It's the Problem, Not the Path: Budget and Difficulty Confounds in LLM Reasoning Trajectories

Reasoning traces of large language models are widely read as containing "breakthrough" moments and early-legible fates. Both readings rest on measurements missing a counterfactual control at the level of the claim; we supply both controls. First, a restart-controlled truncation probe separates when a solution fits the continuation budget from when a prefix carries value that fresh computation cannot buy, comparing per-anchor continuation solve rates against from-scratch restart curves at matched total generated-token budget. Applied to 178 problem-model cells (89 MATH problems x two small open models, an outcome-blind but difficulty-targeted cohort), exactly 1 of 178 cells survives as prefix-limited; restart dose-response separates a compute-starved model from a capability-limited one; and wherever the matched budget lies inside the restart grid, continuing the model's own prefix beats restarting (9 of 9) -- predominantly compute compression rather than expanded reachability. Second, a pre-registered, difficulty-controlled test finds no detectable outcome information in early-window internal signals beyond a problem-difficulty baseline, and two generation-free analyses of public corpora show why this control is needed: a trace-blind difficulty proxy reaches AUROC 0.873 on 192K DeepSeek-R1 generations -- inside the published probe range -- and a closely matched reconstruction of the closest published early-window positive recovers a comparable pooled result (0.849) while within problem it is statistically indistinguishable from chance at all ten anchors (0.496 at t=4); a post-hoc within-targeted probe finds only a small average residual, concentrated in three low-failure problems. High pooled probe AUROCs cannot by themselves establish within-attempt information; a question-only baseline or within-problem evaluation is required.

Trace as State: Reasoning Traces as Conditional States for Long-Context Transformers

Transformers process information causally, but long-context reasoning may depend on task state discovered only later. We formalize this mismatch through conditional state update tasks. For causal state update processors, providing the condition first can require exponentially less memory in the worst case than providing it last. Motivated by this principle, we introduce Trace as State. We use collected reasoning traces as a textual proxy for task state and place it before the long-context block on a fresh pass, allowing information derived previously to guide rereading. We conduct extensive experiments on Trace as State and Trace Append, a matched control that uses the same task state proxy but put it after the context. Across three models and three long-context datasets, Trace as State outperforms Trace Append in 26 of 27 reported combinations of model, task, and metric. On GraphWalks Parents, exact match lifts DeepSeek V4 Pro Preview from 29.2% on the initial pass and 43.0% with Trace Appendto 81.8% with Trace as State, and from 66.4% and 83.2% to 100.0% for GLM-5.2. These results show that placing traces before the context can improve long-context reasoning while retaining the causal transformer structure.

Reflection Steering: Disentangling Reflection from Reasoning in Activation Space for Token-Efficient Inference

Large reasoning models often produce reasoning traces with verification, revision, and backtracking. When reflection merely re-checks established results, it wastes reasoning tokens and increases latency. Most existing reflection steering methods add a label-derived mean-difference direction across preset layers, but its entanglement with reasoning and length signals destabilizes the accuracy-efficiency trade-off. In this paper, we propose Reflection Steering, a training-free framework for controlling reflection-associated computation within LLMs by disentangling reflection-related activations from general reasoning. Specifically, we contrast reflective and non-reflective hidden states at each LLM layer, denoise the resulting reflection directions with PCA, and orthogonalize them against general-reasoning directions. To limit downstream amplification from early-layer interventions, we calibrate each layer across multiple intervention strengths on a small set, retain only stable layers, and apply bounded projection removal to their residual-stream activations. We conduct extensive experiments across two public benchmarks and three open-weight LLMs against state-of-the-art activation-steering baselines. Results show that Reflection Steering reduces reasoning tokens by 16.9% on average across six matched settings. Besides, our method further introduces a bounded reflection intervention-strength parameter $α$, enabling deployment-time adjustment to balance token savings, accuracy, and generation stability.

Thinking in a Low-Resource Language: What SFT Builds, What RL Fixes, What Accuracy Cannot See

