Paper 2512.17901
When Reasoning Meets Its Laws
- Published
- Dec 2025
- Research lab
- Independent
- Citations
- 2
- GitHub
- 38 stars
01 In brief
Summary
The paper introduces the Laws of Reasoning (LORE), a framework formalizing desired reasoning behaviors in Large Reasoning Models (LRMs).
LORE posits a compute law (reasoning compute scales linearly with question complexity) and an accuracy law (accuracy decays exponentially with complexity).
Since complexity is hard to measure, the laws are approximated via two tractable properties: monotonicity and compositionality.
The authors introduce LORE-BENCH, comprising LORE-MONO (synthetic questions with known complexity orderings) and LORE-COMPO (built from MATH500), to evaluate these properties.
Evaluation of 10 LRMs shows they largely satisfy monotonicity but fail compositionality.
To address this, they propose SFT-Compo, a fine-tuning method that enforces compute-law compositionality by selecting reasoning paths where the composite question's compute equals the sum of sub-questions' compute.
Experiments on four models (DeepSeek-R1-Distill 1.5B, 7B, 8B, and Phi-4-mini) show SFT-Compo reduces nMAD (e.g., from 0.528 to 0.314 on 1.5B) and improves average Pass@1 across six benchmarks (e.g., +5.0 on 8B).
They also observe synergistic effects: enforcing compute compositionality improves monotonicity and accuracy compositionality.
02 From the paper
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/