# InftyThink: Breaking the Length Limits of Long-Context Reasoning in Large Language Models

arXiv: https://arxiv.org/abs/2503.06692 · HTML: https://mlsanity.com/paper/2503.06692/

## Key facts

- Cited by 54 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 56 of its 75 references that are in the map.
- First posted on arXiv 9 Mar 2025.

## 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 56)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)

## Built on by (most cited first, 30 of 54)

- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Reasoning Models Can Be Effective Without Thinking](https://mlsanity.com/paper/2504.09858/) (2025)
- [A Survey of Context Engineering for Large Language Models](https://mlsanity.com/paper/2507.13334/) (2025)
- [AdaCoT: Pareto-Optimal Adaptive Chain-of-Thought Triggering via Reinforcement Learning](https://mlsanity.com/paper/2505.11896/) (2025)
- [Efficient Inference for Large Reasoning Models: A Survey](https://mlsanity.com/paper/2503.23077/) (2025)
- [QuestA: Expanding Reasoning Capacity in LLMs via Question Augmentation](https://mlsanity.com/paper/2507.13266/) (2025)
- [Let LRMs Break Free from Overthinking via Self-Braking Tuning](https://mlsanity.com/paper/2505.14604/) (2025)
- [ThinKV: Thought-Adaptive KV Cache Compression for Efficient Reasoning Models](https://mlsanity.com/paper/2510.01290/) (2025)
- [A Survey of Slow Thinking-based Reasoning LLMs using Reinforced Learning and Inference-time Scaling Law](https://mlsanity.com/paper/2505.02665/) (2025)
- [KTAE: A Model-Free Algorithm to Key-Tokens Advantage Estimation in Mathematical Reasoning](https://mlsanity.com/paper/2505.16826/) (2025)
- [The Price of a Second Thought: On the Evaluation of Reasoning Efficiency in Large Language Models](https://mlsanity.com/paper/2505.22017/) (2025)
- [MEMENTO: Teaching LLMs to Manage Their Own Context](https://mlsanity.com/paper/2604.09852/) (2026)
- [Not All Thoughts are Generated Equal: Efficient LLM Reasoning via Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2505.11827/) (2025)
- [LazyEviction: Lagged KV Eviction with Attention Pattern Observation for Efficient Long Reasoning](https://mlsanity.com/paper/2506.15969/) (2025)
- [Generative AI Act II: Test Time Scaling Drives Cognition Engineering](https://mlsanity.com/paper/2504.13828/) (2025)
- [TrimR: Verifier-based Training-Free Thinking Compression for Efficient Test-Time Scaling](https://mlsanity.com/paper/2505.17155/) (2025)
- [Transformers Provably Learn Chain-of-Thought Reasoning with Length Generalization](https://mlsanity.com/paper/2511.07378/) (2025)
- [The Markovian Thinker: Architecture-Agnostic Linear Scaling of Reasoning](https://mlsanity.com/paper/2510.06557/) (2025)
- [Scaling over Scaling: Exploring Test-Time Scaling Plateau in Large Reasoning Models](https://mlsanity.com/paper/2505.20522/) (2025)
- [Self-Compacting Language Model Agents](https://mlsanity.com/paper/2606.23525/) (2026)
- [Exploring the System 1 Thinking Capability of Large Reasoning Models](https://mlsanity.com/paper/2504.10368/) (2025)
- [Multi-Agent Debate with Memory Masking](https://mlsanity.com/paper/2603.20215/) (2026)
- [ResidualKV: Residual-Based KV Cache Compression for Efficient Long-Context Inference](https://mlsanity.com/paper/2602.08005/) (2026)
- [Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models](https://mlsanity.com/paper/2601.11340/) (2026)
- [VTC-R1: Vision-Text Compression for Efficient Long-Context Reasoning](https://mlsanity.com/paper/2601.22069/) (2026)
- [Are Large Reasoning Models Interruptible?](https://mlsanity.com/paper/2510.11713/) (2025)
- [Accordion-Thinking: Self-Regulated Step Summaries for Efficient and Readable LLM Reasoning](https://mlsanity.com/paper/2602.03249/) (2026)
- [Mitigating Overthinking in Large Reasoning Language Models via Reasoning Path Deviation Monitoring](https://mlsanity.com/paper/2603.14251/) (2026)
- [PREMISE: Scalable and Strategic Prompt Optimization for Efficient Mathematical Reasoning in Large Models](https://mlsanity.com/paper/2506.10716/) (2025)
- [Breadcrumbs Reasoning: Memory-Efficient Reasoning with Compression Beacons](https://mlsanity.com/paper/2510.13797/) (2025)

## Abstract (arXiv)

Advanced reasoning in large language models has achieved remarkable performance on challenging tasks, but the prevailing long-context reasoning paradigm faces critical limitations: quadratic computational scaling with sequence length, reasoning constrained by maximum context boundaries, and performance degradation beyond pre-training context windows. Existing approaches primarily compress reasoning chains without addressing the fundamental scaling problem. To overcome these challenges, we introduce InftyThink, a paradigm that transforms monolithic reasoning into an iterative process with intermediate summarization. By interleaving short reasoning segments with concise progress summaries, our approach enables unbounded reasoning depth while maintaining bounded computational costs. This creates a characteristic sawtooth memory pattern that significantly reduces computational complexity compared to traditional approaches. Furthermore, we develop a methodology for reconstructing long-context reasoning datasets into our iterative format, transforming OpenR1-Math into 333K training instances. Experiments across multiple model architectures demonstrate that our approach reduces computational costs while improving performance, with Qwen2.5-Math-7B showing 3-11% improvements across MATH500, AIME24, and GPQA_diamond benchmarks. Our work challenges the assumed trade-off between reasoning depth and computational efficiency, providing a more scalable approach to complex reasoning without architectural modifications.