# HARD-KV: Head-Adaptive Regularization for Decoding-time KV Compression

arXiv: https://arxiv.org/abs/2606.28831 · HTML: https://mlsanity.com/paper/2606.28831/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in KV cache optimization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 38 of its 48 references that are in the map.
- First posted on arXiv 27 Jun 2026.

## Placed in

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

## Builds on (most cited first, 30 of 38)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [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)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [SnapKV: LLM Knows What You are Looking for Before Generation](https://mlsanity.com/paper/2404.14469/) (2024)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [LongBench v2: Towards Deeper Understanding and Reasoning on Realistic Long-context Multitasks](https://mlsanity.com/paper/2412.15204/) (2024)
- [DuoAttention: Efficient Long-Context LLM Inference with Retrieval and Streaming Heads](https://mlsanity.com/paper/2410.10819/) (2024)
- [Ada-KV: Optimizing KV Cache Eviction by Adaptive Budget Allocation for Efficient LLM Inference](https://mlsanity.com/paper/2407.11550/) (2024)
- [MagicPIG: LSH Sampling for Efficient LLM Generation](https://mlsanity.com/paper/2410.16179/) (2024)
- [RazorAttention: Efficient KV Cache Compression Through Retrieval Heads](https://mlsanity.com/paper/2407.15891/) (2024)
- [Not All Heads Matter: A Head-Level KV Cache Compression Method with Integrated Retrieval and Reasoning](https://mlsanity.com/paper/2410.19258/) (2024)
- [ThinK: Thinner Key Cache by Query-Driven Pruning](https://mlsanity.com/paper/2407.21018/) (2024)
- [KeyDiff: Key Similarity-Based KV Cache Eviction for Long-Context LLM Inference in Resource-Constrained Environments](https://mlsanity.com/paper/2504.15364/) (2025)
- [Twilight: Adaptive Attention Sparsity with Hierarchical Top-p Pruning](https://mlsanity.com/paper/2502.02770/) (2025)
- [NACL: A General and Effective KV Cache Eviction Framework for LLMs at Inference Time](https://mlsanity.com/paper/2408.03675/) (2024)
- [StreamingTOM: Streaming Token Compression for Efficient Video Understanding](https://mlsanity.com/paper/2510.18269/) (2025)
- [RocketKV: Accelerating Long-Context LLM Inference via Two-Stage KV Cache Compression](https://mlsanity.com/paper/2502.14051/) (2025)
- [A Systematic Analysis of Hybrid Linear Attention](https://mlsanity.com/paper/2507.06457/) (2025)
- [Accelerating Streaming Video Large Language Models via Hierarchical Token Compression](https://mlsanity.com/paper/2512.00891/) (2025)
- [DiffKV: Differentiated Memory Management for Large Language Models with Parallel KV Compaction](https://mlsanity.com/paper/2412.03131/) (2024)
- [U-MATH: A University-Level Benchmark for Evaluating Mathematical Skills in LLMs](https://mlsanity.com/paper/2412.03205/) (2024)

## Built on by (most cited first, 2 of 2)

- [LOCKS: Page-Local Compact Key Summaries for Efficient Long-Context Decoding](https://mlsanity.com/paper/2607.24555/) (2026)
- [MOIRA: Mass-Oriented Indexing with Ragged Attention for Long-Context Decoding](https://mlsanity.com/paper/2610.04313/) (2026)

## Abstract (arXiv)

Long-context LLM inference faces a fundamental conflict: head-adaptive compression algorithms (e.g., Top-p nucleus sampling) offer superior accuracy by dynamically fluctuating memory budgets, yet modern inference engines (e.g., vLLM) demand rigid, static memory patterns to leverage CUDA Graphs and PagedAttention. We resolve this ``Static-Dynamic'' mismatch with HARD-KV, a unified framework that that bridges dynamic selection with rigid system constraints. HARD-KV introduces a Cascade Cache hierarchy, managing the token lifecycle across dense, sparse, and condensed tiers. Crucially, we propose a Logits Calibration mechanism that normalizes diverse importance metrics into a unified probability space, enabling consistent Top-p budgeting across heterogeneous heads. To bridge the efficiency gap, we offer a system-level solution, which rewrites fragmented, dynamic indices into contiguous physical layouts compatible with high-performance inference engine. Extensive experiments on math-reasoning benchmarks (AIME, U-Math) verify that HARD-KV achieves up to 2× throughput improvement over static baselines while maintaining high-fidelity generation in 10k+ token scenarios. Code is available at https://github.com/SuDIS-ZJU/HARDInfer.