelihood. If the model is highly confident in a wrong path, it receives a larger penalty and for uncertain errors -- where the model is effectively exploring -- are penalized less strictly. Our formal analysis shows how these mechanisms govern token-level updates, allowing the model to leverage prior-guided probability redistribution while providing a natural defense against overfitting. We evaluated these methods on difficult reasoning datasets, including MATH, AIME 2025, and AMC23, using the Qwen2.5-Math-1.5B architecture.

Large Language Models (LLMs) have achieved great improvements in recent years. Nevertheless, it still remains unclear how good LLMs are for reasoning tasks, especially for long-chain ones. In this paper, we evaluate LLMs' performance on the simplest yet long-chain reasoning task, namely the Equivalence Class Problem (ECP), i.e., determining whether two variables are equal given a set of randomly generated equivalence relations. We consider both reasoning and non-reasoning representative LLMs over a large variety of problem instances, ranging over different numbers of variables, connectivity probabilities, prompts, and other factors. The experimental results show that non-reasoning LLMs fail ECP, while reasoning models are significantly better but still struggle to completely solve this problem. Interestingly, considering various connectivity probabilities with a fixed number of variables, we observe that, for non-reasoning models, the hardest problem instances coincide with the phase transition point of ln n/(n-1), suggesting the chaos of the problem; in contrast, for reasoning models, the hardest ones coincide with the biggest diameter, suggesting the reasoning difficulty of the problem.

Large language models (LLMs), especially reasoning models, generate extended chain-of-thought (CoT) reasoning that often contains explicit deliberation over future outcomes. Yet whether this deliberation constitutes genuine planning, how it is structured, and what aspects of it drive performance remain poorly understood. In this work, we introduce a new method to characterize LLM planning by extracting and quantifying search trees from reasoning traces in the four-in-a-row board game. By fitting computational models on the extracted search trees, we characterize how plans are structured and how they influence move decisions. We find that LLMs' search is shallower than humans', and that performance is predicted by search breadth rather than depth. Most strikingly, although LLMs expand deep nodes in their traces, their move choices are best explained by a myopic model that ignores those nodes entirely. A causal intervention study where we selectively prune CoT paragraphs further suggests that move selection is driven predominantly by shallow rather than deep nodes. These patterns contrast with human planning, where performance is driven primarily by deep search. Together, our findings reveal a key difference between LLM and human planning: while human expertise is driven by deeper search, LLMs do not act on deep lookahead. This dissociation offers targeted guidance for aligning LLM and human planning. More broadly, our framework provides a generalizable approach for interpreting the structure of LLM planning across strategic domains.

Large Language Models (LLMs) demonstrate strong capabilities for solving scientific and mathematical problems, yet they struggle to produce valid, challenging, and novel problems - an essential component for advancing LLM training and enabling autonomous scientific research. Existing problem generation approaches either depend on expensive human expert involvement or adopt naive self-play paradigms, which frequently yield invalid problems due to reward hacking. This work introduces VHG, a verifier-enhanced hard problem generation framework built upon three-party self-play. By integrating an independent verifier into the conventional setter-solver duality, our design constrains the setter's reward to be jointly determined by problem validity (evaluated by the verifier) and difficulty (assessed by the solver). We instantiate two verifier variants: a Hard symbolic verifier and a Soft LLM-based verifier, with evaluations conducted on indefinite integral tasks and general mathematical reasoning tasks. Experimental results show that VHG substantially outperforms all baseline methods by a clear margin.

Reinforcement learning (RL) has been applied to improve large language model (LLM) reasoning, yet the systematic study of how training scales with task difficulty has been hampered by the lack of controlled, scalable environments. Observed LLM shortcomings in long-horizon reasoning have raised the prospect that they are fundamental to the autoregressive transformer architecture. To address this, we introduce ScaleLogic, a synthetic logical reasoning framework that offers independent control over two axes of difficulty: the depth of the required proof planning (i.e., the horizon) and the expressiveness of the underlying logic. Our proposed framework supports a wide range of logics: from simple implication-only logic ("if-then") towards more expressive first-order reasoning with conjunction ("and"), disjunction ("or"), negation ("not"), and universal quantification ("for all"). Using this framework, we show that the RL training compute $T$ follows a power law with respect to reasoning depth $D$ ($T \propto D^γ$, $R^{2} > 0.99$), and that the scaling exponent $γ$ increases monotonically with logical expressiveness, from $1.04$ to $2.60$. On downstream mathematics and general reasoning benchmarks, more expressive training settings yield both larger performance gains (up to $+10.66$ points) and more compute-efficient transfer compared to less expressive settings, demonstrating that what a model is trained on, not just how much it is trained, shapes downstream transfer. We further show that the power-law relationship holds across multiple RL methods, and curriculum-based training substantially improves scaling efficiency. More broadly, our results demonstrate that LLM shortcomings in long-horizon reasoning are not fundamental to the underlying architecture, and can be addressed by improved training methodology and data.

