On the Self-awareness of Large Reasoning Models' Capability Boundaries

TL;DR

This work investigates whether Large Reasoning Models exhibit self-awareness of their capability boundaries, addressing unproductive reasoning on hard questions. By analyzing black-box reasoning trajectories and white-box hidden states, it reveals boundary signals that separate solvable from unsolvable questions and proposes two boundary-aware, test-time strategies to curb wasted computation. The Reasoning Expression Monitoring and Hidden States Monitoring approaches maintain accuracy on solvable problems while dramatically reducing token usage and preventing incomplete outputs on unsolvable ones. Overall, the study advances understanding of LRM reasoning by enabling boundary-aware inference that improves reliability and efficiency in challenging mathematical tasks.

Abstract

Large Reasoning Models (LRMs) have shown impressive performance on complex reasoning tasks such as mathematics, yet they also display misbehaviors that expose their limitations. In particular, when faced with hard questions, LRMs often engage in unproductive reasoning until context limit, producing wrong answers while wasting substantial computation. This phenomenon reflects a fundamental issue: current answering paradigms overlook the relationship between questions and LRMs' capability boundaries. In this paper, we investigate whether LRMs possess self-awareness of capability boundaries. We begin by an observation that LRMs may know what they cannot solve through expressed reasoning confidence. For black-box models, we find that reasoning expressions reveal boundary signals, with accelerated growing confidence trajectory for solvable problems but convergent uncertainty trajectory for unsolvable ones. For white-box models, we show that hidden states of the last input token encode boundary information, with solvable and unsolvable problems linearly separable even before reasoning begins. Building on these findings, we propose two simple yet effective optimization strategies: reasoning expression monitoring and hidden states monitoring. Experiments demonstrate that these boundary-aware strategies enable LRMs to avoid unproductive reasoning without sacrificing accuracy, significantly improving reliability and efficiency by cutting token usage up to 62.7 - 93.6%.

Figures (10)

• Figure 1: Capability boundary is encoded in reasoning trajectories as expression density patterns, and in the last token hidden states even before reasoning begins. Reasoning with capability boundary enables LRMs to identify unsolvable questions and provide more reliable and efficient answers.
• Figure 2: Confident vs. uncertain expressions in reasoning.
• Figure 3: Capability boundaries revealed by reasoning expressions. Questions within the boundary exhibit concave trajectory for confident expressions, whereas questions beyond the boundary exhibit convex trajectory for uncertain expressions.
• Figure 4: Accuracy (%) of ConfDiff and ConfCurv to separate unsolvable and solvable questions through out the reasoning stage. ConfDiff is more reliable as it achieves higher accuracy and exhibits smaller fluctuations. Boundary awareness signal appears at an early stage (e.g., 2%).
• Figure 5: Left: Capability boundary revealed by linear classifier clearly separates solvable and unsolvable questions in hidden states. Right: Among solvable questions, those close to capability boundary requires more token usage ($1.5$ – $2\times$) to arrive at the correct answer.