# Characterizing, Evaluating, and Optimizing Complex Reasoning

arXiv: https://arxiv.org/abs/2602.08498 · HTML: https://mlsanity.com/paper/2602.08498/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 40 of its 65 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 40)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [Chain of Draft: Thinking Faster by Writing Less](https://mlsanity.com/paper/2502.18600/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [Judging the Judges: A Systematic Study of Position Bias in LLM-as-a-Judge](https://mlsanity.com/paper/2406.07791/) (2024)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [General-Reasoner: Advancing LLM Reasoning Across All Domains](https://mlsanity.com/paper/2505.14652/) (2025)
- [Is LLM-as-a-Judge Robust? Investigating Universal Adversarial Attacks on Zero-shot LLM Assessment](https://mlsanity.com/paper/2402.14016/) (2024)
- [DeepSeekMath-V2: Towards Self-Verifiable Mathematical Reasoning](https://mlsanity.com/paper/2511.22570/) (2025)
- [SuperGPQA: Scaling LLM Evaluation across 285 Graduate Disciplines](https://mlsanity.com/paper/2502.14739/) (2025)
- [A Chain-of-Thought Is as Strong as Its Weakest Link: A Benchmark for Verifiers of Reasoning Chains](https://mlsanity.com/paper/2402.00559/) (2024)
- [Evaluating Step-by-step Reasoning Traces: A Survey](https://mlsanity.com/paper/2502.12289/) (2025)
- [ExGRPO: Learning to Reason from Experience](https://mlsanity.com/paper/2510.02245/) (2025)
- [ReasonFlux-PRM: Trajectory-Aware PRMs for Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2506.18896/) (2025)
- [R-PRM: Reasoning-Driven Process Reward Modeling](https://mlsanity.com/paper/2503.21295/) (2025)
- [Making Slow Thinking Faster: Compressing LLM Chain-of-Thought via Step Entropy](https://mlsanity.com/paper/2508.03346/) (2025)
- [Topology of Reasoning: Understanding Large Reasoning Models through Reasoning Graph Properties](https://mlsanity.com/paper/2506.05744/) (2025)

## Built on by (most cited first, 5 of 5)

- [Tail-Aware Top-k On-Policy Distillation](https://mlsanity.com/paper/2608.14728/) (2026)
- [TRACE: A Self-Evolving Skill Bank for Consistent, Limit-Aware LLM Agents](https://mlsanity.com/paper/2608.22793/) (2026)
- [ComBench: A Benchmark for Rigorous Proof Reasoning and Constructive Realization in Olympiad-Level Combinatorics](https://mlsanity.com/paper/2606.10479/) (2026)
- [LCoT-GV: Graph Attention Networks for Verifying Long Reasoning Chains in Large Language Models](https://mlsanity.com/paper/2608.30679/) (2026)
- [RGDT-Bench: Benchmarking LLM Reasoning for Rule-Governed Decisions and Their Justifications](https://mlsanity.com/paper/2609.34455/) (2026)

## Abstract (arXiv)

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 ME2 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. Code and data are available at https://github.com/Simplified-Reasoning/TRM.