# TREK: Distill to Explore, Reinforce to Refine

arXiv: https://arxiv.org/abs/2607.05339 · HTML: https://mlsanity.com/paper/2607.05339/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 8 of its 19 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 8 of 8)

- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [Deep metric learning using Triplet network](https://mlsanity.com/paper/1412.6622/) (2014)
- [Learning Fine-grained Image Similarity with Deep Ranking](https://mlsanity.com/paper/1404.4661/) (2014)
- [Deep Learning Face Representation by Joint Identification-Verification](https://mlsanity.com/paper/1406.4773/) (2014)
- [Learning to Compare Image Patches via Convolutional Neural Networks](https://mlsanity.com/paper/1504.03641/) (2015)
- [IncA-DES: An incremental and adaptive dynamic ensemble selection approach using online K-d tree neighborhood search for data streams with concept drift](https://mlsanity.com/paper/2507.12573/) (2025)
- [Using Deep Neural Networks to Quantify Parking Dwell Time](https://mlsanity.com/paper/2411.00158/) (2024)

## Built on by (most cited first, 2 of 2)

- [SHARPO: Segment-Level Credit Assignment for Agentic Reinforcement Learning](https://mlsanity.com/paper/2610.00838/) (2026)
- [What Will Post-Training Fix? Per-Problem Gains Are Shared Across Independent RL Runs, and Existing Checkpoints Predict Them Better Than A Priori Signals](https://mlsanity.com/paper/2610.04978/) (2026)

## Abstract (arXiv)

Group Relative Policy Optimization (GRPO) is effective when the current policy already samples useful reasoning trajectories, but it stalls on hard prompts whose correct solution modes lie outside the student's on-policy support. We propose TREK (Teacher-Routed Exploration via Forward KL), a simple staged procedure that uses distillation not for imitation but for exploration support expansion. A key advantage of TREK is its generality: because it only consumes verified output trajectories, it can use an external black-box teacher, a white-box teacher, or the same model given additional inference-time context, and it can efficiently identify which hard-prompt samples are most worth consolidating even when teacher internals are unavailable. TREK first identifies prompts where the unaided student has very low pass rate, queries a proposal source to produce verified candidate solutions, keeps the top-r proposals ranked by current student likelihood, applies a short forward-KL phase to pull those verified modes into the student's support, and then returns to standard on-policy GRPO refinement. On mathematical reasoning, TREK with DeepSeek-V4 proposals improves Qwen3 models across all tested scales on AIME 2024 and AIME 2025; for Qwen3-8B, it improves AIME 2025 from 36.9 to 40.3 and AIME 2024 from 47.9 to 51.1 (avg@16), while the self-context variant reaches 38.5 and 49.6 without an external teacher. On agentic tasks, TREK raises ALFWorld success rate from 75.8 to 82.8 and ScienceWorld success rate from 12.5 to 26.7; notably, on the hardest task types, TREK achieves high success rates early in training while unaided GRPO requires substantially more optimization steps to reach comparable levels.