# Jacap: Robust KV Cache Eviction via Jacobian-Based Nonlinear Information Capacity Preservation

arXiv: https://arxiv.org/abs/2609.08131 · HTML: https://mlsanity.com/paper/2609.08131/

## 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 32 references that are in the map.
- First posted on arXiv 8 Sep 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)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [From LLM Reasoning to Autonomous AI Agents: A Comprehensive Review](https://mlsanity.com/paper/2504.19678/) (2025)
- [A Survey on Large Language Model Acceleration based on KV Cache Management](https://mlsanity.com/paper/2412.19442/) (2024)
- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)
- [OpenCodeReasoning: Advancing Data Distillation for Competitive Coding](https://mlsanity.com/paper/2504.01943/) (2025)
- [Keep the Cost Down: A Review on Methods to Optimize LLM' s KV-Cache Consumption](https://mlsanity.com/paper/2407.18003/) (2024)
- [A Simple and Effective L2 Norm-Based Strategy for KV Cache Compression](https://mlsanity.com/paper/2406.11430/) (2024)
- [Expected Attention: KV Cache Compression by Estimating Attention from Future Queries Distribution](https://mlsanity.com/paper/2510.00636/) (2025)
- [FlashDecoding++: Faster Large Language Model Inference on GPUs](https://mlsanity.com/paper/2311.01282/) (2023)
- [KeyDiff: Key Similarity-Based KV Cache Eviction for Long-Context LLM Inference in Resource-Constrained Environments](https://mlsanity.com/paper/2504.15364/) (2025)
- [Mind the Memory Gap: Unveiling GPU Bottlenecks in Large-Batch LLM Inference](https://mlsanity.com/paper/2503.08311/) (2025)
- [D2O: Dynamic Discriminative Operations for Efficient Long-Context Inference of Large Language Models](https://mlsanity.com/paper/2406.13035/) (2024)
- [PolarQuant: Quantizing KV Caches with Polar Transformation](https://mlsanity.com/paper/2502.02617/) (2025)
- [LLM-based Agentic Reasoning Frameworks: A Survey from Methods to Scenarios](https://mlsanity.com/paper/2508.17692/) (2025)
- [KeepKV: Achieving Periodic Lossless KV Cache Compression for Efficient LLM Inference](https://mlsanity.com/paper/2504.09936/) (2025)
- [Learning is Forgetting: LLM Training As Lossy Compression](https://mlsanity.com/paper/2604.07569/) (2026)
- [Rethinking KV Cache Eviction via a Unified Information-Theoretic Objective](https://mlsanity.com/paper/2604.25975/) (2026)

## Abstract (arXiv)

Key-value (KV) cache eviction is essential for scaling long-context inference in Large Language Models. However, existing policies predominantly rely on empirical heuristics, lacking a rigorous characterization of token utility under the inherently nonlinear softmax attention mechanism. In this work, we rethink KV cache eviction through the lens of local information geometry, modeling the attention process as a nonlinear Gaussian communication channel. By performing a first-order Taylor expansion of the attention mapping, we derive the Jacobian Information Capacity, a novel objective that explicitly captures query relevance, softmax sensitivity, and structural diversity. Guided by this theory, we introduce Jacap, a capacity-aware eviction method that utilizes softmax-aware importance weighting and statistical leverage scores for subset selection. Extensive experiments across diverse architectures and benchmarks demonstrate that textscJacap delivers superior performance in most scenarios, particularly in high-compression regimes.