Reinforcement learning has become the standard for improving reasoning in large language models, yet evidence increasingly suggests that RL does not teach new strategies; it redistributes probability mass over solutions the base model already contains. In this work, we ask: if RL merely steers the model toward paths it already knows, is the RL optimization loop itself necessary? Through token-level analysis across multiple model families and RL algorithms, we find that RL's beneficial footprint is a sparse, predictable correction concentrated at high-entropy decision points where the model is uncertain which branch to take. Only 1--3% of token positions are affected, the promoted token always lies within the base model's top-5 alternatives, and targeted corrections at those few positions causally recover a large fraction of RL's accuracy gain, while random corrections fail. The base model's own entropy identifies these positions without any RL-trained model, and the entire correction is low-dimensional, representable in a tiny fraction of model parameters. These findings reframe reasoning improvement as sparse policy selection, not capability acquisition. We translate this insight into ReasonMaxxer, a minimal RL-free method that applies contrastive loss only at entropy-gated decision points, using a few hundred base-model rollouts and no online generation. Across three model families, six scales, and six math reasoning benchmarks, ReasonMaxxer matches or exceeds full RL performance while requiring only tens of problems and minutes of single-GPU training, a reduction in training cost of roughly three orders of magnitude.

Although advances such as chain-of-thought, tree-of-thought or reinforcement learning have improved the performance of LLMs in reasoning and planning tasks, they are still brittle and have not achieved human-level performance in many domains, and often suffer from high time and token costs. Inspired by the success of width-based search in planning, we explore how the concept of novelty can be transferred to language domains and how it can improve tree-of-thought reasoning. A tree of thoughts relies on building possible "paths" of consecutive ideas or thoughts. These are generated by repeatedly prompting an LLM. In our paper, a measurable concept of novelty is proposed that describes the uniqueness of a new node (thought) in comparison to nodes previously seen in the search tree. Novelty is estimated by prompting an LLM and making use of embedded general knowledge from pre-training. This metric can then be used to prune branches and reduce the scope of the search. Although this method introduces more prompts per state, the overall token cost can be reduced by pruning and reducing the overall tree size. This procedure is tested and compared using several benchmarks in language-based planning and general reasoning.

Verifiers are crucial components for enhancing modern LLMs' reasoning capability. Typicalverifiers require resource-intensive superviseddataset construction, which is costly and faceslimitations in data diversity. In this paper, wepropose LOVER, an unsupervised verifier regularized by logical rules. LOVER treats theverifier as a binary latent variable, utilizinginternal activations and enforcing three logical constraints on multiple reasoning paths:negation consistency, intra-group consistency,and inter-group consistency (grouped by thefinal answer). By incorporating logical rulesas priors, LOVER can leverage unlabeled examples and is directly compatible with any offthe-shelf LLMs. Experiments on 10 datasetsdemonstrate that LOVER significantly outperforms unsupervised baselines, achieving performance comparable to the supervised verifier(reaching its 95% level on average). The sourcecode is publicly available at https://github.com/wangxinyufighting/llm-lover.

Current reasoning paradigms for LLMs include chain-of-thought, ReAct, and post-hoc self-critique. These paradigms rely on two assumptions that fail on long-horizon, multi-stage tasks. As a result, errors accumulate silently across reasoning steps, leaving an open question: can a reasoning system effectively detect and recover from its own failures? We present ReFlect, a \emph{harness} system for LLM reasoning that creates standalone error detection and recovery logic as a deterministic wrapper around the model. Controlled experiments across 6 reasoning domains show that prompt-level self-critique produces formulaic templates that flag no issues in 90 of 100 audited reflection blocks, and the investigated LLMs wrongly accept a wrong answer in at least 76% of cases. Our ReFlect harness achieves task success rates ranging from 41% on gpt-4o-mini to 56% on Claude Sonnet 4.5 across six models spanning small and frontier scale, with per-model gains over Direct CoT ranging from +7 pp on Qwen2.5-72B to +29 pp on Claude Sonnet 4.5, and additionally raises SWE-bench patch-structural quality from 0% (Direct CoT) to between 82% (Qwen2.5-72B) and 87% (GPT-4o). Notably, the harness gain is inversely proportional to the model's Direct CoT task success rate (the fitted slope is -1.69 with r=-0.76): each pp lost in baseline success rate is mechanically recovered by 1.69 pp of harness gain. We spot that adding structured reasoning state and operators yields only 15.0--18.7% pair-mean on Llama-3.3-70B and Qwen2.5-72B because models at this scale cannot reliably populate the state its operators require. ReFlect is model-agnostic, training-free, and operates entirely at inference time.

