# Sparse Attention as a Range Searching Problem: Towards an Inference-Efficient Index for KV Cache

arXiv: https://arxiv.org/abs/2605.06763 · HTML: https://mlsanity.com/paper/2605.06763/

## 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 40 of its 51 references that are in the map.
- First posted on arXiv 7 May 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 40)

- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [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)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (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)
- [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)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [Quest: Query-Aware Sparsity for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2406.10774/) (2024)
- [Model Tells You What to Discard: Adaptive KV Cache Compression for LLMs](https://mlsanity.com/paper/2310.01801/) (2023)
- [Scissorhands: Exploiting the Persistence of Importance Hypothesis for LLM KV Cache Compression at Test Time](https://mlsanity.com/paper/2305.17118/) (2023)
- [PyramidKV: Dynamic KV Cache Compression based on Pyramidal Information Funneling](https://mlsanity.com/paper/2406.02069/) (2024)
- [MInference 1.0: Accelerating Pre-filling for Long-Context LLMs via Dynamic Sparse Attention](https://mlsanity.com/paper/2407.02490/) (2024)
- [Ada-KV: Optimizing KV Cache Eviction by Adaptive Budget Allocation for Efficient LLM Inference](https://mlsanity.com/paper/2407.11550/) (2024)
- [InfLLM: Training-Free Long-Context Extrapolation for LLMs with an Efficient Context Memory](https://mlsanity.com/paper/2402.04617/) (2024)
- [PyramidInfer: Pyramid KV Cache Compression for High-throughput LLM Inference](https://mlsanity.com/paper/2405.12532/) (2024)
- [XAttention: Block Sparse Attention with Antidiagonal Scoring](https://mlsanity.com/paper/2503.16428/) (2025)
- [ShadowKV: KV Cache in Shadows for High-Throughput Long-Context LLM Inference](https://mlsanity.com/paper/2410.21465/) (2024)
- [A Survey on Large Language Model Acceleration based on KV Cache Management](https://mlsanity.com/paper/2412.19442/) (2024)
- [FlexPrefill: A Context-Aware Sparse Attention Mechanism for Efficient Long-Sequence Inference](https://mlsanity.com/paper/2502.20766/) (2025)
- [SpargeAttention: Accurate and Training-free Sparse Attention Accelerating Any Model Inference](https://mlsanity.com/paper/2502.18137/) (2025)
- [SparQ Attention: Bandwidth-Efficient LLM Inference](https://mlsanity.com/paper/2312.04985/) (2023)
- [RetrievalAttention: Accelerating Long-Context LLM Inference via Vector Retrieval](https://mlsanity.com/paper/2409.10516/) (2024)
- [MagicPIG: LSH Sampling for Efficient LLM Generation](https://mlsanity.com/paper/2410.16179/) (2024)
- [PQCache: Product Quantization-based KVCache for Long Context LLM Inference](https://mlsanity.com/paper/2407.12820/) (2024)
- [Loki: Low-rank Keys for Efficient Sparse Attention](https://mlsanity.com/paper/2406.02542/) (2024)

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

- [Fathom: Per-Query Read Depth for Sparse Decoding over Offloaded KV Caches](https://mlsanity.com/paper/2609.17652/) (2026)

## Abstract (arXiv)

Sparse attention improves LLM inference efficiency by selecting a subset of key-value entries, but at the cost of potential accuracy degradation. In particular, omitting critical KV entries can induce substantial errors in model outputs. Existing methods typically operate under fixed or adaptive token budgets and provide empirical robustness or partial theoretical guarantees, yet they do not ensure zero false negatives in decoding steps, particularly since the set of relevant tokens is both query- and step-dependent. Our empirical observations confirm that missing even one critical key can lead to sharp error spikes, especially in long reasoning tasks where the set of important tokens varies throughout decoding. This observation motivates the need for indexing methods that dynamically adapt to these variations across decoding steps while guaranteeing a full recall of the relevant keys above a certain threshold. We address this challenge by reformulating sparse attention as the halfspace range searching problem. However, existing range searching indices are not suitable for modern LLM inference due to their computational and implementation overheads. To overcome this, we introduce Louver, a novel index structure tailored for efficient KV cache retrieval. Louver (i) guarantees zero false negatives with respect to a specified threshold in both theory and practice, (ii) is lightweight to integrate into existing LLM pipelines, and (iii) incorporates hardware-aware optimizations for both CPU and GPU executions. Our experiments demonstrate that Louver outperforms prior sparse attention methods in both accuracy and runtime, and is faster than highly optimized dense attentions such as FlashAttention. These results highlight that recall guarantees are a critical and overlooked dimension of sparse attention, and open a new direction for building theoretically grounded, efficient KV cache indices.