Consilience for Verifier-Free Test-Time Scaling

2026-08-10

AI Summary

This work addresses the limitation of existing confidence-based, verifier-free test-time scaling methods, which often produce erroneous answers on complex tasks due to premature high-confidence predictions. The authors propose Consilience, a novel framework that introduces confidence trajectory patterns as a new evaluation criterion, emphasizing the dynamic signature of low initial confidence followed by high final confidence. By explicitly penalizing early certainty and enforcing late-stage convergence through a composite metric, Consilience overcomes the constraints of conventional approaches that rely solely on terminal confidence scores. Implemented with negligible computational overhead, the method substantially enhances the reasoning quality of large language models in settings without external verifiers. Empirical results demonstrate that Consilience significantly outperforms current baselines on graduate-level mathematical reasoning and free-form code generation tasks, underscoring the critical role of confidence dynamics in improving inference performance.

Abstract

Test-time scaling often uses an external verifier, such as compilers and test cases in coding or trained value functions in robotics applications, to obtain high-quality rollouts. Verifier-free test-time scaling (or VF-TTS) is gaining extensive attention as a mechanism to enhance Large Language Model (LLM) reasoning, primarily because we do not have access to such high-quality verifiers in many real-world applications. Among existing VF-TTS methods, confidence-based VF-TTS methods, which compute and rank rollouts solely by confidence, are particularly promising. Such methods introduce near-zero overhead for sample evaluation and require minimal access to internal model states, making the methods highly flexible across models and tasks. In this paper, we demonstrate a critical limitation of existing confidence-based VF-TTS methods by showing that such methods catastrophically break down on complex tasks. We observe a very interesting phenomenon: uniformly high confidence frequently indicates a failure to explore, favoring confidently wrong answers. To address this, our core insight is that robust cognitive search requires a specific confidence trajectory pattern: such methods perform exploratory branching at the beginning, as manifested by low initial confidence, and converge to a high final confidence solution. To implement this insight, we introduce consilience, a novel selection framework that explicitly evaluates the temporal asymmetry of confidence in reasoning. We operationalize this via a combinatorial metric that actively penalizes high initial confidence while strictly demanding final certainty. Extensive experiments covering both graduate-level mathematics problems and free-form code generation demonstrate that consilience effectively outperforms existing baselines, validating our novel perspective on completion confidence.

Problem

• verifier-free test-time scaling
• confidence-based reasoning
• exploration failure
• complex reasoning tasks
• LLM reasoning

Innovation

• consilience
• verifier-free test-time scaling
• confidence trajectory
• temporal asymmetry
• LLM reasoning