LLM Reasoning

Large-Language Models (LLMs) can be prone to flawed and unfaithful reasoning that decoding strategies like Self-Consistency (SC) fail to detect as they evaluate only final-answer agreement while ignoring the logical validity of intermediate steps. This raises three fundamental questions: How can we reliably quantify uncertainty in LLM reasoning? Can semantic, structural, and causal awareness select more faithful reasoning compared to naïve majority voting? and How robust is reasoning topology under adversarial conditions? To address these questions, we introduce GRAPHEVAL, a graph-based reasoning framework that re-frames uncertainty quantification (UQ) as a holistic reasoning fidelity problem. We propose a novel UQ metric, Graph Reasoning Coherence Score (GRCS), that quantifies semantic-structural consensus of the reasoning space and captures pathological mode collapse and confident hallucinations. We find that GRCS is the only metric that is consistently negatively correlated with reasoning faithfulness across both more capable and smaller models. Additionally, we introduce Graph Self-Consistency (GSC), a medoid-based decoding strategy that trades nominal accuracy for reasoning fidelity, exposing the degree to which SC is inflated by unfaithful lucky guesses in smaller models, while preserving or improving accuracy in more capable ones. Finally, through adversarial medoid ablation, we demonstrate that the GSC-selected path acts as a "load-bearing path" and forcing models away from it degrades reasoning faithfulness and, in targeted cases, causes drops in accuracy.

Large language models (LLMs) increasingly improve their reasoning at test time via additional computation, yet most existing works treat each problem in isolation. When problems arrive sequentially, accumulating reusable experience across them can further improve performance. Existing memory-based methods either store whole-solution templates that generalize poorly to novel problems or use heuristic step-level selection that is not optimized for final-answer correctness. Learning selection policies requires large-scale training data and fixed action spaces, making such approaches unsuitable for test-time settings where memory expands incrementally and only limited supervision is available. We propose MILES (Modular Instruction Memory with LEarnable Selection for self-improving LLM reasoning), a framework that dynamically expands step-wise memory and applies correctness-optimized memory composition under realistic test-time constraints. MILES maintains modular memory units consisting of asymmetric pairs of sub-goal embeddings and sub-instructions, each associated with a learnable selection head. This memory structure enables a coarse-to-fine retrieval mechanism: The coarse level enables memory expansion and collects supervision for training selection heads from confident samples, while the fine stage applies learned selection heads to rerank coarse-level candidates and guide reasoning for uncertain samples. MILES consistently matches or outperforms prior methods while achieving superior accuracy-efficiency tradeoffs. Extensive experiments demonstrate its effectiveness, robustness, and transferability.

Biomedical question answering requires not only accurate extraction of information from scientific literature but also reliable integration of evidence across multiple documents. This study presents a question-type-specific large language model (LLM) framework for BioASQ 14b Task B, designed to improve answer robustness and evidence grounding in biomedical question answering. Rather than applying a single prompting strategy to all questions, the framework selects different inference procedures for yes/no, factoid, and list questions according to their distinct reasoning and evaluation requirements. For yes/no questions, snippet shuffling and self-reflection are used to reduce sensitivity to evidence ordering and improve decision stability. For factoid questions, full-snippet input is combined with chain-of-thought-based in-context learning to support accurate biomedical entity identification. For list questions, a multi-agent architecture is employed, in which evidence extraction, candidate generation, answer verification, and final aggregation are handled collaboratively. Preliminary experiments on BioASQ 13b were used to identify effective inference strategies for each question type, and the resulting framework was subsequently evaluated in the official BioASQ 14b Task B challenge. In the official evaluation, our framework showed competitive performance across multiple batches and achieved first place in the factoid subtask of Batch 4. These results demonstrate the effectiveness of combining question-type-specific inference, ensemble prediction, and agent-based verification for reliable biomedical question answering.