Take three frontier mixture-of-experts models (Alibaba, OpenAI, NVIDIA; 3.6-4.0B active parameters each) and fine-tune them to reason in a low-resource language. On accuracy benchmarks almost nothing happens, and the benchmark itself is noise at this scale: changing only the random seed moves the score by 7.7 points, more than every data and recipe effect we measured. That null is our first result. The real changes live where accuracy cannot see. Base models never think in Greek: 0 of 1,000 reasoning traces, even when the question is Greek, so the model answers correctly while reasoning in a form its user cannot read, audit, or correct. After supervised fine-tuning (SFT), every released checkpoint reasons in the language of the question on ~98% of items, one family at 3x fewer tokens, with judged grammaticality improving on all four models and general ability within a few points of each base: nothing was forgotten, and fluency was gained. We propose six behavioural dimensions that make such changes measurable, each gated to reject any metric that correlates with output length, and we report how our own instruments lied: six failures, each caught by a control. What SFT cannot do is fix its own defects: a quarter of answers skip the requested format, answers leak into the reasoning channel, and an explicit "think in English" is obeyed under half the time. Reinforcement learning with verifiable rewards, pre-registered before training, fixes the first two outright (fallback 24% to 2.5%, leak 3.5% to 0.0%, both against a flat random-reward control) and moves the third (+9.1pp), while the Greek reasoning habit survives an accuracy-only gradient untouched. We release five checkpoints. The instruments, the controls and the pre-registration travel to any low-resource language; Greek is the case that let us measure them.

Reasoning Jury: Multi-Model Consensus for Evaluating Reasoning Traces

Improving reasoning LLMs requires the ability to judge the quality of long reasoning traces for effective reasoning data curation, strong training signals during reinforcement learning, and an in-depth understanding of reasoning behaviors during model performance evaluation. Additionally, surfacing reasoning mistakes that the model makes would enable improving the model's performance at runtime through providing feedback. Due to the difficulty of this complex task on long reasoning traces, single-model judges (even frontier models) do not do well at identifying reasoning defects. Additionally, leveraging frontier models during online training of reasoning LLMs is generally prohibited due to guardrails in terms of use. In this work, we introduce Reasoning Jury, a system that replaces the single judge with a jury of LLMs and a moderated consensus mechanism, to improve the fidelity of judgments for identifying reasoning defects. In reasoning jury, defects of a reasoning trace and their severity are surfaced through a deliberation where a moderator conducts a discussion amongst the jury where the jurors critique each other's judgments and get to modify their initial votes. The moderator derives a consensus through deliberation amongst jurors or consolidation of judgements. We show that Reasoning Jury with a jury of open-weight models (e.g., gpt-oss-120b) is able to significantly outperform frontier models (opus-4.6, sonnet-4.6, and gemini-3.1-pro) at correctly identifying reasoning defects. Besides accuracy performance improvements, the aggregated cost of the jury (initial verdicts, deliberations, consolidation, etc.) is a fraction (8 to 15%) of the cost of running frontier models in LLM-as-a-judge setup. We also show how these judgements can be leveraged to understand failure modes of reasoning LLMs on benchmarks, which allows much deeper understanding of a model's performance.

Reasoning Denoiser: Denoising Reasoning Traces for Hallucination Detection in Large Reasoning Models

Large reasoning models (LRMs) generate long reasoning traces before producing final answers. While these traces may contain useful signals for hallucination detection, harnessing them is non-trivial because long trajectories often include noisy steps that obscure the cues relevant to truthfulness assessment. In this paper, we identify two prevalent forms of reasoning noises, i.e., irrelevant steps and repetitive steps, and show that both substantially degrade hallucination detection performance. Existing confidence-based scores and naive embedding-based filtering fail to reliably separate noisy from informative steps. To address this challenge, we propose REDE, a novel learning framework for denoising reasoning traces for hallucination detection. Specifically, REDE leverages final-answer attention as an automatic supervision signal to shape the step-level representation space, yielding refined embeddings in which noisy steps can be reliably identified and filtered. REDE can be readily plugged into diverse hallucination detectors by operating on the filtered reasoning trajectory after removing noisy steps. Extensive experiments on multiple reasoning benchmarks show that REDE consistently improves detection performance over competitive baselines.

Improving LLM Interpretability with User-Centric Chain-of-Thought Reasoning

Advancing reasoning capabilities allow large language models (LLMs) to tackle increasingly complex problems, while reasoning traces - intermediate steps toward solutions - open up high-stakes applications by enabling human inspection of AI decision-making. However, current approaches prioritize model performance over human interpretability, limiting effective human-AI collaboration. In this study, we design and evaluate a human-centered approach that structures reasoning traces based on self-contained, verifiable steps, enabling users to independently assess and correct AI reasoning. Our approach uses XML-like tags to encode reasoning content and metadata, facilitating targeted feedback. Evaluation on mathematical reasoning tasks shows our approach maintains equivalent performance to standard Chain-of-Thought reasoning while enhancing interpretability. User studies demonstrate significant improvements in perceived usefulness and ease of use. This work advances understanding of how user-centric design of LLM outputs can better serve human collaboration needs in high-stakes AI deployments.

