# A Probabilistic Interpretation of KV Cache Eviction

arXiv: https://arxiv.org/abs/2608.28293 · HTML: https://mlsanity.com/paper/2608.28293/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in KV cache optimization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 19 of its 27 references that are in the map.
- First posted on arXiv 28 Aug 2026.

## Placed in

- Efficient LLM inference and serving / [KV cache optimization](https://mlsanity.com/inference/kv-cache-optimization/)

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [SnapKV: LLM Knows What You are Looking for Before Generation](https://mlsanity.com/paper/2404.14469/) (2024)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization](https://mlsanity.com/paper/2401.18079/) (2024)
- [PyramidKV: Dynamic KV Cache Compression based on Pyramidal Information Funneling](https://mlsanity.com/paper/2406.02069/) (2024)
- [Ada-KV: Optimizing KV Cache Eviction by Adaptive Budget Allocation for Efficient LLM Inference](https://mlsanity.com/paper/2407.11550/) (2024)
- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)
- [Transformers are Multi-State RNNs](https://mlsanity.com/paper/2401.06104/) (2024)
- [A Simple and Effective L2 Norm-Based Strategy for KV Cache Compression](https://mlsanity.com/paper/2406.11430/) (2024)
- [Cartridges: Lightweight and general-purpose long context representations via self-study](https://mlsanity.com/paper/2506.06266/) (2025)
- [Expected Attention: KV Cache Compression by Estimating Attention from Future Queries Distribution](https://mlsanity.com/paper/2510.00636/) (2025)
- [The Pitfalls of KV Cache Compression](https://mlsanity.com/paper/2510.00231/) (2025)
- [BR-SNIS: Bias Reduced Self-Normalized Importance Sampling](https://mlsanity.com/paper/2207.06364/) (2022)
- [Attention: Marginal Probability is All You Need?](https://mlsanity.com/paper/2304.04556/) (2023)
- [Bayesian Attention Mechanism: A Probabilistic Framework for Positional Encoding and Context Length Extrapolation](https://mlsanity.com/paper/2505.22842/) (2025)

## Abstract (arXiv)

The premise and promise of KV (cache) eviction is simple: higher throughput can be achieved by evicting some entries from the KV cache, at a negligible cost to quality. This holds empirically for many existing methods, though most rely on creative heuristics for selecting which entries to drop. Despite recent advances, the problem of KV eviction has remained informal in the literature. This paper aims to properly formalize this problem through the lens of probabilistic reasoning and reveal what can be learned from this perspective. Concretely, we (1) formalize the problem of KV eviction and, unfortunately, prove that it is computationally hard, (2) show that by framing it probabilistically, KV eviction reduces to the problem of expectation estimation, which can be approximated through sampling, (3) show that through this probabilistic interpretation, correcting for evicted entries during decoding---a previously ignored problem---becomes feasible, and (4) reveal that existing methods in the literature are zero-variance biased estimators that can be easily adapted in order to enable decode time correction. In practice, we show that this probabilistic version of KV eviction coupled with decode time correction is more robust to different tasks compared to existing eviction methods and achieves competitive performance at the same compression budget.