We present an empirical study of structural routing failure in large language models (LLMs) over a formally verified algebraic corpus. The task requires selecting the correct proof-mechanism label from a fixed closed template set for compact mathematical objects drawn from the FiberRing formalization in Lean 4, where each item is anchored to a Lean-verified artifact and assigned a label from the corresponding certificate family. Our central finding is a mechanism-level routing ceiling: under blind conditions, gpt-oss-120b achieves 80.3% template accuracy on 22 FiberRing items (n=66; temperature=0, seed=0), while Llama 3.3 70B reaches 68.2%. Exposing a mechanism-bearing Lean verdict/witness cue (Condition A2) raises accuracy to 90.9% and 81.8% -- gaps of +10.6 and +13.6 pp termed cue-induced routing uplift. The dominant failure is a CRT-to-ring-equivalence misroute: gpt-oss-120b misroutes 7 of 12 CRT items (58.3%) blind, zero under A2. A cross-model dissociation in Llama is notable: verdict accuracy is identical in both conditions (95.5%), while template accuracy improves 13.6 pp -- confirming that truth inference and proof-mechanism classification are separable capacities. A cross-corpus extension (Set B; 6 POM/CollisionKernel items, 72 evaluations) provides a small cross-module check: CRT-granularity compression reappears with different labels, and an inverse cross-model dissociation emerges. These findings extend the router hypothesis (Cazares 2026) to formal algebraic structures. The full pipeline, manifest, and results are at https://github.com/bytepro-ai/fiber-routing-eval.

Diffusion large language models (dLLMs) generate text by iteratively denoising a masked sequence, offering a parallel alternative to autoregressive models, but eliciting strong reasoning through post-training remains difficult: supervised fine-tuning is off-policy and suffers from exposure bias, while reinforcement learning gives only sparse, sequence-level rewards and is hard to apply without tractable sequence likelihoods. On-policy self-distillation (OPSD) offers a promising alternative, using one model as both student and teacher to provide dense, token-level, on-policy supervision, but its effectiveness hinges on giving the teacher privileged information (PI) - typically an instance-specific ground-truth reference unavailable at inference - so the student ends up distilling a weak PI-free consensus policy that yields little improvement on dLLM reasoning. We introduce dOPSD, which instead derives the teacher's privilege directly from the student's own denoising trajectory, evaluating masked positions using later, more-decoded steps of that same trajectory rather than an external label, so the teacher's advantage emerges from the model's own decoding process; on Dream and LLaDA, dOPSD improves both in-domain math reasoning and out-of-domain code generation, outperforming supervised and on-policy baselines.

On-policy distillation is a powerful way to transfer reasoning ability from a strong teacher to a smaller student: the student samples trajectories from its own policy, and the teacher provides dense token-level supervision on the states the student actually visits. However, this supervision is not always reliable: a teacher can assign high likelihood to plausible but incorrect solutions, or low likelihood to correct student solutions that follow different reasoning paths. Unconditionally distilling the teacher can therefore reinforce bad modes or erase useful student behavior. To address these limitations, we introduce RG-OPD: Reward-Gated On-Policy Distillation that uses verifier feedback to decide when teacher logits should be trusted. RG-OPD bridges sparse verifier rewards and dense teacher logits, preserving token-level supervision while filtering misleading teacher signals. Across reasoning and coding benchmarks, RG-OPD produces stronger distilled students, outperforming both vanilla reverse-KL distillation and the recent TSD-KD baseline. At 1K generation length, RG-OPD improves over reverse-KL by 2.9 points and over TSD-KD by 4.9 points; in the long-generation setting, it improves over the untuned student by 8.2 points. Our code is available at https://github.com/UoC-tail/RG-OPD.

Frontier LLMs can perform multi-step reasoning over content-free filler tokens like dots or counting sequences, producing correct answers with no visible chain-of-thought (CoT). This is a limit case for behavioral oversight, where surface tokens carry no information about the underlying reasoning. But hidden from the output is not the same as hidden from us. On four task families (fact retrieval, parallel numeric composition, string manipulation, and in-context computation), two open-weights frontier models (DeepSeek V3, Kimi K2) compute over filler tokens in a legible way: attention routes the question through the filler region to the answer, logit-lens readouts show retrieved facts emerging early and their composition crystallizing in late layers, and KV-cache transplants at filler positions causally swap outputs between examples. We introduce an unsupervised decoding pipeline that takes only hidden states as input and recovers intermediate values with 82-94% accuracy (best LLM judge) across both models and all four tasks, without ground-truth labels or training. Even without a judge, the hidden values are already directly in the pipeline's top-2 tokens 35-85% of the time. The uplift persists whether the filler is prefilled or the model generates the filler itself. On these cleanly decomposable tasks, hidden computation that defeats behavioral CoT monitoring is readable from the residual stream, which suggests that monitorability is a property of the model's full computational trace rather than only its surface tokens.

