Fractional Reasoning via Latent Steering Vectors Improves Inference Time
  Compute
Authors: name: Sheng Liu, name: Tianlang Chen, name: Pan Lu, name: Haotian Ye, name: Yizheng Chen, name: Lei Xing, name: James Zou

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.