# EntmaxKV: Support-Aware Decoding for Entmax Attention

arXiv: https://arxiv.org/abs/2605.21649 · HTML: https://mlsanity.com/paper/2605.21649/

## 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 22 of its 25 references that are in the map.
- First posted on arXiv 20 May 2026.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (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)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [Quest: Query-Aware Sparsity for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2406.10774/) (2024)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [Kimi Linear: An Expressive, Efficient Attention Architecture](https://mlsanity.com/paper/2510.26692/) (2025)
- [Sparse Sequence-to-Sequence Models](https://mlsanity.com/paper/1905.05702/) (2019)
- [Adaptively Sparse Transformers](https://mlsanity.com/paper/1909.00015/) (2019)
- [Transformers are Multi-State RNNs](https://mlsanity.com/paper/2401.06104/) (2024)
- [Dynamic Memory Compression: Retrofitting LLMs for Accelerated Inference](https://mlsanity.com/paper/2403.09636/) (2024)
- [MagicPIG: LSH Sampling for Efficient LLM Generation](https://mlsanity.com/paper/2410.16179/) (2024)
- [Loki: Low-rank Keys for Efficient Sparse Attention](https://mlsanity.com/paper/2406.02542/) (2024)
- [A Simple and Effective L2 Norm-Based Strategy for KV Cache Compression](https://mlsanity.com/paper/2406.11430/) (2024)
- [Twilight: Adaptive Attention Sparsity with Hierarchical Top-p Pruning](https://mlsanity.com/paper/2502.02770/) (2025)
- [Learning Classifiers with Fenchel-Young Losses: Generalized Entropies, Margins, and Algorithms](https://mlsanity.com/paper/1805.09717/) (2018)
- [Tactic: Adaptive Sparse Attention with Clustering and Distribution Fitting for Long-Context LLMs](https://mlsanity.com/paper/2502.12216/) (2025)
- [Long-Context Generalization with Sparse Attention](https://mlsanity.com/paper/2506.16640/) (2025)
- [AdaSplash: Adaptive Sparse Flash Attention](https://mlsanity.com/paper/2502.12082/) (2025)
- [AdaSplash-2: Faster Differentiable Sparse Attention](https://mlsanity.com/paper/2604.15180/) (2026)

## Abstract (arXiv)

Long-context decoding is increasingly limited by KV-cache memory traffic as each generated token attends over a cache whose size grows linearly with context length. Existing sparse decoding methods reduce this cost by selecting subsets of tokens or pages, but are designed for softmax attention, whose dense tails make any truncation discard nonzero probability mass. In contrast, α-entmax produces exact zeros, turning sparse decoding from dense-tail approximation into support recovery: if the selected candidates contain the entmax support, sparse decoding remains exact. While recent entmax kernels enable efficient training, they do not address the autoregressive decoding bottleneck, where dense inference still streams the full KV cache before sparsity is known. In this work, we introduce EntmaxKV, an entmax-native sparse decoding framework that exploits sparsity before KV pages are loaded. EntmaxKV combines query-aware page scoring, support-aware candidate selection, and sparse entmax attention. We analyze truncation error through the dropped probability mass δ, showing that output error is controlled by δ and vanishes when the entmax support is recovered. We further introduce a Gaussian-aware entmax selector that estimates the entmax threshold from lightweight page statistics, adapting the selected budget to the score distribution. Empirically, EntmaxKV drops less probability mass, retains more support tokens, and achieves lower output error than softmax-based sparse decoding at matched KV budgets. On long-context and language modeling benchmarks, it closely matches full-cache entmax while using a small fraction of the KV cache, achieving up to 2.88× (softmax) and 5.5× (entmax) speedup over full attention baselines as well as over 2× speedup over softmax and entmax top-k at 1M context length.