When to Vote, When to Rewrite: Disagreement-Guided Strategy Routing for Test-Time Scaling

TL;DR

This paper introduces a disagreement-guided, training-free framework for dynamically selecting test-time scaling strategies in large reasoning models, improving accuracy and efficiency on mathematical benchmarks.

Contribution

It proposes a novel instance-level routing approach based on output disagreement, enabling adaptive strategy selection without additional training.

Findings

Improves accuracy by 3-7% on mathematical benchmarks.

Reduces sampling cost compared to existing test-time scaling methods.

Effectively handles diverse instance difficulties through dynamic strategy routing.

Abstract

Large Reasoning Models (LRMs) achieve strong performance on mathematical reasoning tasks but remain unreliable on challenging instances. Existing test-time scaling methods, such as repeated sampling, self-correction, and tree search, improve performance at the cost of increased computation, yet often exhibit diminishing returns on hard problems. We observe that output disagreement is strongly correlated with instance difficulty and prediction correctness, providing a useful signal for guiding instance-level strategy selection at test time. Based on this insight, we propose a training-free framework that formulates test-time scaling as an instance-level routing problem, rather than allocating more computation within a single strategy, dynamically selecting among different scaling strategies based on output disagreement. The framework applies lightweight resolution for consistent cases, majority voting for moderate disagreement, and rewriting-based reformulation for highly ambiguous instances. Experiments on seven mathematical benchmarks and three models show that our method improves accuracy by 3% - 7% while reducing sampling cost compared to existing approaches.