# Training Large Reasoning Models Efficiently via Progressive Thought Encoding

arXiv: https://arxiv.org/abs/2602.16839 · HTML: https://mlsanity.com/paper/2602.16839/

## Key facts

- Cited by 1 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 39 of its 55 references that are in the map.
- First posted on arXiv 18 Feb 2026.

## 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 39)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [A Survey on In-context Learning](https://mlsanity.com/paper/2301.00234/) (2022)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [Humanity's Last Exam](https://mlsanity.com/paper/2501.14249/) (2025)
- [PyramidKV: Dynamic KV Cache Compression based on Pyramidal Information Funneling](https://mlsanity.com/paper/2406.02069/) (2024)
- [Agent Laboratory: Using LLM Agents as Research Assistants](https://mlsanity.com/paper/2501.04227/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [Retrieval-Augmented Generation with Graphs (GraphRAG)](https://mlsanity.com/paper/2501.00309/) (2024)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [LLM Maybe LongLM: Self-Extend LLM Context Window Without Tuning](https://mlsanity.com/paper/2401.01325/) (2024)
- [Right Question is Already Half the Answer: Fully Unsupervised LLM Reasoning Incentivization](https://mlsanity.com/paper/2504.05812/) (2025)
- [Act Only When It Pays: Efficient Reinforcement Learning for LLM Reasoning via Selective Rollouts](https://mlsanity.com/paper/2506.02177/) (2025)
- [Not All Heads Matter: A Head-Level KV Cache Compression Method with Integrated Retrieval and Reasoning](https://mlsanity.com/paper/2410.19258/) (2024)
- [Efficient Reasoning Models: A Survey](https://mlsanity.com/paper/2504.10903/) (2025)
- [Unlocking Efficient Long-to-Short LLM Reasoning with Model Merging](https://mlsanity.com/paper/2503.20641/) (2025)
- [Test-Time Learning for Large Language Models](https://mlsanity.com/paper/2505.20633/) (2025)

## Built on by (most cited first, 1 of 1)

- [Do Language Models Need Sleep? Offline Recurrence for Improved Online Inference](https://mlsanity.com/paper/2605.26099/) (2026)

## Abstract (arXiv)

Large reasoning models (LRMs) excel on complex problems but face a critical barrier to efficiency: reinforcement learning (RL) training requires long rollouts for outcome-based rewards, where autoregressive decoding dominates time and memory usage. While sliding-window cache strategies can bound memory, they disrupt long-context reasoning and degrade performance. We introduce Progressive Thought Encoding, a parameter-efficient fine-tuning method that enables LRMs to reason effectively under fixed-size caches. By progressively encoding intermediate reasoning into fixed-size vector representations, our approach eliminates the need to backpropagate through full-cache rollouts, thereby reducing memory usage, while maintaining constant memory during inference. Experiments on three models, including Qwen2.5-3B-Instruct, Qwen2.5-7B-Instruct, and DeepSeek-R1-Distill-Llama-8B, on six widely used challenging mathematical benchmarks show consistent gains: our method achieves +19.3% improvement over LoRA-based fine-tuning and +29.9% over LRMs without fine-tuning on average, with up to +23.4 accuracy improvement on AIME2024/2025 under the same tight cache budgets. These results demonstrate that Progressive Thought Encoding not only improves reasoning accuracy but also makes RL training of LRMs substantially more efficient and scalable under real-world memory constraints.