Rethinking On-Policy Self-Distillation for Thinking Models

Self-distillation is a promising recipe for self-improvement in language models. In this setting, a model can serve as its own teacher when given privileged information, such as a solution to a math problem. This seems especially appealing for thinking models, which can use test-time reasoning to absorb the privileged information. Surprisingly, we show that privileged self-distillation degrades thinking models on long reasoning traces: across five Qwen3 and OLMo thinking models evaluated on AIME24, AIME25, and HMMT25, privileged-context distillation causes a relative drop of up to 17% in avg@16 accuracy. The degradation scales with the amount of privileged context withheld from the student and is most pronounced at long rollout budgets, where thinking models otherwise obtain their largest gains. This failure mode is not specific to self-distillation: on-policy distillation (OPD) improves thinking models, but privileged OPD reverses these gains. Our diagnostics link this failure mode to how privileged teacher context reshapes learning at high-entropy forking positions, where multiple continuations remain plausible and may lead to different reasoning paths. Privileged context lowers fork rates in thinking-model rollouts but not in instruction-model rollouts. This leads to an interesting dichotomy, where privileged context can help instruction-tuned models but hurts stronger thinking models. The effect is visible when the student begins a self-correction branch, where privileged OPD penalizes sampled reconsideration tokens that vanilla OPD supports. Thinking models trained with a privileged teacher produce fewer verification, backtracking, and hedging markers, even after length normalization. These findings indicate that self-distillation for strong thinking models requires attention to token-level signal, especially around correction and reasoning steps.

ThinkProbe: Beyond Accuracy -- Structural Profiling of Open-Ended LLM Reasoning Traces via Non-Generative Thought Graphs

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.

Cognitive Episodes in LLM Reasoning Traces Enable Interpretable Human Item Difficulty Prediction

Predicting human item difficulty is central to educational assessment, where reliable estimates support fairness and effective test construction. Existing methods often depend on costly human calibration or item-level textual representations, providing limited evidence about the cognitive processes that make items difficult. We argue that difficulty should be viewed not only as a property of item text, but also as an observable consequence of the problem-solving burden an item induces. Large Reasoning Models (LRMs) offer scalable process evidence through reasoning traces, but such evidence must be structured to support interpretable modeling. To this end, we introduce Epi2Diff (Episode to Difficulty), a framework that maps LRM reasoning traces into cognitively grounded episode sequences. These episodes group trace segments into functional problem-solving states, enabling difficulty to be modeled through reasoning scale, effort allocation, and state transitions. Epi2Diff extracts compact episode-dynamic features and combines them with semantic item representations for human difficulty prediction. Experiments on four real-world human difficulty datasets show that Epi2Diff consistently outperforms strong baselines, including fine-tuned small language models, LLM in-context learning, and supervised LLM adaptation. On SAT-derived classification benchmarks, Epi2Diff achieves an 8.1% average relative gain over supervised LLM fine-tuning baselines. Further analyses show that harder items induce more effortful, iterative, and implementation-centered episode dynamics, rather than merely longer responses. These results demonstrate that cognitive episodes in LRM reasoning traces provide a predictive and interpretable process representation for human item difficulty, offering a new lens for educational measurement with reasoning models.

Reasoning Quality Emerges Early: Data Curation for Reasoning Models

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.

MARS: Margin-Adversarial Risk-controlled Stopping for Parallel LLM Test-time Scaling

Parallel test-time scaling samples many reasoning traces and majority-votes their answers, improving LLM accuracy but requiring traces to run to completion, incurring substantial computational overhead. We observe that probing partial traces at intermediate checkpoints can extract current answers without disrupting generation, revealing an evolving aggregate vote. Based on this observation, we introduce MARS, a margin-adversarial stopping rule that estimates which active traces are likely to change their answers and stops once the leader remains safe under a conservative bound on future vote movement. The rule separates two sources of uncertainty. It learns the trace-level switch probabilities that determine how much of the current margin is likely to be retained, while handling the harder question of where switching traces land through an adversarial bound calibrated from warmup traces. With true switch probabilities, MARS guarantees with high probability that the early-stopped answer matches the full-budget vote. In practice, a five-feature logistic model closely matches oracle switching behavior. Across three reasoning models and three competition-math benchmarks, MARS saves 25-47% of self-consistency tokens and 14-29% on top of DeepConf Online, a strong confidence-weighted baseline that already filters and truncates weak traces, while matching the accuracy of the corresponding full-budget baselines.