Reinforcement learning with verifiable rewards, particularly Group Relative Policy Optimization (GRPO), has significantly advanced the reasoning capabilities of Large Language Models (LLMs). However, in complex tasks, GRPO frequently suffers from the ``zero-advantage problem'': when all sampled rollouts for a query fail, the relative advantage collapses to zero. Consequently, the model loses effective training signals for these questions, wasting the training data and computational budget. While simply increasing the sampling budget for these questions is a common remedy, the static sampling policy inherently constrains reasoning exploration, limiting the success rate. In this paper, we propose Lorem Perturbation for Exploration (LoPE), a simple yet effective training framework to break this exploration bottleneck. We posit that task-irrelevant prompt-space perturbations can shift the model's output distribution enough to unlock orthogonal reasoning pathways for hard questions. Specifically, LoPE prepends sequences stochastically assembled from Lorem Ipsum vocabulary (a pseudo-Latin placeholder text) to the prompts before resampling. Experiments across 1.7B, 4B, and 7B models demonstrate that LoPE significantly outperforms resampling with the original prompts. Further analysis reveals that other Latin-based random sequences with low perplexity are also effective perturbations. Our results establish LoPE as a strong baseline for broadening exploration in LLM reinforcement learning.

LLMs can solve program synthesis tasks but remain inefficient and unreliable on hard instances requiring large combinatorial search. Given a small set of reasoning traces, we use coding agents to compile them into reusable symbolic program synthesizers over constrained DSLs. The resulting solvers require no LLM calls at test time and are strong standalone systems: symbolic solver ensembles reach 91.3% accuracy on PBEBench-Lite and 84.7% on PBEBench-Hard, outperforming LLMs with test-time scaling for the latter by +16.3 percentage points at zero LLM inference cost. They also complement LLM search, improving PBEBench-Hard accuracy from 68.4% to 85.8% while reducing reported token usage by 78%, and raising SLR-Bench hard-tier accuracy from 34.4% to 58.0% in a neuro-symbolic hybrid setting. Compared to directly using coding agents as per-instance solvers, induced solvers are substantially more Pareto-efficient, amortizing a small one-time construction cost over many zero-token executions. Finally, most solvers transfer zero-shot to a real historical linguistics task - predicting sound changes in natural language data - reaching 80.1% accuracy under ensembling and recovering some plausible linguistic rules. Together, these results show that reasoning traces can be compiled into reusable symbolic solvers that solve many tasks directly, complement LLM inference on hard cases, and provide a scalable route to domain-general solver induction. We release code and data for reproducibility.

Large language models increasingly operate in interactive settings where solving a task requires multiple rounds of information exchange with a user. However, most current systems treat dialogue reactively and lack a principled mechanism to reason about what information is missing and which question should be asked next. We propose BALAR (Bayesian Agentic Loop for Active Reasoning), a task-agnostic outer-loop algorithm that requires no fine-tuning and enables structured multi-turn interaction between an LLM agent and a user. BALAR maintains a structured belief over latent states, selects clarifying questions by maximizing expected mutual information, and dynamically expands its state representation when the current one proves insufficient. We evaluate BALAR on three diverse benchmarks: AR-Bench-DC (detective cases), AR-Bench-SP (thinking puzzles), and iCraft-MD (clinical diagnosis). BALAR significantly outperforms all baselines across all three benchmarks, with $14.6\%$ higher accuracy on AR-Bench-DC, $38.5\%$ on AR-Bench-SP, and $30.5\%$ on iCraft-MD.

This paper describes our system submitted to SemEval-2026 Task 11: Disentangling Content and Formal Reasoning in Large Language Models. We present an efficient modular neuro-symbolic approach, combining a symbolic prover with small reasoning LLMs (4B parameters). The system consists of an LLM-based parser that translates natural language syllogisms to a first-order logic (FOL) representation, an automated theorem prover, and two optional modules: machine translation for multilingual inputs and a symbolic retrieval component for the identification of relevant premises. The system achieves competitive accuracy and relatively low content effect on most subtasks. Our ablations show that this approach outperforms LLM-based zero-shot baselines in this parameter size range, but also reveal limited multilingual capabilities of small LLMs. Finally, we include a discussion of the task's main ranking metric and analyze its limitations.

This paper presents NoisyCoconut, a novel inference-time method that enhances large language model (LLM) reliability by manipulating internal representations. Unlike fine-tuning methods that require extensive retraining, NoisyCoconut operates directly on model representations during inference and requires no retraining. Rather than training models to reason in latent space, we inject controlled noise into latent trajectories to generate diverse reasoning paths. Agreement among these paths provides a confidence signal, enabling models to abstain when uncertain. We demonstrate that this approach achieves effective coverage-accuracy tradeoffs across multiple reasoning benchmarks without requiring access to training data or modification of model parameters. This approach provides a practical pathway to improving the reliability of LLM outputs while maintaining compatibility with existing models. Our experiments show that unanimous agreement among noise-perturbed paths reduces error rates from 40-70% to below 15%, enabling models to exceed 95% accuracy on mathematical reasoning tasks through selective abstention.