Recent large language models (LLMs) have demonstrated remarkable progress in 3D spatial reasoning, spatial grounding, and fine-grained geometric understanding. However, their ability to reason about densely packed object placement under strict spatial and functional constraints remains largely unexplored, despite being a fundamental challenge in practical electronic design automation (EDA) workflows. To bridge this gap, we introduce OmniLayout, the first benchmark designed to evaluate LLMs on printed-circuit-board (PCB) layout placement reasoning under real-world geometric, routing, and connectivity constraints. OmniLayout contains 1,681 industrial-grade schematic-coupled PCB layouts and includes four tasks: (1) geometric reasoning for IC physical placement, with 77.24K placement instances constrained within PCB board boundaries; (2) routability-aware placement reasoning, generating physically valid component placements; (3) electrical functionality, preserving schematic-specified connectivity and electronic functional correctness; and (4) tool-augmented agentic reasoning for invoking external tools to accomplish tasks (1)-(3). Our results reveal substantial limitations of current LLMs in PCB layout placement, including weak geometric reasoning, poor routability optimization, and inconsistent preservation of electrical functionality.

Reasoning Language Models (RLMs) have significantly improved performance on complex tasks by extending the reasoning chain. However, these chains are prone to containing factual errors, particularly in knowledge-intensive tasks. To address this issue, we propose CheckRLM, a framework that improves the reliability of the reasoning process through Retrieval-Augmented Generation (RAG) by timely checking and correcting factual errors. Specifically, CheckRLM extracts factual claims from the reasoning chain to identify and localize subtle knowledge inconsistencies during inference. Upon detection of errors, a refinement mechanism performs minimal-cost yet precise corrections by leveraging external knowledge, ensuring coherence between the reasoning chain and correct knowledge. Extensive experiments demonstrate that CheckRLM substantially outperforms existing baselines, exhibiting a strong capability to mitigate error accumulation in long-horizon reasoning with lower costs. The code and data are available at https://github.com/AI9Stars/CheckRLM.

On-policy self-distillation (OPSD) has emerged as a promising paradigm for improving LLM reasoning, where a privileged teacher with access to reference solutions provides token-level supervision on the student's own generated trajectories. However, we find that OPSD consistently fails on long chain-of-thought (long-CoT) reasoning models, yielding at best marginal gains while destabilizing the reflective reasoning capability these models depend on. Through a novel decomposition of the teacher's supervision signal, we identify the root cause: the teacher's supervision is dominated by a reference-induced component that drives rote memorization of reference-specific shortcuts, while the question-conditioned, inference-transferable component is ignored or actively opposed. Based on this diagnosis, we propose a two-step solution. First, we construct a reference-only teacher (the same model conditioned on the reference without the question) to isolate the non-transferable component of the supervision signal; the residual after subtracting this component captures the question-conditioned, inference-transferable correction. Second, we use pointwise mutual information (PMI) as the mechanism to transform this residual into a well-formed PMI target distribution that the student can directly distill from, filtering out the reference-induced shortcut. Experiments on four long-CoT models across two datasets demonstrate consistent improvements over both the base model and standard OPSD, while preserving the models' natural epistemic behavior throughout training.

