Geometry of Divergence: Tracking Hidden-State Trajectories for Adaptive Multi-Turn Reasoning

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.

Users interacting with Large Language Models (LLMs) in a multi-turn conversation routinely refine their requests or pivot to new topics. LLMs, however, often miss these topic shifts and carry over irrelevant context from previous turns, leading to inaccurate responses. In this paper, we stress-test the multi-turn understanding of LLMs and study the following two sub-tasks: (1) detecting whether the user pivots or refines in the current turn, and (2) shortlisting relevant context from previous turns. To this end, we construct synthetic benchmarks based on real-world datasets from varied domains, as to simulate context shifts of different levels of difficulty. We then evaluate the zero-shot performance of ten LLMs (open-weight, closed-source and reasoning), and demonstrate that only some reasoning and strongly instructed LLMs are accurate in detecting pivots; open-weight LLMs struggle with the task and frequently carry stale context even with explicit cues; and all models suffer from a position bias. Based on the results, we discuss key takeaways for improving long-term robustness in multi-turn capabilities for LLMs.

Large reasoning models improve performance by generating extended chain-of-thought (CoT) reasoning, but this behavior becomes inefficient when applied to LLM agents. Current LLM agents often generate verbose textual reasoning at every decision step and allocate reasoning effort nearly uniformly across turns, leading to substantial inefficiency in multi-turn agentic trajectories. We propose Adaptive Latent Agentic Reasoning (ALAR), a dual-mode framework that uses compact latent reasoning for routine turns and selectively escalates to explicit chain-of-thought when deeper deliberation is needed. ALAR learns latent reasoning by using the agent's actions as supervision anchors and is further optimized to use latent reasoning when it is sufficient for task success and reserve explicit CoT for harder decisions. Experiments on agentic search and tool-use benchmarks show that ALAR maintains comparable or better task accuracy while substantially reducing generated tokens by up to 43.6% in search and 84.6% in tool use. These results demonstrate that ALAR improves the accuracy-efficiency trade-off of LLM agents by reducing unnecessary textual reasoning while preserving explicit deliberation for harder decision steps.