Can LLMs simulate how humans form and change beliefs in social networks? We put this to the test by replicating an established study on belief dynamics, evaluating 12 LLMs across multiple model families and parameter sizes. The answer is a clear no, and in systematic ways. LLMs fail to capture initial human belief distributions and tend to be overall more conformist than humans, shifting their responses to align with those around them. They also take a nuanced approach to emulating human homophilic tendencies within networks. Our findings carry a double payoff: they highlight fundamental properties of LLM behavior, and they raise a sharp warning against deploying LLMs as human proxies in social simulations.

Causal reasoning in natural language requires identifying relevant variables, understanding their interactions, and reasoning about effects and interventions, often under noisy or ambiguous conditions. While large language models (LLMs) exhibit strong general reasoning abilities, they struggle to disentangle correlation from causation, particularly when observations are partially incorrect or irrelevant information is present. In this work, we introduce NoisyCausal, a new benchmark designed to evaluate causal reasoning under structured noise. Each instance is generated from a ground-truth causal graph and contextualized with a natural language scenario by injecting controllable forms of noise, such as irrelevant distractors, value perturbations, confounding, and partial observability. Moreover, we propose a modular reasoning framework that combines LLMs with explicit causal structure to address these challenges. Our method prompts the LLM to extract variables, construct a causal graph from context, and then reformulates the reasoning task as a structured prompt grounded in this graph. Rather than relying on statistical patterns alone, the LLM is guided by symbolic structure, enabling more interpretable and robust inference. Experimental results show that our method significantly outperforms standard prompting and reasoning baselines on NoisyCausal. Furthermore, it generalizes well to external benchmarks such as Cladder without task-specific tuning. Our findings highlight the importance of combining causal abstractions with language-driven reasoning to achieve faithful and robust causal understanding in LLMs.

Large Language Models (LLMs) are increasingly explored as high-level reasoning engines for cyber-physical systems, yet their application to real-time UAV swarm management remains challenging due to heterogeneous interfaces, limited grounding, and the need for long-running closed-loop execution. This paper presents a mission-agnostic, agent-enhanced LLM framework for UAV swarm control, where users express mission objectives in natural language and the system autonomously executes them through grounded, real-time interactions. The proposed architecture combines an LLM-based Agent Core with a Model Context Protocol (MCP) gateway and a Web-of-Drones abstraction based on W3C Web of Things (WoT) standards. By exposing drones, sensors, and services as standardized WoT Things, the framework enables structured tool-based interaction, continuous state observation, and safe actuation without relying on code generation. We evaluate the framework using ArduPilot-based simulation across four swarm missions and six state-of-the-art LLMs. Results show that, despite strong reasoning abilities, current general-purpose LLMs still struggle to achieve reliable execution - even for simple swarm tasks - when operating without explicit grounding and execution support. Task-specific planning tools and runtime guardrails substantially improve robustness, while token consumption alone is not indicative of execution quality or reliability.

In single-stream autoregressive interfaces, the same tokens both update the model state and constitute an irreversible public commitment. This coupling creates a silence tax: additional deliberation postpones the first task-relevant content, while naive early streaming risks premature commitments that bias subsequent generations. We introduce Side-by-Side (SxS) Interleaved Reasoning, which makes disclosure timing a controllable decision within standard autoregressive generation. SxS interleaves partial disclosures with continued private reasoning in the same context, but releases content only when it is supported by the reasoning so far. To learn such pacing without incentivizing filler, we construct entailment-aligned interleaved trajectories by matching answer prefixes to supporting reasoning prefixes, then train with SFT to acquire the dual-action semantics and RL to recover reasoning performance under the new format. Across two Qwen3 architectures/scales (MoE Qwen3-30B-A3B, dense Qwen3-4B) and both in-domain (AIME25) and out-of-domain (GPQA-Diamond) benchmarks, SxS improves accuracy--content-latency Pareto trade-offs under token-level proxies such as inter-update waiting.

Travel planning serves as a critical task for long-horizon reasoning, exposing significant deficits in LLMs. However, existing benchmarks and evaluations primarily assess final plans in an end-to-end manner, which lacks interpretability and makes it difficult to analyze the root causes of failures. To bridge this gap, we decompose travel planning into five constituent atomic sub-capabilities, including \emph{Constraint Extraction}, \emph{Tool Use}, \emph{Plan Generation}, \emph{Error Identification}, and \emph{Error Correction}. We implement a decoupled evaluation protocol leveraging oracle intermediate contexts to rigorously isolate these components, thereby measuring the atomic performance boundary without the noise of cascading errors. Our results highlight a clear contrast in performance: while LLMs are proficient in extracting explicit constraints, they struggle to infer implicit, open-world requirements. Furthermore, they exhibit structural biases in plan generation and suffer from ineffective self-correction, characterized by excessive sensitivity and erroneous persistence. These findings offer precise directions for improving LLM reasoning and planning abilities.

