# TrajSelector: Harnessing Latent Representations for Efficient and Effective Best-of-N in Large Reasoning Model

arXiv: https://arxiv.org/abs/2510.16449 · HTML: https://mlsanity.com/paper/2510.16449/

## 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 36 of its 52 references that are in the map.
- First posted on arXiv 18 Oct 2025.

## 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 36)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Reasoning Models Can Be Effective Without Thinking](https://mlsanity.com/paper/2504.09858/) (2025)
- [Seed1.5-Thinking: Advancing Superb Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.13914/) (2025)
- [The Impact of Reasoning Step Length on Large Language Models](https://mlsanity.com/paper/2401.04925/) (2024)
- [Reinforcement Learning for LLM Post-Training: A Survey](https://mlsanity.com/paper/2407.16216/) (2024)
- [Evaluating Mathematical Reasoning Beyond Accuracy](https://mlsanity.com/paper/2404.05692/) (2024)
- [Parallel-R1: Towards Parallel Thinking via Reinforcement Learning](https://mlsanity.com/paper/2509.07980/) (2025)
- [Deep Learning using Rectified Linear Units (ReLU)](https://mlsanity.com/paper/1803.08375/) (2018)
- [The Majority is not always right: RL training for solution aggregation](https://mlsanity.com/paper/2509.06870/) (2025)
- [ReasonFlux-PRM: Trajectory-Aware PRMs for Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2506.18896/) (2025)
- [Long-Short Chain-of-Thought Mixture Supervised Fine-Tuning Eliciting Efficient Reasoning in Large Language Models](https://mlsanity.com/paper/2505.03469/) (2025)
- [No Free Lunch: Rethinking Internal Feedback for LLM Reasoning](https://mlsanity.com/paper/2506.17219/) (2025)

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

- [A decodability criterion predicts when hidden-state selection beats majority voting in large language models](https://mlsanity.com/paper/2608.17124/) (2026)
- [Entropy Centroids as Intrinsic Rewards for Test-Time Scaling](https://mlsanity.com/paper/2604.26173/) (2026)
- [JPO: Juris Policy Optimization for Structured Legal Reasoning in Criminal Judgment Prediction](https://mlsanity.com/paper/2608.29616/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have shown remarkable progress in complex reasoning tasks, largely enabled by test-time scaling (TTS) paradigms that allocate additional compute during inference. Among these, external TTS (particularly the Best-of-N selection paradigm) yields scalable performance improvements by selecting from multiple independently generated reasoning trajectories. However, this approach faces key limitations: (i) the high computational overhead of deploying process reward models, (ii) the underutilization of the LLM's intrinsic latent representations. We introduce TrajSelector, an efficient and effective Best-of-N framework that exploit the hidden states in the sampler LLM for process-level scoring. A lightweight verifier (with only 0.6B parameters) evaluates the quality of step-wise trajectory, and then aggregates these scores to identify the optimal reasoning trajectory. Our framework employs a fully data-driven, end-to-end training recipe that eliminates reliance on massive step-level annotations. Experiential results across five benchmarks demonstrate that TrajSelector delivers consistent performance gains. In Best-of-32 settings, it surpasses majority voting by 4.61% accuracy and outperforms existing process reward models by 4.31% to 12.21%, all while maintaining lower inference costs.