PRISM: A Dual View of LLM Reasoning through Semantic Flow and Latent Computation

This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space. We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth. This structure already exists in base models, while reasoning training primarily accelerates convergence toward termination-related subspaces rather than introducing new representational organization. While early reasoning steps follow similar trajectories, correct and incorrect solutions diverge systematically at late stages. This late-stage divergence enables mid-reasoning prediction of final-answer correctness with ROC-AUC up to 0.87. Furthermore, we introduce trajectory-based steering, an inference-time intervention framework that enables reasoning correction and length control based on derived ideal trajectories. Together, these results establish reasoning trajectories as a geometric lens for interpreting, predicting, and controlling LLM reasoning behavior.

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.

Large language models (LLMs) have demonstrated strong capabilities in complex reasoning tasks, yet their decision-making processes remain difficult to interpret. Existing explanation methods often lack trustworthy structural insight and are limited to single-instance analysis, failing to reveal reasoning stability and systematic failure mechanisms. To address these limitations, we propose the Trustworthy Unified Explanation Framework (TRUE), which integrates executable reasoning verification, feasible-region directed acyclic graph (DAG) modeling, and causal failure mode analysis. At the instance level, we redefine reasoning traces as executable process specifications and introduce blind execution verification to assess operational validity. At the local structural level, we construct feasible-region DAGs via structure-consistent perturbations, enabling explicit characterization of reasoning stability and the executable region in the local input space. At the class level, we introduce a causal failure mode analysis method that identifies recurring structural failure patterns and quantifies their causal influence using Shapley values. Extensive experiments across multiple reasoning benchmarks demonstrate that the proposed framework provides multi-level, verifiable explanations, including executable reasoning structures for individual instances, feasible-region representations for neighboring inputs, and interpretable failure modes with quantified importance at the class level. These results establish a unified and principled paradigm for improving the interpretability and reliability of LLM reasoning systems.