# Thought-Aware KV Cache Compaction for Reasoning via Adaptive Attention Matching

arXiv: https://arxiv.org/abs/2608.12331 · HTML: https://mlsanity.com/paper/2608.12331/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 1 Jun 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, 9 of 9)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [LongNet: Scaling Transformers to 1,000,000,000 Tokens](https://mlsanity.com/paper/2307.02486/) (2023)
- [Cartridges: Lightweight and general-purpose long context representations via self-study](https://mlsanity.com/paper/2506.06266/) (2025)
- [Fast KV Compaction via Attention Matching](https://mlsanity.com/paper/2602.16284/) (2026)
- [Reasoning Path Compression: Compressing Generation Trajectories for Efficient LLM Reasoning](https://mlsanity.com/paper/2505.13866/) (2025)

## Abstract (arXiv)

Reasoning language models generate lengthy chain-of-thought (CoT) sequences whose key-value (KV) cache grows linearly and becomes a memory bottleneck during decoding. Existing compaction methods treat reasoning trajectories as flat token sequences and apply uniform compression, ignoring the hierarchical structure of CoT reasoning where different steps vary drastically in importance. We propose Thought-Aware Attention Matching (TAM), which exploits this structure through three mechanisms: (i)~thought segmentation that decomposes the trajectory into reasoning blocks, (ii)~adaptive budget allocation that assigns compression budget based on each segment's importance and size, and (iii)~pivotal token protection that preserves high-attention reasoning anchors. We prove that the allocation rule is optimal under a convex error model and that cumulative error under sequential compaction remains bounded. Experiments on AIME 2024 and MATH-500 with Qwen3-4B show that TAM improves accuracy over uniform compaction at the same memory footprint, with periodic compaction bounding peak memory to 3.1--3.2,GB (a 65% reduction) while maintaining competitive accuracy.