# Autonomy-of-Heads: Data-Free Sparse Attention from Frozen Query-Key Geometry

arXiv: https://arxiv.org/abs/2608.06849 · HTML: https://mlsanity.com/paper/2608.06849/

## Key facts

- Cited by 1 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 23 of its 34 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [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)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [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)
- [SnapKV: LLM Knows What You are Looking for Before Generation](https://mlsanity.com/paper/2404.14469/) (2024)
- [Quest: Query-Aware Sparsity for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2406.10774/) (2024)
- [SARATHI: Efficient LLM Inference by Piggybacking Decodes with Chunked Prefills](https://mlsanity.com/paper/2308.16369/) (2023)
- [You Only Cache Once: Decoder-Decoder Architectures for Language Models](https://mlsanity.com/paper/2405.05254/) (2024)
- [Reducing Transformer Key-Value Cache Size with Cross-Layer Attention](https://mlsanity.com/paper/2405.12981/) (2024)
- [RazorAttention: Efficient KV Cache Compression Through Retrieval Heads](https://mlsanity.com/paper/2407.15891/) (2024)
- [NACL: A General and Effective KV Cache Eviction Framework for LLMs at Inference Time](https://mlsanity.com/paper/2408.03675/) (2024)
- [IndexCache: Accelerating Sparse Attention via Cross-Layer Index Reuse](https://mlsanity.com/paper/2603.12201/) (2026)
- [Kascade: A Practical Sparse Attention Method for Long-Context LLM Inference](https://mlsanity.com/paper/2512.16391/) (2025)
- [LycheeDecode: Accelerating Long-Context LLM Inference via Hybrid-Head Sparse Decoding](https://mlsanity.com/paper/2602.04541/) (2026)
- [Linear Predictability of Attention Heads in Large Language Models](https://mlsanity.com/paper/2603.13314/) (2026)

## Built on by (most cited first, 1 of 1)

- [Power law graph attention: exact generalization of scaled dot-product attention, empirical collapse at inference](https://mlsanity.com/paper/2608.10288/) (2026)

## Abstract (arXiv)

Long-context LLM inference is bottlenecked by quadratic attention computation and growing KV-cache costs. Existing sparse attention and KV-compression methods typically decide which tokens or heads to preserve from runtime attention scores, observation windows, calibration prompts, or learned gates, making head diagnosis input-dependent and costly to deploy. We propose Autonomy-of-Heads (AoH), a data-free method that identifies retrieval and streaming heads from the spectral geometry of query-key projections. AoH defines the kernel attention operator Mh = WKhtopWQh and uses its effective-rank as a weight-space measure of head function: concentrated spectra indicate a small number of dominant query-key matching directions and are associated with retrieval heads, whereas diffuse spectra indicate the absence of a dominant global matching direction and are associated with streaming heads. We further derive an efficient dhead-dimensional computation that avoids constructing the full dmodel× dmodel matrix. We conducted extensive experiments across models demonstrating that at 50% sparsity, AoH retains 96.5% of Full Attention performance on average while reducing prefill and decode latency by up to 41.4% and 66.0%, respectively, and KV-cache memory by 50.0% at 256K tokens.