Chain-of-thought (CoT) reasoning in large language models often produces redundant steps that increase generation cost and obscure when reasoning has effectively completed. Existing stopping methods rely on output-level or token-level signals, overlooking internal representation dynamics that reflect reasoning progress. We propose STARS (STate-Aware Reasoning Stopping), a framework that leverages spectral analysis of hidden-state representations to detect transitions in reasoning phases. Our key insight is that structural changes in the representation space capture shifts in reasoning states, enabling early and reliable stopping decisions. To address representation instability, where semantically similar steps can induce different hidden states, we focus on spectral structure rather than raw activations, improving robustness to context-dependent drift. Experiments on four mathematical and logical reasoning benchmarks show that STARS reduces generation cost by over 45% under fixed token budgets while improving accuracy over standard CoT baselines.

Large language models (LLMs) tool-use policies select actions from a finite candidate set at each reasoning step. We observe that this action-selection interface is already a linear contextual scorer: under a restricted output vocabulary, the LM head computes per-action scores from the last-layer hidden state, exactly the structure assumed by linear contextual bandits. Existing online adaptation methods for LLMs operate indirectly through prompts or retrieved memories, leaving this decision layer fixed and providing no explicit mechanism for action-level credit assignment or uncertainty-aware exploration. We propose OLIVIA, a lightweight online adaptation layer that replaces the frozen action-selection head with a per-action contextual linear bandit, selects actions via LinUCB exploration on the LLM’s hidden state and updates only its per-action sufficient statistics from step-level feedback via a rank-one Sherman–Morrison rule. Without backbone fine-tuning and additional LLM calls per step, OLIVIA adds negligible overhead relative to LLM inference. Across four tool-use benchmarks ToolBench, TaskBench, TaskBench-MM, BFCL and two backbones Qwen3-4B, Mistral-7B, OLIVIA outperforms prompt-based online adaptation and contextual-bandit variants.

Skills, as a useful abstraction for the procedural capabilities of large language models (LLMs), capture how models perform structured, multi-step reasoning and program execution. Existing approaches typically treat skills as explicit, surface-level constructs specified through prompts or programs, leaving open the question of how such procedural capabilities are represented inside the model and whether they can be manipulated as structured objects in latent space. In this empirical study, we investigate whether procedural LLM skills can be represented as directions in activation space and whether vector-space operations over these directions can express skill-level behaviors. We find that procedural skills admit a vector-space representation: individual skill directions can be activated to shift model behavior; independently extracted directions can compose to form higher-level skills. Contrastive directions yield context-conditioned algorithmic personalization and optimization trajectories over skill directions evolve non-monotonically, with intermediate states often surpassing fully optimized solutions. These results support a representation-level view of procedural LLM skills: they admit a latent vector-space organization that allows direct manipulation through internal interventions.

Recent advances in chain-of-thought (CoT) prompting have demonstrated the ability of large language models (LLMs) to perform multi-step reasoning. While prior work focuses on improving CoT generation quality or attributing token-level importance, we propose a novel framework to structurally analyze the latent dynamics of CoT trajectories for interpretability. Our method segments generated CoT into discrete reasoning steps, abstracts each step into a spectral embedding based on the eigenvalues of token-level Gram matrices, and clusters these embeddings into semantically meaningful latent states. We model the global evolution of reasoning as a first-order Markov chain over latent clusters, yielding interpretable transition structures. Through t-SNE visualizations and Monte Carlo rollouts, we uncover consistent trajectories across tasks and models, supporting the hypothesis that LLM reasoning follows globally coherent yet abstract paths.