Characterizing, Evaluating, and Optimizing Complex Reasoning

TL;DR

This paper introduces a unified framework for defining, evaluating, and optimizing complex reasoning in large models, using DAG-based evaluation and a learned reward model to improve reasoning quality and task performance.

Contribution

It proposes the ME$^2$ principle for reasoning quality, models reasoning traces as DAGs, and develops a TRM-Preference dataset and Thinking Reward Model for scalable evaluation and optimization.

Findings

Thinking rewards improve reasoning outcomes by up to 19.3%.

Better reasoning selection enhances performance by up to 3.9%.

DAG-based evaluation effectively captures complex reasoning structures.

Abstract

Large Reasoning Models (LRMs) increasingly rely on reasoning traces with complex internal structures. However, existing work lacks a unified answer to three fundamental questions: (1) what defines high-quality reasoning, (2) how to reliably evaluate long, implicitly structured reasoning traces, and (3) how to use such evaluation signals for reasoning optimization. To address these challenges, we provide a unified perspective. (1) We introduce the ME$^2$ principle to characterize reasoning quality along macro- and micro-level concerning efficiency and effectiveness. (2) Built on this principle, we model reasoning traces as directed acyclic graphs (DAGs) and develop a DAG-based pairwise evaluation method, capturing complex reasoning structures. (3) Based on this method, we construct the TRM-Preference dataset and train a Thinking Reward Model (TRM) to evaluate reasoning quality at scale. Experiments show that thinking rewards serve as an effective optimization signal. At test time, selecting better reasoning leads to better outcomes (up to 19.3% gain), and during RL training, thinking rewards enhance reasoning and performance (up to 3.9% gain) across diverse tasks.