# Prism: Spectral-Aware Block-Sparse Attention

arXiv: https://arxiv.org/abs/2602.08426 · HTML: https://mlsanity.com/paper/2602.08426/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 24 references that are in the map.
- First posted on arXiv 9 Feb 2026.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [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)
- [VBench: Comprehensive Benchmark Suite for Video Generative Models](https://mlsanity.com/paper/2311.17982/) (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)
- [Video-MME: The First-Ever Comprehensive Evaluation Benchmark of Multi-modal LLMs in Video Analysis](https://mlsanity.com/paper/2405.21075/) (2024)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [LongVideoBench: A Benchmark for Long-context Interleaved Video-Language Understanding](https://mlsanity.com/paper/2407.15754/) (2024)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models](https://mlsanity.com/paper/2508.06471/) (2025)
- [MInference 1.0: Accelerating Pre-filling for Long-Context LLMs via Dynamic Sparse Attention](https://mlsanity.com/paper/2407.02490/) (2024)
- [XAttention: Block Sparse Attention with Antidiagonal Scoring](https://mlsanity.com/paper/2503.16428/) (2025)
- [Scaling Laws of RoPE-based Extrapolation](https://mlsanity.com/paper/2310.05209/) (2023)
- [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)
- [Sparser Block-Sparse Attention via Token Permutation](https://mlsanity.com/paper/2510.21270/) (2025)

## Built on by (most cited first, 3 of 3)

- [Vortex: Efficient and Programmable Sparse Attention Serving for AI Agents](https://mlsanity.com/paper/2606.06453/) (2026)
- [LOCKS: Page-Local Compact Key Summaries for Efficient Long-Context Decoding](https://mlsanity.com/paper/2607.24555/) (2026)
- [Block-Sparse Attention with Semantic-Geometric Decoupled Routing](https://mlsanity.com/paper/2609.22884/) (2026)

## Abstract (arXiv)

Block-sparse attention is promising for accelerating long-context LLM pre-filling, yet identifying relevant blocks efficiently remains a bottleneck. Existing methods typically employ coarse-grained attention as a proxy for block importance estimation, but often resort to expensive token-level searching or scoring, resulting in significant selection overhead. In this work, we trace the inaccuracy of standard coarse-grained attention via mean pooling to a theoretical root cause: the interaction between mean pooling and Rotary Positional Embeddings (RoPE). We prove that mean pooling acts as a low-pass filter that induces destructive interference in high-frequency dimensions, effectively creating a "blind spot" for local positional information (e.g., slash patterns). To address this, we introduce Prism, a training-free spectral-aware approach that decomposes block selection into high-frequency and low-frequency branches. By applying energy-based temperature calibration, Prism restores the attenuated positional signals directly from pooled representations, enabling block importance estimation using purely block-level operations, thereby improving efficiency. Extensive evaluations confirm that Prism maintains accuracy parity with full attention while delivering up to 5.1× speedup.