This paper presents TUDUM (Türkçe Düşünen Üretken Model), a project pipeline for adapting a Qwen-family 27B thinking model toward Turkish reasoning. The central problem is not only to answer Turkish prompts in Turkish, but to make the explicit reasoning trace itself Turkish. A thinking model may translate a Turkish prompt into an English-centered internal or visible scratchpad, solve the problem mostly in English, and only localize the final answer. TUDUM instead treats the generated <think>...</think> block as a trainable behavior. The pipeline starts from the project base checkpoint unsloth/Qwen3.5-27B, applies supervised fine-tuning (SFT) on 15,991 Turkish reasoning examples using LoRA adapters, and then applies GRPO-family reinforcement learning on a proxy-filtered Turkish mathematics environment. The results are mixed. SFT made the model shorter and more consistently Turkish in its reasoning behavior, with large reductions in average response length and thinking exhaustion, but reduced benchmark accuracy. RL recovered some mathematical performance, especially AIME24 at the best early checkpoint, yet did not uniformly improve all benchmarks and did not exceed the base model on the reported Macro-6 average. The contribution is therefore best framed as a technically honest Turkish-thinking reasoning pipeline and evaluation, not as a claim of state-of-the-art Turkish reasoning. The released step-50 model is publicly available.

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 \emph{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 $d_ρ$ 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 and current 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, $d_ρ$ achieves $0.93$ AUC in distinguishing easy from hard problems, while kinematic features potentially can predict 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.

We introduce ISOSCI, a benchmark of isomorphic cross-domain science problem pairs that separates reasoning ability from domain knowledge retrieval in LLM evaluation. Each pair shares identical logical structure but requires different domain-specific knowledge, enabling controlled attribution of reasoning-mode gains. Across five model pairs spanning four model families, we find that 91.3% of reasoning-mode gains are knowledge-dependent rather than structure-invariant (63/69 gains; Wilson 95% CI [82.3%, 96.0%]), directly challenging the assumption that chain-of-thought reasoning improves short-horizon procedural scientific problem-solving. Reasoning toggles on highly capable models provide less than 5 percentage points accuracy gain across all domains, and a reasoning-specialized model (o3-mini) that outperforms its standard counterpart on GPQA Diamond (+19.2 percentage points) underperforms on ISOSCI (-24.7 percentage points), showing that benchmark choice determines conclusions about reasoning utility. We release ISOSCI at https://huggingface.co/datasets/isosci/isosci

Reasoning language models frequently overthink: generating extended chains of behaviors such as hedging, approach abandonment, and self contradiction that consume tokens without improving answers. We show that these behaviors are not merely a consequence of length; even when controlling for response length, incorrect traces exhibit higher rates of unproductive self-reflection than correct ones. Addressing this requires identifying where self-reflection helps vs hurts, but obtaining these step-level annotations is costly. We observe that intermediate answer commitments within reasoning traces can provide a cheap proxy: by comparing each final answer candidate in the trace to the ground truth, we can determine whether subsequent reflection is productive without any additional supervision. Building on this insight, we propose DASH (Drift Aware advantage SHaping), which assigns segment-level credit based on whether each reasoning segment leads toward or away from correctness. On competition-level math benchmarks, DASH achieves the highest accuracy where overthinking is prevalent (AIME25: 50.8% vs. 45.4% GRPO) while reducing overthinking behaviors and achieving more productive self-correction than baselines.

We present Seed2.0, a model series that takes a meaningful step toward solving complex, real-world tasks. Our approach begins with identifying users' genuine needs and constructing a reliable, forward-looking evaluation system by selecting and abstracting benchmarks grounded in these needs and in realistic, complex scenarios. Guided by this evaluation system, Seed2.0 targets two persistent challenges, long-tail knowledge and complex instruction following, substantially improving the model's reliability on intricate, long-horizon tasks. Beyond these, Seed2.0 delivers world-leading reasoning intelligence, visual understanding, and search capabilities that address the most common needs of a broad user base. Through extensive real-world use cases documented in this model card, we demonstrate that Seed2.0 begins to exhibit the ability to handle initial complex real-world tasks, delivering greater value to hundreds of millions of users.

