# Breadcrumbs Reasoning: Memory-Efficient Reasoning with Compression Beacons

arXiv: https://arxiv.org/abs/2510.13797 · HTML: https://mlsanity.com/paper/2510.13797/

## Key facts

- Cited by 5 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 16 of its 40 references that are in the map.
- First posted on arXiv 15 Oct 2025.

## 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, 16 of 16)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [TokenSkip: Controllable Chain-of-Thought Compression in LLMs](https://mlsanity.com/paper/2502.12067/) (2025)
- [CoT-Valve: Length-Compressible Chain-of-Thought Tuning](https://mlsanity.com/paper/2502.09601/) (2025)
- [DAST: Difficulty-Adaptive Slow-Thinking for Large Reasoning Models](https://mlsanity.com/paper/2503.04472/) (2025)
- [Stream of Search (SoS): Learning to Search in Language](https://mlsanity.com/paper/2404.03683/) (2024)
- [Transformers are Multi-State RNNs](https://mlsanity.com/paper/2401.06104/) (2024)
- [Dynamic Memory Compression: Retrofitting LLMs for Accelerated Inference](https://mlsanity.com/paper/2403.09636/) (2024)
- [Self-Training Elicits Concise Reasoning in Large Language Models](https://mlsanity.com/paper/2502.20122/) (2025)
- [Expected Attention: KV Cache Compression by Estimating Attention from Future Queries Distribution](https://mlsanity.com/paper/2510.00636/) (2025)
- [InftyThink: Breaking the Length Limits of Long-Context Reasoning in Large Language Models](https://mlsanity.com/paper/2503.06692/) (2025)

## Built on by (most cited first, 5 of 5)

- [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)
- [Do LLMs Encode Functional Importance of Reasoning Tokens?](https://mlsanity.com/paper/2601.03066/) (2026)
- [Neural Garbage Collection: Learning to Forget while Learning to Reason](https://mlsanity.com/paper/2604.18002/) (2026)
- [When Less is Enough: Efficient Inference via Collaborative Reasoning](https://mlsanity.com/paper/2605.01111/) (2026)

## Abstract (arXiv)

The scalability of large language models for long-context reasoning is severely constrained by the linear growth of their Transformer key-value cache, which incurs significant memory and computational costs. We posit that as a model generates reasoning tokens, the informational value of past generated tokens diminishes, creating an opportunity for compression. In this work, we propose to periodically compress the generation KV cache with a learned, special-purpose token and evict compressed entries. We train the model to perform this compression via a modified joint distillation and reinforcement learning (RL) framework. Our training method minimizes overhead over the conventional RL process, as it leverages RL outputs for distillation. Empirically, our method achieves a superior memory-accuracy Pareto frontier compared to both the model without cache compression and training-free compression techniques.