# Accordion-Thinking: Self-Regulated Step Summaries for Efficient and Readable LLM Reasoning

arXiv: https://arxiv.org/abs/2602.03249 · HTML: https://mlsanity.com/paper/2602.03249/

## Key facts

- Cited by 6 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 28 of its 46 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Efficient LLM inference and serving / [Efficient reasoning and agent inference](https://mlsanity.com/inference/efficient-reasoning-and-agent-inference/)

## Builds on (most cited first, 28 of 28)

- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [Compressed Chain of Thought: Efficient Reasoning Through Dense Representations](https://mlsanity.com/paper/2412.13171/) (2024)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [InftyThink: Breaking the Length Limits of Long-Context Reasoning in Large Language Models](https://mlsanity.com/paper/2503.06692/) (2025)
- [Post-Training Sparse Attention with Double Sparsity](https://mlsanity.com/paper/2408.07092/) (2024)
- [Rethinking Reflection in Pre-Training](https://mlsanity.com/paper/2504.04022/) (2025)
- [Depth-Breadth Synergy in RLVR: Unlocking LLM Reasoning Gains with Adaptive Exploration](https://mlsanity.com/paper/2508.13755/) (2025)
- [SeePhys: Does Seeing Help Thinking? -- Benchmarking Vision-Based Physics Reasoning](https://mlsanity.com/paper/2505.19099/) (2025)
- [Break the Chain: Large Language Models Can be Shortcut Reasoners](https://mlsanity.com/paper/2406.06580/) (2024)
- [Inference-Time Hyper-Scaling with KV Cache Compression](https://mlsanity.com/paper/2506.05345/) (2025)
- [Efficient Reasoning for Large Reasoning Language Models via Certainty-Guided Reflection Suppression](https://mlsanity.com/paper/2508.05337/) (2025)
- [The Price of a Second Thought: On the Evaluation of Reasoning Efficiency in Large Language Models](https://mlsanity.com/paper/2505.22017/) (2025)
- [TL;DR: Too Long, Do Re-weighting for Efficient LLM Reasoning Compression](https://mlsanity.com/paper/2506.02678/) (2025)
- [The Markovian Thinker: Architecture-Agnostic Linear Scaling of Reasoning](https://mlsanity.com/paper/2510.06557/) (2025)
- [Exploring and Exploiting the Inherent Efficiency within Large Reasoning Models for Self-Guided Efficiency Enhancement](https://mlsanity.com/paper/2506.15647/) (2025)

## Built on by (most cited first, 6 of 6)

- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [Prune-OPD: Efficient and Reliable On-Policy Distillation for Long-Horizon Reasoning](https://mlsanity.com/paper/2605.07804/) (2026)
- [MEMENTO: Teaching LLMs to Manage Their Own Context](https://mlsanity.com/paper/2604.09852/) (2026)
- [Self-Compacting Language Model Agents](https://mlsanity.com/paper/2606.23525/) (2026)
- [Flash-OPD: Fast On-Policy Distillation](https://mlsanity.com/paper/2610.06105/) (2026)
- [TreeFlex: Agents Navigating Their Own Search Trees](https://mlsanity.com/paper/2610.20334/) (2026)

## Abstract (arXiv)

Scaling test-time compute via long Chain-of-Thought unlocks remarkable gains in reasoning capabilities, yet it faces practical limits due to the linear growth of KV cache and quadratic attention complexity. In this paper, we introduce Accordion-Thinking, an end-to-end framework where LLMs learn to self-regulate the granularity of the reasoning steps through dynamic summarization. This mechanism enables a Fold inference mode, where the model periodically summarizes its thought process and discards former thoughts to reduce dependency on historical tokens. We apply reinforcement learning to incentivize this capability further, uncovering a critical insight: the accuracy gap between the highly efficient Fold mode and the exhaustive Unfold mode progressively narrows and eventually vanishes over the course of training. This phenomenon demonstrates that the model learns to encode essential reasoning information into compact summaries, achieving effective compression of the reasoning context. Our Accordion-Thinking demonstrates that with learned self-compression, LLMs can tackle complex reasoning tasks with minimal dependency token overhead without compromising solution quality, and it achieves a three times throughput while maintaining accuracy on a 48GB GPU memory configuration, while the structured step summaries provide a human-readable account of the reasoning process.