Vision-language models achieve strong general perception but often struggle with the spatial reasoning required for embodied tasks. We present RoboSpatialBrain, our submission to the RoboSpatial Challenge at the Embodied Reasoning in Action Workshop, CVPR 2026, built on RoboBrain2.5-8B-NV. RoboSpatialBrain combines two training-free, inference-time mechanisms: a forced <think> prefix activation strategy paired with a task-specific post-prompt that elicits deliberate reasoning on context and compatibility tasks, and an explicit reference-frame redirection pipeline that resolves camera-centric and object-centric ambiguity for context tasks. We additionally explore fine-tuning RoboBrain2.5 on compatibility data and present a detailed analysis of its interaction with prompting. RoboSpatialBrain achieved first place in the RoboSpatial Challenge, with an overall success rate of 80.9% on RoboSpatial-Home. Code is available at https://github.com/YuxiangXie2003/RoboSpatialBrain.

Parallel thinking has enjoyed great success for boosting LLM performance on reasoning tasks without the need for any re-training. However, existing methods follow a think-first-then-decide paradigm, i.e., they first sample multiple reasoning paths, which inevitably leads to overgeneration, then prune or stop unnecessary paths to compensate. In contrast, decide-first-then-think, i.e., first identifying points that are likely to lead to desirable generations, has been underexplored so far. Following this paradigm, we propose Fork-think with confidence, that first identifies forking points using model confidence in a single seeding path, then triggers thinking, sampling multiple continuations and aggregating them for the final response. Our experiments across three models and three reasoning benchmarks show that Fork-think reduces the token consumption by up to 30% and run-time by up to 57%, while performing comparable to or better than parallel thinking. Our analysis reveals that Fork-think is able to identify forking points that are meaningful with respect to the downstream task and that sampling at later positions can lead to substantially better generations. Finally, we demonstrate how combining Fork-think with existing mechanisms such as early stopping and weighted voting can further boost the performance and perform comparably to existing state-of-the-art methods, without requiring any warm-up or offline training. Our results establish pre-determined forking as a promising research direction for efficient LLM reasoning.

Human reasoning is inherently multimodal: when problems become difficult, we rarely think in words alone. We often externalize our reasoning by sketching diagrams or drawing grids to understand the underlying conceptual structure and avoid mistakes. Building on this premise, our research investigates: (a) whether grounding multi-hop textual-spatial stories into geometry-aware modalities, such as layouts or grids, improves reasoning compared to natural language-based inference; and (b) whether a model can decide when to rely on natural language reasoning and when to switch to a structured modality. We address these questions by introducing a switching metric based on trustworthiness and complexity signals, which estimates when grounding a spatial story into structure is likely to improve performance. This takes a first step toward principled modality selection in Large Language Model (LLM) reasoning. Across our settings, switching from natural language-based reasoning to a grid-based representation improves LLM performance by up to 42%, highlighting the importance of modality choice in shaping reasoning outcomes.

Large language models (LLMs) are typically deployed in multi-turn conversations, where each turn provides new evidence that should reduce epistemic uncertainty about their environment. Acting rationally then requires inferring the unobserved quantities that govern it and updating beliefs about them as evidence accumulates. Yet most evaluations only score the model's final-turn answer in a single-turn format, leaving this process unexamined. We ask how closely LLMs' belief updates match those of a rational Bayesian reasoner in multi-turn settings, and introduce BayesBench, a suite of simulation environments that probe this across three progressively complex tasks: (i) Bayesian estimation, where the model infers an unknown parameter from sequential evidence; (ii) Bayesian prediction, where the model turns inferred beliefs about a latent variable into outcome forecasts; and (iii) latent-framed Bayesian prediction, where observations are filtered through a user-persona framing, requiring joint inference over the latent state and the persona. Across seven LLMs (3B--70B), scaling improves latent inference and evidence accumulation, with updates occasionally matching the Bayesian posterior. However, these gains do not reliably carry over to downstream prediction, exposing a gap between inferring latent structure and using it to rationally update beliefs about the target outcome.

