Fractional Reasoning via Latent Steering Vectors Improves Inference Time Compute

TL;DR

Fractional Reasoning introduces a model-agnostic, training-free method to dynamically control reasoning depth at inference time, enhancing accuracy and efficiency in large language models across various tasks.

Contribution

It proposes a novel latent steering vector approach that allows continuous adjustment of reasoning intensity during inference, surpassing fixed prompt limitations.

Findings

Consistently improves performance on GSM8K, MATH500, and GPQA datasets.

Enhances both breadth-based and depth-based reasoning strategies.

Demonstrates effectiveness across diverse models and reasoning tasks.

Abstract

Test-time compute has emerged as a powerful paradigm for improving the performance of large language models (LLMs), where generating multiple outputs or refining individual chains can significantly boost answer accuracy. However, existing methods like Best-of-N, majority voting, and self-reflection typically apply reasoning in a uniform way across inputs, overlooking the fact that different problems may require different levels of reasoning depth. In this work, we propose Fractional Reasoning, a training-free and model-agnostic framework that enables continuous control over reasoning intensity at inference time, going beyond the limitations of fixed instructional prompts. Our method operates by extracting the latent steering vector associated with deeper reasoning and reapplying it with a tunable scaling factor, allowing the model to tailor its reasoning process to the complexity of each input. This supports two key modes of test-time scaling: (1) improving output quality in breadth-based strategies (e.g., Best-of-N, majority voting), and (2) enhancing the correctness of individual reasoning chains in depth-based strategies (e.g., self-reflection). Experiments on GSM8K, MATH500, and GPQA demonstrate that Fractional Reasoning consistently improves performance across diverse reasoning tasks and models.