Answer-Distribution Trajectories: A Stochastic-Dynamics View of LLM Reasoning
Abstract
Chain-of-thought reasoning provides a structured computation between a model's input and final answer. Yet it is often evaluated through endpoint accuracy, which ignores the path taken to reach that answer. An emerging line of work addresses this limitation using entropy profiles, which track how uncertainty evolves over the reasoning process but do not reveal which competing hypotheses account for that uncertainty. We introduce answer-distribution trajectories, a stochastic-dynamics-inspired representation that tracks the model's full predictive distribution over answers as reasoning unfolds. As a strictly finer representation than endpoint and entropy summaries, answer-distribution trajectories enable us to characterize a trace through a dynamical reasoning profile spanning exploration, revision, motion, and commitment, and to distinguish different dynamical mechanisms of reasoning success and failure. Across sixteen open-weight language models and four reasoning benchmarks, we show that traces with the same endpoint and similar entropy profiles can exhibit substantially different reasoning dynamics. We further find substantial variation in these dynamics both within and across models and tasks, with different objectives favoring different dynamical profiles. Additionally, we show that training and inference choices systematically reshape these profiles. Our results suggest that answer-distribution trajectories provide a rich framework for analysing and evaluating the dynamics of LLM reasoning.
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BibTeX
@misc{catala2026answerdistribution,
title = {{Answer-Distribution Trajectories: A Stochastic-Dynamics View of LLM Reasoning}},
author = {Mar Gonzàlez I Català and Haitz Sáez de Ocáriz Borde and Davide Murari and Carola-Bibiane Schönlieb and Pietro Liò and George Montañez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.09030},
eprint = {2609.09030},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09030},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Answer-Distribution Trajectories: A Stochastic-Dynamics View of LLM Reasoning
AU - Mar Gonzàlez I Català
AU - Haitz Sáez de Ocáriz Borde
AU - Davide Murari
AU - Carola-Bibiane Schönlieb
AU - Pietro Liò
AU - George Montañez
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.09030
UR - https://arxiv.org/abs/2609.09030
AB - Chain-of-thought reasoning provides a structured computation between a model's input and final answer. Yet it is often evaluated through endpoint accuracy, which ignores the path taken to reach that answer. An emerging line of work addresses this limitation using entropy profiles, which track how uncertainty evolves over the reasoning process but do not reveal which competing hypotheses account for that uncertainty. We introduce answer-distribution trajectories, a stochastic-dynamics-inspired representation that tracks the model's full predictive distribution over answers as reasoning unfolds. As a strictly finer representation than endpoint and entropy summaries, answer-distribution trajectories enable us to characterize a trace through a dynamical reasoning profile spanning exploration, revision, motion, and commitment, and to distinguish different dynamical mechanisms of reasoning success and failure. Across sixteen open-weight language models and four reasoning benchmarks, we show that traces with the same endpoint and similar entropy profiles can exhibit substantially different reasoning dynamics. We further find substantial variation in these dynamics both within and across models and tasks, with different objectives favoring different dynamical profiles. Additionally, we show that training and inference choices systematically reshape these profiles. Our results suggest that answer-distribution trajectories provide a rich framework for analysing and evaluating the dynamics of LLM reasoning.
ER -