Research map / Large language models / Reasoning and chain of thought

When Reasoning Meets Its Laws

NeurIPS 2026 · Large language models › Reasoning and chain of thought · approach: Long CoT dynamics and efficiency · 0 citations (OpenAlex)

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Proposes the Laws of Reasoning (LoRe), a compute law and accuracy law for LRMs, tests them via monotonicity and compositionality on the LoRe-Bench, and improves compositionality with an SFT method (SFT-Compo) that yields gains on math benchmarks.

Problem

Large reasoning models often allocate reasoning compute in counterintuitive ways (overthinking simple questions, underthinking complex ones), and there is no formal principle or tractable test for desirable reasoning behavior relative to question complexity.

Approach

Formalizes an ideal relationship where reasoning compute scales linearly with minimal solution complexity (compute law) and accuracy decays exponentially with complexity (accuracy law), and makes these checkable through tractable proxies: monotonicity and compositionality over independent question pairs. Fine-tunes LRMs on reasoning traces selected so that the compute of a composed question approx

Key results

• SFT-Compo cuts nMAD of reasoning compute on LoRe-Compo for the 1.5B model from 0.528 to 0.314 (40.5% reduction) and for 8B from 0.423 to 0.328.
• SFT-Compo raises average Pass@1 across six benchmarks: DeepSeek-R1-1.5B from 47.6 to 52.4 and DeepSeek-R1-8B from 54.5 to 59.5; it outperforms the SFT control on all cases.
• Most evaluated LRMs show strong monotonicity (overall compute Spearman up to 0.99) but large compositionality deviations; the 1.5B model's overall compute monotonicity rises from 0.875 to 0.977 after SFT-Compo.

Surprising findings

• Compositional questions can receive far fewer tokens than their parts: DeepSeek-R1-1.5B used about 732 tokens on the composite question versus 2177 and 3547 on its sub-questions, with accuracy dropping to 0.25.
• Enforcing compositionality on reasoning compute also improved compositionality of log accuracy (nMAD drop from 2.368 to 0.685 on 1.5B), an unexpected cross-law effect.

Limitations

• LoRe-Mono includes only 40 seed questions across four domains, limiting coverage.
• Independence is operationalized as disjoint sets of math concepts, which is a non-rigorous proxy.
• Only open-source LRMs were evaluated due to budget constraints; closed models were not tested.

Experimental setup

Datasets: DeepScaleR MATH500

Benchmarks: LoRe-Mono LoRe-Compo GSM8K MATH500 AIME 2024 AIME 2025 AMC 2023 OlympiadBench

Metrics: Spearman correlation normalized mean absolute deviation (nMAD) Pass@1

Baselines: Thinkless-1.5B AdaptThink-7B SFT

Builds on: DeepSeek-R1 DeepScaleR OpenAI o1

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