# Select and Improve: Understanding the Mechanics of Post-Training for Reasoning

arXiv: https://arxiv.org/abs/2606.13125 · HTML: https://mlsanity.com/paper/2606.13125/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 19 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)
- [The Invisible Leash: Why RLVR May or May Not Escape Its Origin](https://mlsanity.com/paper/2507.14843/) (2025)
- [Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening](https://mlsanity.com/paper/2506.02355/) (2025)
- [On the Interplay of Pre-Training, Mid-Training, and RL on Reasoning Language Models](https://mlsanity.com/paper/2512.07783/) (2025)
- [OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization](https://mlsanity.com/paper/2506.18880/) (2025)
- [From f(x) and g(x) to f(g(x)): LLMs Learn New Skills in RL by Composing Old Ones](https://mlsanity.com/paper/2509.25123/) (2025)
- [RL Squeezes, SFT Expands: A Comparative Study of Reasoning LLMs](https://mlsanity.com/paper/2509.21128/) (2025)
- [RL Grokking Recipe: How Does RL Unlock and Transfer New Algorithms in LLMs?](https://mlsanity.com/paper/2509.21016/) (2025)
- [Reshaping Reasoning in LLMs: A Theoretical Analysis of RL Training Dynamics through Pattern Selection](https://mlsanity.com/paper/2506.04695/) (2025)
- [How Reinforcement Learning After Next-Token Prediction Facilitates Learning](https://mlsanity.com/paper/2510.11495/) (2025)

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

- [The Model Knows Another Way: Strategy Switching for Effective RLVR Exploration](https://mlsanity.com/paper/2609.33085/) (2026)
- [SFT Leaves a Reproducible Signature in Activation Geometry: Calibrating Post-Training Interpretability Against Run-to-Run Noise](https://mlsanity.com/paper/2610.17093/) (2026)

## Abstract (arXiv)

Reinforcement learning has rapidly emerged as a key component in the training of reasoning and coding models, yet it remains poorly understood from a mechanistic perspective. We study how and through what underlying processes capabilities are acquired or enhanced via reinforcement learning post-training. Our analysis, based on controlled math reasoning experiments with Qwen-2.5-1.5B, reveals two core mechanisms: strategy selection and strategy improvement. Our results highlight the role of SFT data and reinforcement learning data in activating these mechanisms, in particular showing how supervising the model on diverse reasoning strategies can enable strategy selection and how increasing difficulty in reinforcement learning data can enable strategy improvement. Taken together, our results provide mechanistic insight into RL training and suggest practical interventions to continue scaling reasoning capabilities.