# OpenDeepThink: Parallel Reasoning via Bradley-Terry Aggregation

arXiv: https://arxiv.org/abs/2605.15177 · HTML: https://mlsanity.com/paper/2605.15177/

## Key facts

- Cited by 3 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 23 of its 36 references that are in the map.
- First posted on arXiv 14 May 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, 23 of 23)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Humanity's Last Exam](https://mlsanity.com/paper/2501.14249/) (2025)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [EvoPrompt: Connecting LLMs with Evolutionary Algorithms Yields Powerful Prompt Optimizers](https://mlsanity.com/paper/2309.08532/) (2023)
- [LiveCodeBench Pro: How Do Olympiad Medalists Judge LLMs in Competitive Programming?](https://mlsanity.com/paper/2506.11928/) (2025)
- [ParaThinker: Native Parallel Thinking as a New Paradigm to Scale LLM Test-time Compute](https://mlsanity.com/paper/2509.04475/) (2025)
- [Learning to Reason Across Parallel Samples for LLM Reasoning](https://mlsanity.com/paper/2506.09014/) (2025)
- [Multiverse: Your Language Models Secretly Decide How to Parallelize and Merge Generation](https://mlsanity.com/paper/2506.09991/) (2025)
- [Rethinking Thinking Tokens: LLMs as Improvement Operators](https://mlsanity.com/paper/2510.01123/) (2025)
- [PaCoRe: Learning to Scale Test-Time Compute with Parallel Coordinated Reasoning](https://mlsanity.com/paper/2601.05593/) (2026)
- [V1: Unifying Generation and Self-Verification for Parallel Reasoners](https://mlsanity.com/paper/2603.04304/) (2026)
- [Escaping the Cognitive Well: Efficient Competition Math with Off-the-Shelf Models](https://mlsanity.com/paper/2602.16793/) (2026)
- [Squeeze Evolve: Unified Multi-Model Orchestration for Verifier-Free Evolution](https://mlsanity.com/paper/2604.07725/) (2026)
- [Population-Evolve: a Parallel Sampling and Evolutionary Method for LLM Math Reasoning](https://mlsanity.com/paper/2512.19081/) (2025)

## Built on by (most cited first, 3 of 3)

- [When Agents Slow Down: Understanding LLM Agents' Test-Time Strategies via Elo-per-token Analysis](https://mlsanity.com/paper/2609.15309/) (2026)
- [Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Science](https://mlsanity.com/paper/2609.15983/) (2026)
- [Second Thought: Reasoning in Parallel as LLM Agents Act and Observe](https://mlsanity.com/paper/2608.13667/) (2026)

## Abstract (arXiv)

Test-time compute scaling is a primary axis for improving LLM reasoning. Existing methods primarily scale depth by extending a single reasoning trace. Scaling breadth by sampling multiple candidates in parallel is straightforward, but introduces a selection bottleneck: choosing the best candidate without a ground-truth verifier, since pointwise LLM judging is noisy and biased. To address this, we introduce OpenDeepThink, a population-based test-time compute framework that selects via pairwise Bradley-Terry comparison. Each generation, the LLM judges random pairs of candidates and aggregates votes via Bradley-Terry into a global ranking; top-ranked candidates are preserved and the top three quarters are mutated using the natural-language critiques produced during comparison; the bottom quarter is discarded. OpenDeepThink raises Gemini 3.1 Pro's effective Codeforces Elo by +405 points in eight sequential LLM-call rounds (~27 minutes wall-clock). The pipeline transfers across weaker and stronger models without retuning, and on the multi-domain HLE benchmark, gains appear concentrated in objectively verifiable domains and reverse in subjective ones. We release CF-73, a curated set of 73 expert-rated Codeforces problems with International Grandmaster annotation and 99% local-evaluation agreement against the official verdict.