When Reasoning Meets Its Laws

TL;DR

This paper introduces the Laws of Reasoning (LoRe), a theoretical framework for understanding and improving reasoning behaviors in large reasoning models through properties like monotonicity and compositionality.

Contribution

It formalizes reasoning behaviors with LoRe, proposes a benchmark LoRe-Bench for property measurement, and develops a finetuning method to enhance model reasoning by enforcing the compute law.

Findings

Models generally show monotonic reasoning but lack compositionality.

Enforcing the compute law improves reasoning performance.

Better compliance with LoRe laws leads to consistent reasoning improvements.

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/