Chain-of-thought (CoT) prompting improves LLM reasoning, but the source is contested: do the intermediate steps help because they carry useful semantic content, or because conditioning on more tokens buys extra computation before the model commits to an answer? We bring two lines of evidence to bear. First, in distribution: we repeatedly sample each model on the same question and pair a shorter with a longer of its own natural generations that follow the same reasoning plan, so nothing is rewritten and both traces are genuinely in-distribution. Across 25 models the extra tokens leave accuracy essentially unchanged for every independently-trained reasoner, and a blind analysis of the surplus tokens shows that what gain exists elsewhere tracks validation- and checking-content, not verbosity per se. Second, as a controlled intervention, we ask whether two traces expressing the same semantic content (the same facts, operations, and intermediate values, verified through directed acyclic graph equivalence) produce different outcomes when one is more verbose, using a dual-validator design across four targets and eight benchmarks with number-redacted completion and stratified bootstrap confidence intervals. Verbose traces do improve accuracy (25 of 32 benchmark-target cells are positive under at least one validator), but the effects are modest (typically 1-4 points) and depend on the quality of the verbose prose, not merely its length. Under maximum numerical redaction the effect is amplified (median 3.24x across four arithmetic benchmarks), and length-matched non-reasoning filler recovers none of it. Both lines converge: what matters is what the extra tokens do (the reasoning and validation content they carry), not how many there are, a picture neither a pure forward-pass-compute nor a pure semantic-content account fully explains.

A growing body of work suggests that the reasoning capabilities of large language models are largely latent in their base form, with post-training primarily amplifying rather than introducing them. However, this evidence comes mainly from mathematical and coding benchmarks, leaving the boundary conditions of that claim largely unexplored, namely which cognitive tasks can be recovered through elicitation and where that recovery fails. To investigate this, we introduce NeuReasoner, a theory-grounded elicitation instrument. At each step, an orchestrator pairs a Neuro Lens, inspired by functional specificity, with a Cognitive Lens, drawn from the Erotetic Theory of Reasoning, and integrates their outputs through internal modularization of a single model, without external tools. We evaluate NeuReasoner on CogBench, a suite of behavioral tasks from cognitive psychology, alongside standard mathematical and coding benchmarks, measuring both its improvement over vanilla inference and its ability to match a model's post-trained thinking mode. At sufficient scale, NeuReasoner matches or exceeds thinking-mode baselines on arithmetic reasoning, code generation, Bayesian reasoning, and reward learning; these gains persist against self-consistency and iterative-refinement baselines matched to NeuReasoner's per-decision call budget. Using NeuReasoner allows us to find clear boundaries: risk-taking and decision making under uncertainty remains hard to recover through elicitation alone, and model scale interacts with elicitation in both directions: widening its advantage on some cognitive signatures while erasing it on others. Overall, through NeuReasoner as a modular, interpretable, theory-grounded elicitation instrument, we empirically map where reasoning elicitation succeeds and fails, beyond the mathematical and coding benchmarks where prior claims have rested.

Distilling historical trajectories into reusable experience to enhance future problem-solving has become a focal point of recent LLM research. However, existing methods predominantly operate at the task level, leveraging general summaries or rules under the assumption that analogous tasks share universal solution patterns. This approach often fails in complex reasoning, which typically falters at local bottlenecks that require precise, state-specific guidance rather than broad heuristics. We introduce HippoSpark, a state-level experience system that performs on-demand retrieval tailored to the immediate needs of the current reasoning state. Across mathematical, scientific, and programming benchmarks, HippoSpark consistently outperforms both standard prompting and task-level experience baselines. Our findings reveal that the most effective experience systems are those that provide actionable guidance at critical bottlenecks rather than serving as generic task-level context. Our code is available at https://github.com/DanlingMeng/HippoSpark.

Large language models achieve high reasoning performance via explicit chain-of-thought and reinforcement learning, but require long output sequences and extended inference time. Latent reasoning reduces this cost by shifting computation into a latent space; however, continuous latent methods are hard to train, suffering from unstable and uninterpretable reasoning trajectories. We argue these issues stem from a misalignment between continuous-space reasoning and discrete symbolic supervision, as continuous states lack explicit anchors for step-by-step alignment. To resolve this, we propose \textbf{Discrete Latent Reasoning~(DLR)}, the first method that converts continuous latent states into explicit discrete tokens. Inspired by render-based compression, we render textual chains of thought into images, extract visual features, and construct a discrete latent vocabulary via clustering-based fine-tuning. Expanding the vocabulary and output head enables standard autoregressive modeling over both natural language and latent tokens, supporting pretraining alignment, SFT, and RL. Experiments on five reasoning benchmarks and two model series~(Qwen3-VL and LLaMA-3) confirm that \textbf{DLR} outperforms prior latent reasoning baselines with up to \textbf{20$\times$ compression}. Furthermore, the learned latent trajectories retain an interpretable semantic structure. Overall, discrete latent tokens provide a controllable and interpretable basis for efficient latent reasoning.

