# Learning to Reason as Action Abstractions with Scalable Mid-Training RL

arXiv: https://arxiv.org/abs/2509.25810 · HTML: https://mlsanity.com/paper/2509.25810/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 34 of its 52 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 34)

- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [A Deep Reinforced Model for Abstractive Summarization](https://mlsanity.com/paper/1705.04304/) (2017)
- [Aguvis: Unified Pure Vision Agents for Autonomous GUI Interaction](https://mlsanity.com/paper/2412.04454/) (2024)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [Is Reinforcement Learning (Not) for Natural Language Processing: Benchmarks, Baselines, and Building Blocks for Natural Language Policy Optimization](https://mlsanity.com/paper/2210.01241/) (2022)
- [TACO: Topics in Algorithmic COde generation dataset](https://mlsanity.com/paper/2312.14852/) (2023)
- [OpenCUA: Open Foundations for Computer-Use Agents](https://mlsanity.com/paper/2508.09123/) (2025)
- [SimpleTIR: End-to-End Reinforcement Learning for Multi-Turn Tool-Integrated Reasoning](https://mlsanity.com/paper/2509.02479/) (2025)
- [OpenCoder: The Open Cookbook for Top-Tier Code Large Language Models](https://mlsanity.com/paper/2411.04905/) (2024)
- [SWEET-RL: Training Multi-Turn LLM Agents on Collaborative Reasoning Tasks](https://mlsanity.com/paper/2503.15478/) (2025)
- [OctoThinker: Mid-training Incentivizes Reinforcement Learning Scaling](https://mlsanity.com/paper/2506.20512/) (2025)
- [Human-centric Dialog Training via Offline Reinforcement Learning](https://mlsanity.com/paper/2010.05848/) (2020)
- [ACECODER: Acing Coder RL via Automated Test-Case Synthesis](https://mlsanity.com/paper/2502.01718/) (2025)
- [Reinforcing General Reasoning without Verifiers](https://mlsanity.com/paper/2505.21493/) (2025)
- [Reinforcement Learning for Bandit Neural Machine Translation with Simulated Human Feedback](https://mlsanity.com/paper/1707.07402/) (2017)
- [Sample Complexity of Multi-task Reinforcement Learning](https://mlsanity.com/paper/1309.6821/) (2013)
- [Reasoning to Learn from Latent Thoughts](https://mlsanity.com/paper/2503.18866/) (2025)
- [Phi-4-Mini-Reasoning: Exploring the Limits of Small Reasoning Language Models in Math](https://mlsanity.com/paper/2504.21233/) (2025)
- [Reinforcement Pre-Training](https://mlsanity.com/paper/2506.08007/) (2025)
- [Scaling Agents via Continual Pre-training](https://mlsanity.com/paper/2509.13310/) (2025)
- [Reverse-Engineered Reasoning for Open-Ended Generation](https://mlsanity.com/paper/2509.06160/) (2025)

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

- [Internalizing the Future: A Unified Agentic Training Paradigm for World Model Planning](https://mlsanity.com/paper/2606.27483/) (2026)
- [On Advantage Estimates for Max@K Policy Gradients](https://mlsanity.com/paper/2606.06080/) (2026)
- [OrderGrad: Optimizing Beyond the Mean with Order-Statistic Policy Gradient Estimation](https://mlsanity.com/paper/2606.06096/) (2026)

## Abstract (arXiv)

Large language models excel with reinforcement learning (RL), but fully unlocking this potential requires a mid-training stage. An effective mid-training phase should identify a compact set of useful actions and enable fast selection among them through online RL. We formalize this intuition by presenting the first theoretical result on how mid-training shapes post-training: it characterizes an action subspace that minimizes both the value approximation error from pruning and the RL error during subsequent planning. Our analysis reveals two key determinants of mid-training effectiveness: pruning efficiency, which shapes the prior of the initial RL policy, and its impact on RL convergence, which governs the extent to which that policy can be improved via online interactions. These results suggest that mid-training is most effective when the decision space is compact and the effective horizon is short, highlighting the importance of operating in the space of action abstractions rather than primitive actions. Building on these insights, we propose Reasoning as Action Abstractions (RA3), a scalable mid-training algorithm. Specifically, we derive a sequential variational lower bound and optimize it by iteratively discovering temporally-consistent latent structures via RL, followed by fine-tuning on the bootstrapped data. Experiments on code generation tasks demonstrate the effectiveness of our approach. Across multiple base models, RA3 improves the average performance on HumanEval and MBPP by 8 and 4 points over the base model and the next-token prediction baseline. Furthermore, RA3 achieves faster convergence and higher asymptotic performance in RLVR on HumanEval+, MBPP+, LiveCodeBench, and Codeforces.