When Reasoning Meets Its Laws

Junyu Zhang, Yifan Sun, Tianang Leng, Jingyan Shen, Liu Ziyin, Paul Pu Liang, Huan Zhang

Keywords: Large Reasoning Models, Reasoning Laws

TL;DR: This paper presents the Laws of Reasoning (LoRe), a unified framework that formalizes intrinsic reasoning patterns in large reasoning models.

Abstract: Despite the superior performance of Large Reasoning Models (LRMs), their reasoning behaviors are often counterintuitive, leading to suboptimal reasoning capabilities. To theoretically formalize the desired reasoning behaviors, this paper presents the Laws of Reasoning (LoRe), a unified framework that characterizes intrinsic reasoning patterns in LRMs. We first propose *compute law* with the hypothesis that the reasoning compute should scale linearly with question complexity. Beyond compute, we extend LoRe with a supplementary *accuracy law*. Since the question complexity is difficult to quantify in practice, we examine these hypotheses by two properties of the laws, *monotonicity* and *compositionality*. We therefore introduce LoRe-Bench, a benchmark that systematically measures these two tractable properties for large reasoning models. Evaluation shows that most reasoning models exhibit reasonable monotonicity but lack compositionality. In response, we develop an effective finetuning approach that enforces compute-law compositionality. Extensive empirical studies demonstrate that better compliance with compute laws yields consistently improved reasoning performance on multiple benchmarks, and uncovers synergistic effects across properties and laws. Project page: https://lore-project.github.io.

Submission Number: 273