Reviewing nuclear regulatory documents requires multi-hop reasoning across tens of thousands of pages, where judgments depend on evidence assembled across multiple chapters. We frame this task as planning: an LLM-based agent observes the evidence collected so far, picks the next document fragment to inspect, and stops when the evidence is sufficient. The agent operates over a vectorless document tree using browse, read, and search tools, and maintains a dynamic knowledge graph (KG) as state. On a 200-question benchmark over NuScale Final Safety Analysis Report (FSAR) documents, the system reaches 81.5% accuracy with a RAGAS Faithfulness of 0.93. The dominant performance factor is planning: against PageIndex, which uses the same document tree without state-conditioned action selection, the gap is +38.0pp (43.5% to 81.5%, p<0.001). The system also outperforms LightRAG (73.0%, p<0.05), HippoRAG (70.5%, p<0.01), and GraphRAG (49.5%, p<0.001), and matches RAPTOR (75.5%, p=0.11) without offline indexing. Edge inference adds 2.8x cost without raising accuracy; we retain it as a traceability module. Of 7,391 inferred edges, 3 Violates edges (0.04%) flag scope boundaries (Q058) and partial conformance (Q176) as typed annotations that a human reviewer can audit.

We introduce the Complexity Ceiling Benchmark (CCB), a controlled evaluation of how language-model reasoning decays as the number of required sequential steps grows. CCB fixes the semantic content of a task and varies only its depth N in {5,...,50} across three structurally distinct regimes: grounded spatial state-tracking, abstract symbolic pointer manipulation, and transitive relational inference. Across 6,000 trials over five frontier and open-weight LLMs we find a consistent pattern of geometric per-step decay with widely separated domain ceilings: on the first two regimes the strongest models retain pd>0.92 across N=50; on the third every model collapses by N=5, with the best model's 50%-success horizon at H0.5~4.7 steps despite pd=0.863. A trace-level metric (TFBC) shows that 14.5% of correct answers across the benchmark are reached via incorrect intermediate reasoning. Forced verbose state-tracking does not move the ceiling (McNemar p=1.000), and the mean step at which reasoning first diverges, k*, predicts within-domain accuracy better than parameter count. CCB and the geometric decay model together reduce a model's long-horizon reasoning profile to one interpretable number per task family.

We present ThinkProbe, a framework for structural analysis of LLM reasoning traces. ThinkProbe converts each trace into a Thought Graph a directed graph with cycles, 8 node types, and 6 edge types and derives a 19-metric five-dimensional cognitive profile (5D-CP: Breadth, Depth, Structure, Metacognitive, Efficiency) through a fully non-generative pipeline combining rule-based segmentation and discriminative semantic linking. Applied to 4{,}200 traces from 7 native reasoning models across 200 open-ended questions and 10 cognitive domains, ThinkProbe reveals that reasoning structure is a stable, model-level property: between-model variance exceeds between-domain variance by up to fourfold across four of five cognitive dimensions, with Structure showing genuine sensitivity to question domain, exposing qualitatively distinct cognitive profiles invisible to accuracy-based evaluation.