Compress-Distill: Reasoning Trace Compression for Efficient Knowledge Distillation

Reasoning models produce long chain-of-thought traces that are costly to distill and encourage verbose student outputs. We study post-hoc compression of such traces before knowledge distillation. Two teachers, Qwen3.5-397B-A17B and gpt-oss-120B, generate about 283k correct traces each; two instruction-tuned models then compress them to 8.6-21.0% of their original character length. Across a 48-run main grid plus seven Qwen-teacher truncation ablations, compressed traces reduce training tokens to 12-30% of raw, speed up training by 2.0-7.6x, and shorten inference outputs by 3-19x with smaller reductions under the shorter gpt-oss teacher. However, raw traces retain the highest downstream accuracy at every scale and for both teachers. A length-matched raw-trace truncation ablation shows that compression is not merely benefiting from a smaller token budget: model-compressed traces usually beat or match naive truncation, especially for smaller students, while maintaining shorter inference outputs. Overall, reasoning-trace compression offers an accuracy-efficiency trade-off rather than a free improvement: students retain up to 96% of raw-trace accuracy while gaining up to 18x higher per-token efficiency, and at the 0.8B scale under LoRA compressed traces narrow the raw-vs-compressed gap but do not exceed raw.

ReasoningFlow: Discourse Structures for Understanding LLM Reasoning Traces

Large reasoning models (LRMs) produce reasoning traces with non-linear structures, such as backtracking and self-correction, that complicate the evaluation and monitoring of the reasoning process. We introduce ReasoningFlow, a framework that captures the discourse structures of LRM reasoning traces into fine-grained directed acyclic graphs (DAGs). We develop and validate our annotation schema through careful manual annotation of 31 traces (2.1k steps), achieving high inter-annotator agreement, then scale to automatic annotation of 1,260 traces (247.7k steps) spanning three tasks (math, science, argumentation) and five models (Qwen2.5-32B-Inst, QwQ-32B, DeepSeek-V3, DeepSeek-R1, GPT-oss-120B). By analyzing ReasoningFlow graphs, we find: (1) LRMs exhibit structurally similar traces, despite being trained from different base models and potentially non-overlapping post-training data. (2) ReasoningFlow reveals diverse fine-grained reasoning behaviors (e.g., local verification, self-reflection, and assumptions) that can be used for better reasoning trace monitorability. (3) In LRMs, most of the erroneous steps are not used to derive final answers. (4) Mechanistic causal dependencies between steps do not reflect the language-level discourse structure. We release the dataset and code in: https://github.com/jinulee-v/reasoningflow.

Synthetic Contrastive Reasoning for Multi-Table Q&A

Multi-table question answering requires models to retrieve relevant evidence, link schemas, and perform compositional reasoning across relational tables. Existing multi-table Q&A resources typically provide questions and final answers but lack reasoning supervision that explains how answers are derived. To address this gap, we construct a synthetic contrastive reasoning-trace dataset for MMQA by generating validated positive traces and plausible negative traces with heterogeneous LLMs. We then use the resulting preference pairs to fine-tune open-weight LLMs with Contrastive Preference Optimization (CPO). Across Qwen3-14B, Mistral-8B, and Llama-3.1-8B, CPO achieves absolute average improvements over Q&A supervised fine-tuning ranging from 9.7%-16.3%, with gains up to 21 percentage points on MMQA. Ablations show that heterogeneous positive and negative trace generators strengthen the contrastive signal, and automated as well as human evaluations indicate that the generated pairs are largely faithful, coherent, and meaningfully contrastive.

Reasoning-Trace Collapse: Evaluating the Loss of Explicit Reasoning During Fine-Tuning

Explicit reasoning models are trained to produce intermediate reasoning traces before final answers, but downstream fine-tuning is often performed on ordinary instruction-response data that contains no such traces. We show that this mismatch can induce reasoning-trace collapse: a fine-tuned model continues to produce plausible final answers while losing the structurally valid explicit reasoning traces that made it a reasoning model in the first place. We introduce a structural evaluation framework that separates answer correctness from reasoning-trace validity, measuring valid, empty, missing, and truncated reasoning alongside reasoning-conditioned task performance. Using this framework, we study four open-weight reasoning models and find that standard supervised fine-tuning can rapidly suppress valid reasoning traces, and that answer-only metrics can substantially obscure this failure: in several settings, performance conditional on valid reasoning remains high while the rate of valid reasoning falls sharply. We further show that simple loss-masking strategies can substantially mitigate collapse without requiring teacher-generated reasoning traces. These results suggest that evaluations of fine-tuned reasoning models should report structural reasoning reliability metrics in addition to final-answer performance, especially when adaptation data does not contain explicit reasoning traces.

Shorthand for Thought: Compressing LLM Reasoning via Entropy-Guided Supertokens

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.