Large language models (LLMs) can generate syntactically valid optimization programs, yet often struggle to reliably choose an effective modeling strategy, leading to incorrect formulations and inefficient solver behavior. We propose SAGE, a strategy-aware framework that makes Modeling Strategy explicit in both data construction and post-training. SAGE builds a solver-verified multi-strategy dataset and trains a student model with supervised fine-tuning followed by Segment-Weighted GRPO using a composite reward over format compliance, correctness, and solver efficiency. Across eight benchmarks spanning synthetic and real-world settings, SAGE improves average pass@1 from 72.7 to 80.3 over the strongest open-source baseline. With multiple generations, SAGE discovers more distinct correct formulations and improves component-level diversity at pass@16 by 19-29%. At the largest scale, SAGE produces more compact constraint systems with 14.2% fewer constraints than the baseline, consistent with solver-efficient modeling. Overall, these results show that making Modeling Strategy explicit improves automated optimization modeling. Code is available at https://github.com/rachhhhing/SAGE.

With the rapid advancement of large language models (LLMs), classic graph learning tasks have greatly benefited from LLMs, including improved encoding of textual features, more efficient construction of graphs from text, and enhanced reasoning over knowledge graphs. In this paper, we ask a complementary question: How can graphs help LLMs? We address this question from three perspectives: 1) graphs provide an up-to-date knowledge source that helps reduce LLM hallucinations, 2) graph-based prompting techniques-such as Chain-of-Thought (CoT), Tree-of-Thought (ToT), and Graph-of-Thought (GoT)-enhance LLM reasoning capabilities, and 3) integrating graphs into LLMs improves their understanding of structured data, expanding their applicability to domains such as e-commerce, code, and relational databases (RDBs). We further outlook some future directions including designing sparse LLM architectures based on graphs and brain-inspired memory systems.

Recent diffusion large language models (dLLMs) have demonstrated both effectiveness and efficiency in reasoning via a block-based semi-autoregressive generation paradigm. Despite their progress, the fixed-size block generations remain a critical bottleneck for effective and coherent reasoning. 1. From a global perspective, different reasoning tasks would correspond to different optimal decoding block sizes, which makes a ``one-size-fits-all'' assumption ineffective. 2. Even within a single reasoning task, the rigid block partitioning would break the logical flow and reduce reasoning coherence. Through empirical observations, we reveal that for block-wise entropy, incorrect reasoning exhibits a fluctuating and unsteady trend between blocks, whereas the correctly generated tasks follow a consistent descending trend. Therefore, this paper proposes b1, a novel post-training framework for dLLMs that learns dynamic-size reasoning blocks via a Monotonic Entropy Descent objective with reinforcement learning to enhance reasoning coherence.b1 integrates seamlessly as a plug-and-play module with existing dLLM's post-training algorithms. Extensive experiments across various reasoning benchmarks showcase b1's consistent improvement over existing fixed-size block baselines. Our code has been released at https://github.com/YanJiangJerry/Block-R1.

Mathematical reasoning is a key benchmark for large language models. Reinforcement learning is a standard post-training mechanism for improving the reasoning capabilities of large language models, yet performance remains sensitive to the design of the reward function that drives policy optimization. This paper introduces a search-driven framework that treats the reward specification itself as an object of optimization. The setting of interest is one in which the base model is held fixed and the reward specification is the primary remaining design lever. Candidate reward functions are generated by a frontier language model, validated automatically, screened through 500-step Group Relative Policy Optimization (GRPO) training runs on a Llama-3.2-3B-Instruct base model with Low-Rank Adaptation (LoRA), and ranked by F1 on the GSM8K test set. Ranked summaries from prior rounds are then fed back into the next round of generation. Over five rounds, the search produces 50 candidate rewards. The mean F1 rises from 0.596 in Round 1 to 0.632 in Round 5, and the top individual reward reaches F1 = 0.787. Seven ensemble configurations of top-ranked rewards are evaluated. The best ensemble achieves F1 = 0.795 (95% bootstrap CI [0.756, 0.832]) and accuracy 0.660 [0.635, 0.686], a 0.19 absolute F1 gain over a base-rewards-only GRPO baseline (F1 = 0.609). Pairwise McNemar tests with Bonferroni correction show all five-or-more-reward configurations are statistically indistinguishable at α = 0.05/21. A three-seed re-training of the best ensemble yields F1 of 0.785. A randomly drawn 5-reward control collapses to F1 = 0.047, which shows that the ranked-feedback loop, not the additive signal of having more rewards, drives the gain.

