# Moment-KV: Momentum-Based Decode-Time KV Cache Compression for Long Generation

arXiv: https://arxiv.org/abs/2605.29873 · HTML: https://mlsanity.com/paper/2605.29873/

## 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 11 of its 14 references that are in the map.
- First posted on arXiv 28 May 2026.

## Placed in

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

## Builds on (most cited first, 11 of 11)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [SnapKV: LLM Knows What You are Looking for Before Generation](https://mlsanity.com/paper/2404.14469/) (2024)
- [PyramidKV: Dynamic KV Cache Compression based on Pyramidal Information Funneling](https://mlsanity.com/paper/2406.02069/) (2024)
- [∞Bench: Extending Long Context Evaluation Beyond 100K Tokens](https://mlsanity.com/paper/2402.13718/) (2024)
- [PyramidInfer: Pyramid KV Cache Compression for High-throughput LLM Inference](https://mlsanity.com/paper/2405.12532/) (2024)
- [A Simple and Effective L2 Norm-Based Strategy for KV Cache Compression](https://mlsanity.com/paper/2406.11430/) (2024)
- [SCOPE: Optimizing Key-Value Cache Compression in Long-context Generation](https://mlsanity.com/paper/2412.13649/) (2024)
- [FlowKV: Enhancing Multi-Turn Conversational Coherence in LLMs via Isolated Key-Value Cache Management](https://mlsanity.com/paper/2505.15347/) (2025)

## Abstract (arXiv)

Key-Value (KV) cache remains a major bottleneck for deploying Large Language Models (LLMs) in long-generation tasks. Prior work often applies uniform compression across both prefill and decoding caches, but compressing the prefill cache degrades performance by corrupting critical context. While preserving the prefill cache is essential, decoding-phase compression remains underexplored, with existing methods relying on rigid recency windows or instantaneous attention. Our analysis of attention dynamics reveals strong temporal patterns: critical tokens receive sustained attention over long horizons, while local reasoning involves short-lived bursts. Static heuristics fail to capture this behavior, leading to premature eviction of important tokens or retention of stale ones. We propose Moment-KV, a decoding-time KV cache compression method based on momentum-driven temporal attention aggregation. Our method models token importance as a continuously evolving state, where attention is aggregated with decay, capturing both long-term influence and recent relevance. Experiments show that Moment-KV significantly improves generation fidelity in long-generation tasks (2.3-3.2 %) while maintaining decoding latency.