Current approaches to enhance Large Language Model (LLM) reasoning, such as Chain-of-Thought and "Wait" prompts, primarily encourage models to think more, yet often fail to guide them toward Truth. While Representation Editing (RepE) offers a intrinsic control, its application to dynamic reasoning trajectories remains underexplored. In this work, we bridge this gap by investigating the geometry of truth within unfolding reasoning chains. We uncover three critical insights: (1) Truth is encoded at the sentence level and is entangled with latent reasoning patterns; (2) Effective intervention follows an Uncertainty Principle and a Decay Effect, requiring localization to early, high-entropy forks; (3) Naive steering vectors suffer from noise, risking collateral damage to correct trajectories. Based on these findings, we propose DynaSteer, a dynamic RepE framework. DynaSteer employs pattern clustering to disentangle reasoning manifolds and utilizes Fisher-LDA to project purified truth. By dynamically monitoring lookahead entropy, it selectively steers and rolls back trajectories only when necessary. Comprehensive experimental results on several MATH benchmark verify the effectiveness of DynaSteer, and experiments on out-of-domain coding tasks further confirm its generalization ability. Our code is publicly available at https://github.com/tianlwang/DynaSteer.

Humans flexibly adapt their reasoning strategies to the requirements of a given problem. Large language models (LLMs) have performed well on many cognitive tasks, however, it is unclear whether this accuracy is a result of pattern matching from training data or flexible reasoning. Here, we introduce a novel paradigm to test this question: the riddle riddle paradigm. Riddle riddles are word problems written to mimic popular riddles, but altered so their answers only require literal interpretations. Identifying correct answers requires looking past the structure of each question and flexibly apply different reasoning strategies based on the content. If LLMs respond to surface features, such as form, a riddle-like structure should cause models to use an inventive reasoning strategy even when a literal interpretation suffices. Alternatively, if LLMs reason based on content, they should flexibly switch strategies when appropriate. Across two experiments with nine state-of-the-art LLMs and 100 human participants, we show humans and LLMs fail on this paradigm in opposite directions. LLMs were far more accurate on genuine riddles than on riddle riddles (84.9% vs. 50.7%); whereas humans showed the reverse effect (50.5% vs. 80.5%). Error analysis shows that 90.8% of LLM errors on riddle riddles (the condition where they show diminished performance) were due to inappropriate use of inventive reasoning while only 57.6% of human errors on genuine riddles were due to overextending literal reasoning. Thus, while both groups make mistakes, reasoning mistakes are made more often by LLMs than by humans. Overall, LLMs' strong performance on genuine riddles may reflect memory retrieval rather than flexible strategy selection, and without stimuli designed to elicit this contrast, it becomes easy to conflate LLM-generated outputs that look like reasoning with genuine reasoning.

Does intelligence require the ability to reason about phenomena beyond direct experience? It is natural to suspect that some complex thought cannot be captured through language alone. However, of particular concern to this work, is whether visualising counterfactual events can complement language as a mechanism for complex thought. We ask whether LLMs can be trained to utilise such visualisation mechanisms, in a way that benefits their reasoning abilities. Motivated by this question, we propose Einstein World Models. EWMs are a blueprint for LLM-based reasoning systems that place visual-temporal rollouts inside the reasoning trace, allowing them to reason in ways that text alone may not support well. In an EWM, the LLM calls a world-module (not to be confused with a world model), to produce short rollouts of scenes under consideration. The returned rollout is treated not as the answer, but as an inspectable hypothesis that can support later reasoning. Einstein World Models extend the capability of LLMs for tool calling (such as web search or code execution), into the domain of visual thought experiments.

Supervised fine-tuning (SFT) on a small, high-quality set of long reasoning traces is an effective approach for eliciting strong reasoning capabilities in Large Language Models (LLMs). However, existing methods for curating high-quality SFT data rely heavily on strong reasoning models to filter examples based on diversity and difficulty, making the curation process costly while often yielding suboptimal data quality. In this work, we show that diverse and challenging reasoning examples can be identified using only the initial reasoning tokens. Specifically, we demonstrate that difficult problems can be reliably detected based on the loss of the first 100 reasoning tokens evaluated at a randomly perturbed checkpoint of the pretrained model. We further show that examples exhibiting similar loss patterns over their first 1k reasoning tokens across a small number of perturbed checkpoints extrapolating along the fine-tuning trajectory provably induce similar gradients. We validate our approach through extensive experiments on fine-tuning Qwen2.5-7B and Llama3.1-8B models on the M23K medical reasoning and OpenThoughts-Math datasets. Our method outperforms existing baselines by up to 1.7% while being 91% more token efficient.