When copies of the same language model are prompted to debate, they produce diverse phrasings of one perspective rather than diverse perspectives. Multi-agent debate (MAD), and more broadly closed-system reasoning where agents iteratively transform each other's outputs, tends to preserve answer accuracy while degrading the reasoning behind those answers. We name the multi-agent case the Debate Trap and the broader phenomenon the Reasoning Trap, offering a programmatic theory of evidence-grounded reasoning failure.The framework has three parts: (i) SFS (Supported Faithfulness Score), a claim-level metric verifying decomposed atomic claims against provided evidence (decomposer-invariant rankings: Spearman rho=1.0); (ii) EGSR (Evidence-Grounded Socratic Reasoning), replacing adversarial argumentation with evidence-grounded inquiry; (iii) Theorem 1 (DPI Bound): under standard MAD, the chain E -> O^0 -> O^1 -> ... is Markov, and the Data Processing Inequality implies E[I(E;O^{t+1})] <= E[I(E;O^t)]. Three companion results -- open-system recovery (Theorem 2), EGSR accumulation (Lemma 2), and vote-aggregation floor (Proposition 1) -- partition multi-step LLM reasoning by its information-theoretic relationship to E. Across 16 conditions on SciFact (300 claims) and FEVER (1,000 claims), DebateCV (C13) preserves 88% of baseline accuracy while SFS drops 43%; majority-vote MAD (C15) reduces SFS to 1.7% of baseline (p < 10^{-6}, d = -0.96); EGSR recovers 98%. An R6 cohort study (Korean n=10x30 FEVER; English n=3x200 SciFact) finds inter-rater Fleiss kappa <= +0.018 with 0.8-1.4 Likert intra-rater shifts across language and domain -- the human agreement that faithfulness metrics have been calibrated against is not itself stable. We offer one falsifiable conjecture: any closed-system reasoning protocol preserving Theorem 1's Markov structure is, in expectation, subject to the same DPI bound.

Reasoning in large language models is predominantly evaluated through labeled benchmarks, conflating task performance with the quality of internal inference. Here we study reasoning as an intrinsic dynamical process by examining the evolution of internal representations during inference. We find that inference-time dynamics consistently self-organize into low-dimensional manifolds embedded within high-dimensional representation spaces. we find that such geometric compression, although pervasive, is not sufficient for stable or reliable reasoning. Instead, effective reasoning dynamics emerge within a constrained structural regime characterized by three conditions: adequate representational expressivity, spontaneous manifold compression, and preservation of non-degenerate information volume within the compressed subspace. Models outside this regime exhibit characteristic pathological inference dynamics. Based on these insights, we introduce a unified, label-free diagnostic computed solely from internal dynamics. These findings suggest that reasoning in LLMs is fundamentally governed by geometric and informational constraints, offering a complementary framework to benchmark-centric assessment.

Reasoning language models often generate long chain-of-thought (CoT), which accumulates a massive KV cache during the decoding phase and incurs high decoding latency and limited throughput. To address these issues, KV cache compression has emerged as a promising technique for reducing memory overhead by selectively removing unimportant KV pairs while preserving useful ones for subsequent decoding. Nevertheless, we identify two key limitations in existing KV cache compression methods: 1) their threshold-triggered compression policy may provide limited throughput improvement or even reduce throughput, and may fully eliminate KV pairs from certain blocks of the sequence, potentially worsening information loss. 2) they typically retain either isolated KV pairs or fixed-size chunks with rigid boundaries, failing to preserve important flexible-sized chunks at arbitrary token positions. To overcome these limitations, we propose Kara, a sliding-window KV cache compression method that performs decoding-time compression by operating only on the recently generated context. Kara leverages bidirectional attention to score and select informative KV pairs in the window. To enable flexible preservation of important semantic information, we design a Token2Chunk module to expand a subset of selected KV pairs into chunks. Furthermore, we adapt Kara to PagedAttention and develop KvLLM, an inference framework built upon vLLM, which reduces KV cache memory usage and effectively improves output throughput. Extensive experiments demonstrate consistent performance improvements of proposed Kara and KvLLM.

Reinforcement Learning with Verifiable Rewards (RLVR) enhances reasoning of Large Language Models (LLMs) but usually exhibits limited generation diversity due to the over-incentivization of positive rewards. Although methods like Negative Sample Reinforcement (NSR) mitigate this issue by upweighting penalty from negative samples, they may suppress the semantic distributions shared between positive and negative responses. To boost reasoning ability without losing diversity, this paper proposes negative sample projection Residual Reinforcement Learning (ResRL) that decouples similar semantic distributions among positive and negative responses. We theoretically link Lazy Likelihood Displacement (LLD) to negative-positive head-gradient interference and derive a single-forward proxy that upper-bounds representation alignment to guide conservative advantage reweighting. ResRL then projects negative-token hidden representations onto an SVD-based low-rank positive subspace and uses projection residuals to modulate negative gradients, improving reasoning while preserving diversity and outperforming strong baselines on average across twelve benchmarks spanning Mathematics, Code, Agent Tasks, and Function Calling. Notably, ResRL surpasses NSR on mathematical reasoning by 9.4% in Avg@16 and 7.0% in Pass@128. Code is available at https://github.com/1229095296/ResRL.git.

