Is Your Model Thinking or Just Stagnating? PUMA: Diagnosing Reasoning Pathology via Phase-Momentum Alignment

2026-07-19

AI Summary

This work addresses the challenge that large reasoning models often suffer from computational redundancy and suboptimal accuracy during inference due to over-reasoning, while existing approaches struggle to distinguish effective reasoning from unproductive stagnation in real time. The authors propose a phase-momentum alignment hypothesis and introduce a cognitive energy model that characterizes reasoning dynamics along two orthogonal dimensions: geometric cognitive effort and entropy-based uncertainty. Building upon this, they develop PUMA—a training-agnostic framework that enables real-time diagnosis and intervention in the reasoning process. PUMA pioneers the integration of phase-momentum alignment into reasoning analysis, combining lightweight phase monitoring with event-triggered geometric evaluation to construct a hierarchical diagnostic mechanism based on latent-space velocity, tortuosity, and uncertainty. Experiments across models ranging from 1.5B to 32B parameters demonstrate that PUMA consistently outperforms existing methods, achieving superior accuracy-efficiency trade-offs and strong cross-domain generalization.

Abstract

Test-time scaling empowers Large Reasoning Models (LRMs) to tackle complex tasks via extensive Chain-of-Thought (CoT). However, this often induces the "overthinking" paradox, where redundant reasoning increases computational overhead without guaranteeing accuracy. Existing test-time efficiency optimization methods primarily fall into two categories: information-theoretic approaches, which are prone to "deceptive convergence" where low uncertainty masks hallucinations, and latent representation analyses, which are often post-hoc, lacking the real-time sensitivity for dynamic reasoning. To bridge this gap, we first posit the Phase-Momentum Alignment Hypothesis, asserting that reasoning correctness hinges on the temporal synchronization between geometric momentum and uncertainty resolution. We then theoretically formulate the Cognitive-Energy Model to characterize these dynamics through two orthogonal dimensions: Geometric Cognitive Effort, quantified by latent velocity and tortuosity, and Entropic Cognitive Uncertainty. To operationalize this, we introduce PUMA (Phase-Uncertainty Momentum Alignment), a training-free framework employing a tiered diagnostic architecture. By coupling lightweight phase monitoring with event-triggered geometric analysis, PUMA effectively distinguishes active exploration from passive stagnation, enabling precise interventions through adaptive truncation or corrective measures. Extensive experiments on LRMs spanning 1.5B to 32B demonstrate that PUMA consistently outperforms state-of-the-art baselines across diverse benchmarks, achieving a superior accuracy-efficiency trade-off and robust cross-domain generalization.

Problem

• overthinking
• reasoning pathology
• test-time scaling
• Large Reasoning Models
• deceptive convergence

Innovation

• Phase-Momentum Alignment
• Cognitive-Energy Model
• Geometric Cognitive Effort
• Test-time Scaling
• Reasoning Pathology Diagnosis