# Reasoning Cache: Continual Improvement Over Long Horizons via Short-Horizon RL

arXiv: https://arxiv.org/abs/2602.03773 · HTML: https://mlsanity.com/paper/2602.03773/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 40 of its 49 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Placed in

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

## Builds on (most cited first, 30 of 40)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [Language Models can Solve Computer Tasks](https://mlsanity.com/paper/2303.17491/) (2023)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [MEM1: Learning to Synergize Memory and Reasoning for Efficient Long-Horizon Agents](https://mlsanity.com/paper/2506.15841/) (2025)
- [Compressing Context to Enhance Inference Efficiency of Large Language Models](https://mlsanity.com/paper/2310.06201/) (2023)
- [Recursive Introspection: Teaching Language Model Agents How to Self-Improve](https://mlsanity.com/paper/2407.18219/) (2024)
- [Dynamic Cheatsheet: Test-Time Learning with Adaptive Memory](https://mlsanity.com/paper/2504.07952/) (2025)
- [Evo-Memory: Benchmarking LLM Agent Test-time Learning with Self-Evolving Memory](https://mlsanity.com/paper/2511.20857/) (2025)
- [Optimizing Test-Time Compute via Meta Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.07572/) (2025)
- [DeepSeekMath-V2: Towards Self-Verifiable Mathematical Reasoning](https://mlsanity.com/paper/2511.22570/) (2025)
- [AceReason-Nemotron: Advancing Math and Code Reasoning through Reinforcement Learning](https://mlsanity.com/paper/2505.16400/) (2025)
- [Scaling Test-Time Compute Without Verification or RL is Suboptimal](https://mlsanity.com/paper/2502.12118/) (2025)
- [Diagnosing Bottlenecks in Deep Q-learning Algorithms](https://mlsanity.com/paper/1902.10250/) (2019)
- [Towards Robust Mathematical Reasoning](https://mlsanity.com/paper/2511.01846/) (2025)

## Built on by (most cited first, 12 of 12)

- [Self-Compacting Language Model Agents](https://mlsanity.com/paper/2606.23525/) (2026)
- [Recursive Agent Optimization](https://mlsanity.com/paper/2605.06639/) (2026)
- [QED-Nano: Teaching a Tiny Model to Prove Hard Theorems](https://mlsanity.com/paper/2604.04898/) (2026)
- [LLM Agents Are Latent Context Managers: Eliciting Self-Managed Context via State Proprioception](https://mlsanity.com/paper/2606.30005/) (2026)
- [OpenProver: Agentic and Interactive Theorem Proving with Lean 4](https://mlsanity.com/paper/2607.09217/) (2026)
- [KV-streams for Efficient Compaction in Agentic Reinforcement Learning](https://mlsanity.com/paper/2609.35750/) (2026)
- [Addressing Over-Refusal in LLMs with Competing Rewards](https://mlsanity.com/paper/2606.31748/) (2026)
- [Register Tokens for Bounded-State Reasoning in Diffusion Language Models](https://mlsanity.com/paper/2609.16372/) (2026)
- [Knowing When Thinking Is Not Enough: Teaching Small Reasoning Models to Reason Beyond Their Parametric Knowledge](https://mlsanity.com/paper/2609.34327/) (2026)
- [Hermes: Learning Contextual Reasoning Unlocks Test-Time Scaling](https://mlsanity.com/paper/2609.38332/) (2026)
- [Towards Better Exploration in Sequential Test-Time Scaling](https://mlsanity.com/paper/2609.39632/) (2026)
- [Explore with Memory, Learn without It: In-Context Exploration and Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2610.17734/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) that can continually improve beyond their training budgets are able to solve increasingly difficult problems by adapting at test time, a property we refer to as extrapolation. However, standard reinforcement learning (RL) operates over fixed problem distributions and training budgets, which limits extrapolation amidst distribution shift at test time. To address this, we introduce RC, an iterative decoding algorithm that replaces standard autoregressive decoding during both training and inference. RC exploits an asymmetry between the response generation and summarization capabilities of LLMs to construct reasoning chains that consistently improve across iterations. Models trained to use RC can extrapolate and continually improve over reasoning horizons more than an order of magnitude longer than those seen during training. Empirically, training a 4B model with RC using a 16k-token training budget improves performance on HMMT 2025 from 40% to nearly 70% with 0.5m tokens at test time, outperforming both comparably sized models and many larger reasoning LLMs. Finally, we also show that models trained with RC can more effectively leverage existing scaffolds to further scale test-time performance, due to the improved summary-conditioned generation abilities learned through training.