Animal-welfare advocates produce a lot of writing, and increasingly that writing trains the language models that millions of people then ask about animal welfare. Using vocabulary-matched stance-contrast probes on a held-out animal-welfare benchmark, we measure how each of ten linguistic features changes Llama-3.2-1B's preference for pro-animal-welfare reasoning when used as fine-tuning data. Eight of the ten features produce statistically significant shifts. Seven move the model toward stronger pro-animal-welfare reasoning: assertive certainty, explicit moral vocabulary, emotion words, evaluative claims, narrative structure, depicted harm severity, and immediate temporal framing. Two move it the other way: hedged language and concrete sensory description both dilute the pro-animal-welfare stance. First-person perspective has no statistically significant effect. The practical recommendation for anyone writing animal-welfare text that may end up in LLM training corpora: assert a position rather than describe a scene neutrally. The features that shift the model are the ones that make the writer's position explicit; the features that dilute it hold animal-welfare content but withhold stance.

When a language model answers a table question, users have no way to verify which cells informed which reasoning steps. We introduce RSAT, a method that trains small language models (SLMs, 1-8B) to produce step-by-step reasoning with cell-level citations grounded in table evidence. Phase 1 (SFT) teaches a structured JSON output format from verified reasoning traces. Phase 2 (GRPO) optimizes a composite reward centered on NLI-based faithfulness, alongside citation validity and parsimony. Across six models from two families-Qwen 2.5 (1.5B/3B/7B) and Llama 3 (1B/3B/8B)-RSAT improves faithfulness 3.7$\times$ over SFT alone (0.224$\rightarrow$0.826), with near-perfect citation validity (0.992). Post-hoc attribution collapses below 13% format success, confirming that attribution must be integrated into reasoning, not retrofitted. Ablations show the faithfulness reward is essential: removing it drops faithfulness from 0.97 to 0.03.

Recent advances in large language models (LLMs) have increasingly relied on reinforcement learning (RL) to improve their reasoning capabilities. Three types of approaches have been widely adopted: The first relies on a deep neural network to estimate the value function of the learning policy in order to reduce the variance of the policy gradient. However, estimating and maintaining such a value network incurs substantial computational and memory overhead. The second avoids training a value network by approximating the value function using sample averages. However, it samples a large number of reasoning traces per prompt for accurate value function approximation, making it computationally expensive. The third samples only a single reasoning trajectory per prompt, which reduces computational cost but suffers from poor sample efficiency. This paper focuses on a practical, resource-constrained setting in which only a small number of reasoning traces can be sampled per prompt, while low-variance gradient estimation remains essential for high-quality policy learning. To address this challenge, we bring classical nonparametric statistical methods, which are both computationally and statistically efficient, to LLM reasoning. We employ kernel smoothing as a concrete example for value function estimation and the subsequent policy optimization. Numerical and theoretical results demonstrate that our proposal achieves accurate value and gradient estimation, leading to improved policy optimization.

Scientific reasoning rarely stops at what is directly observable; it often requires uncovering hidden structure from data. From estimating reaction constants in chemistry to inferring demand elasticities in economics, this latent structure recovery is what distinguishes scientific reasoning from curve fitting. Large language models (LLMs) can often recall and apply relevant scientific formulas, but we show that this ability is surprisingly easy to suppress. We show that adding in-context examples makes models rely less on pretrained domain knowledge, even when those examples are generated by the very same formula. Rather than reinforcing knowledge-driven derivation, examples shift computation toward empirical pattern fitting. We document this knowledge displacement on 60 latent structure recovery tasks across five scientific domains, 6,000 trials, and four models. This displacement is consistent across domains, but its accuracy consequences depend on how the displaced strategy compares to the one that replaces it: the same shift can lower accuracy, leave it unchanged, or appear to improve it. In all cases, however, the model shifts away from knowledge-driven reasoning. For practitioners deploying LLMs on scientific tasks, the message is cautionary: in-context examples may displace, rather than reinforce, the knowledge they are intended to support.

Large Language Models (LLMs) are known to acquire reasoning capabilities through shared inference patterns in pre-training data, which are further elicited via Chain-of-Thought (CoT) practices. However, whether fundamental reasoning patterns, such as induction, deduction, and abduction, can be decoupled from specific problem instances remains a critical challenge for model controllability, and for shedding light on reasoning controllability. In this paper, we present the first systematic investigation of this problem through the lens of reasoning conflicts: an explicit tension between parametric and contextual information induced by mandating logical schemata that deviate from those expected for a target task. Our evaluation reveals that LLMs consistently prioritize sensibility over compliance, favoring task-appropriate reasoning patterns despite conflicting instructions. We further demonstrate that reasoning conflicts are internally detectable, as confidence scores significantly drop during conflicting episodes. Probing experiments confirm that reasoning types are linearly encoded from middle-to-late layers, indicating the potential for activation-level controllability. Leveraging these insights, we steer models towards compliance, increasing instruction following by up to 29%. Overall, our findings establish that while LLM reasoning is anchored to concrete instances, active mechanistic interventions can effectively decouple logical schemata from data, offering a path toward improved controllability, faithfulness, and generalizability.

