Consilience for Verifier-Free Test-Time Scaling
2026-08-10 • Computation and Language
Computation and LanguageMachine Learning
AI summaryⓘ
The authors studied ways to improve how large language models (LLMs) check their own answers without using external tools. They found that methods relying only on the model’s confidence scores fail on complex tasks because the model can be confidently wrong early on. To fix this, they propose a new method called consilience that looks at how confidence changes over time, favoring approaches that start uncertain but end confident. Their experiments show this method works better on hard math problems and coding tasks than older techniques. This gives a new way to evaluate reasoning quality based on confidence patterns rather than just confidence levels.
Large Language ModelsTest-time scalingVerifier-free test-time scalingConfidence-based methodsCognitive searchConfidence trajectoryExploratory branchingConsilienceMathematics problem solvingCode generation
Authors
Lecheng Kong, Like Hui, Haitao Mao, Jun Huan
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.