Answer-Distribution Trajectories: A Stochastic-Dynamics View of LLM Reasoning

Chain-of-thought traces from large reasoning models can span tens of thousands of tokens, yet we lack a vocabulary for describing their internal structure. Previous methods developed to analyze chain-of-thought traces are either too rigid or not expressive enough, failing to capture features across domains and models. To remedy this, we develop ReasonOps, an unsupervised, expressive method for annotating chain-of-thought traces, providing succinct universal operators. Using ReasonOps, we analyze 44,662 traces from 12 thinking LLMs spanning 6 families across 8 reasoning benchmarks and discover that they share a common compositional structure: 7 recurring reasoning operators -- discourse-level moves such as backtracking, inferring, and hypothesizing -- that emerge from unsupervised clustering of sentence-initial 3-token pivots. These operators appear across every model family and benchmark domain, confirmed by three independent LLM judges who classify held-out samples at 70 -76% accuracy. We analyze the structure of operators on easy vs. hard problems, revealing that reflective operators are more helpful on hard problems and harm performance on easy problems. Operator sequences are highly model-identifying: a classifier trained on operator distributions alone recovers the source model with macro-AUC, revealing that each model family has a distinctive reasoning fingerprint. Structural operator features predict within-problem answer correctness well above baselines. Classifiers built on these operators reach WP-AUC and on AIME specifically. ReasonOps further enables early quality estimation well before the trace completes: we predict at WP-AUC for only 50% of the trace. The ReasonOps pipeline is unsupervised and annotation-free, enabling deep insights into LLM reasoning traces as well as strong downstream results on model identification and correctness prediction.

Chain-of-thought (CoT) reasoning has become the default strategy for enhancing LLM capabilities, yet its application raises a fundamental question: when is explicit reasoning actually beneficial? Empirical evidence reveals a striking paradox: CoT often provides marginal or even negative gains on factual and open-ended tasks while multiplying token consumption. In this work, we show that LLM reasoning is not a static property of tasks or models, but a \emph{dynamic decoding state} that emerges during generation. Through systematic analysis, we find early-stage entropy dynamics provide a reliable signal of this state: tasks benefiting from CoT exhibit consistent entropy reduction, while others display unstable or increasing patterns. This behavior can be interpreted as a phase-transition-like shift from a high-entropy exploratory regime to a low-entropy structured reasoning regime. Based on these insights, we propose \textbf{EDRM} (Entropy Dynamics-based Reasoning Manifold), a lightweight and training-free routing framework that leverages early decoding entropy to adaptively select inference strategies. EDRM embeds entropy trajectories into a compact and interpretable manifold representation, enabling both zero-shot deployment and fine-grained instance-level adaptation. Across 15 benchmarks and 4 LLMs of varying scales and architectures, EDRM consistently outperforms static baselines. At the dataset level, EDRM achieves \textbf{41--55%} token reduction while improving accuracy with as few as 50 calibration samples. At the instance level, it further improves accuracy by up to \textbf{4.7%} while maintaining \textbf{27--45%} token savings. These results suggest that reasoning should be invoked selectively rather than by default, and demonstrate the effectiveness of entropy-driven decoding control for efficient and adaptive LLM inference.

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.