Small language models (SLMs) offer efficient deployment, yet they often lag behind their larger counterparts (LLMs) in reasoning. Existing remedies either invoke an LLM at points of reasoning divergence, incurring substantial latency and cost, or rely on standard distillation, which is limited by the SLM's capacity to accurately mimic the LLM's complex generative distribution. We address this dilemma by identifying local sufficiency: at divergence points, the LLM's preferred token often resides within the SLM's top-K next-token predictions, even when failing to emerge as the SLM top-1 choice. We therefore propose Select to Think (S2T), which reframes the LLM's role from open-ended generation to selection among the SLM's proposals, simplifying the supervision signal to discrete candidate rankings. Leveraging this, we introduce S2T-Local, which distills the selection logic into the SLM, empowering it to perform autonomous re-ranking without inference-time LLM dependency. Empirically, a 1.5B SLM's top-8 candidates contain the 32B LLM's choice with a 95% hit rate, and S2T-Local improves the 1.5B SLM's Math Avg. over greedy decoding by 24.1% relative gain, matching the efficacy of 8-path self-consistency with single-trajectory efficiency.

Improving large language model (LLM) reasoning requires supervision that is both aligned with the model's own test-time states and informative at the token level. Reinforcement learning with verifiable rewards provides on-policy exploration but offers sparse, high-variance credit; supervised fine-tuning and distillation provide dense targets but often train on fixed trajectories or rely on stronger teachers. Recent privileged on-policy self-distillation explores a middle ground by scoring student rollouts with the same model under verified solution context. We revisit this setting through a contextual re-scoring lens: for reasoning, the important choices are not only whether privileged context is available, but how much of it should be revealed and where its distribution should shape the student. We propose PAINT (Partial-solution Adaptive INterpolated Training), which masks the verified solution according to rollout-reference overlap and applies a small energy-space interpolation on a sparse set of entropy-mismatch token positions. Across competition-level math benchmarks, PAINT consistently improves over a strong prior on-policy self-distillation baseline at all three Qwen3 scales. On Qwen3-8B, it raises macro Avg@12 by 2.1 points over this prior baseline and 2.9 points over GRPO.

Reasoning in Large Language Models incurs significant inference-time compute, yet the token-level information structure of reasoning traces remains underexplored. We observe that reasoning tokens split into two functional types: low-entropy \textit{structural} tokens (recurring phrases that scaffold the reasoning process) and higher-entropy \textit{organic} tokens (problem-specific content that drives toward a solution). This asymmetry motivates a simple, model-agnostic compression pipeline: apply cross-word BPE merges on a model's own reasoning traces to derive \textit{supertokens} that capture frequent structural patterns, then teach the model to adopt them via supervised fine-tuning. Across three model families and five mathematical reasoning benchmarks, our approach shortens reasoning traces by 8.1% on average with no statistically significant accuracy loss on any model--benchmark pair. Beyond compression, supertokens act as interpretable reasoning-move annotations (backtracking, verification, strategy shifts), exposing the model's high-level strategy at a glance. Analyzing transitions between structural categories reveals systematic differences between correct and incorrect traces: correct traces show productive recovery (backtracking followed by strategy shifts and verification), while incorrect traces are dominated by confusion cycles (repeated hedging and unresolved contradictions). These diagnostic signals suggest applications in reward shaping and early stopping for RL-based reasoning training.

Large Language Models (LLMs) often fail to utilize their latent reasoning capabilities due to a distributional mismatch between ambiguous human inquiries and the structured logic required for machine activation. Existing alignment methods either incur prohibitive $O(N)$ costs by fine-tuning each model individually or rely on static prompts that fail to resolve query-level structural complexity. In this paper, we propose ReQueR (\textbf{Re}inforcement \textbf{Que}ry \textbf{R}efinement), a modular framework that treats reasoning elicitation as an inference-time alignment task. We train a specialized Refiner policy via Reinforcement Learning to rewrite raw queries into explicit logical decompositions, treating frozen LLMs as the environment. Rooted in the classical Zone of Proximal Development from educational psychology, we introduce the Adaptive Solver Hierarchy, a curriculum mechanism that stabilizes training by dynamically aligning environmental difficulty with the Refiner's evolving competence. ReQueR yields consistent absolute gains of 1.7%--7.2% across diverse architectures and benchmarks, outperforming strong baselines by 2.1% on average. Crucially, it provides a promising paradigm for one-to-many inference-time reasoning elicitation, enabling a single Refiner trained on a small set of models to effectively unlock reasoning in diverse unseen models. Code is available at https://github.com/newera-xiao/ReQueR.