# Elastic Threshold Attention: Learned Contextual Sparsity for Long-Context Decoding

arXiv: https://arxiv.org/abs/2609.20888 · HTML: https://mlsanity.com/paper/2609.20888/

## 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 16 Sep 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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [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)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Quest: Query-Aware Sparsity for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2406.10774/) (2024)
- [Efficient Content-Based Sparse Attention with Routing Transformers](https://mlsanity.com/paper/2003.05997/) (2020)
- [Native Sparse Attention: Hardware-Aligned and Natively Trainable Sparse Attention](https://mlsanity.com/paper/2502.11089/) (2025)
- [MInference 1.0: Accelerating Pre-filling for Long-Context LLMs via Dynamic Sparse Attention](https://mlsanity.com/paper/2407.02490/) (2024)
- [Efficient Attention: Attention with Linear Complexities](https://mlsanity.com/paper/1812.01243/) (2018)
- [SeerAttention: Learning Intrinsic Sparse Attention in Your LLMs](https://mlsanity.com/paper/2410.13276/) (2024)
- [SpargeAttention: Accurate and Training-free Sparse Attention Accelerating Any Model Inference](https://mlsanity.com/paper/2502.18137/) (2025)
- [MagicPIG: LSH Sampling for Efficient LLM Generation](https://mlsanity.com/paper/2410.16179/) (2024)
- [HashAttention: Semantic Sparsity for Faster Inference](https://mlsanity.com/paper/2412.14468/) (2024)
- [Trainable Dynamic Mask Sparse Attention](https://mlsanity.com/paper/2508.02124/) (2025)

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

- [MOIRA: Mass-Oriented Indexing with Ragged Attention for Long-Context Decoding](https://mlsanity.com/paper/2610.04313/) (2026)

## Abstract (arXiv)

Massive KV caches can cause severe memory-bandwidth bottlenecks during long-context decoding. Sparse attention methods mitigate this problem, but often drop necessary context, leading to quality degradation. We introduce Elastic Threshold Attention (ETA), an end-to-end trainable architecture that rivals dense model quality under hardware-aligned block-sparse decoding. ETA predicts dynamic, contextual thresholds directly from query representations, adjusting context retention depending on the task at hand. To learn this policy from scratch while enabling near lossless KV cache pruning at inference time, we filter attention logits through a shifted SiLU gate during training. We show theoretically and empirically that this creates a smooth, near-uniform attention floor that neutralizes sub-threshold value contributions while simultaneously causing localized attention sinks on initial tokens to disappear. To materialize these advantages, we implement a fused inference-time kernel in Triton that screens KV blocks in O(1) time using cached geometric-probabilistic bounds. Across language modeling, reasoning, and RULER benchmarks, our 1.45B ETA model matches or exceeds dense quality, outperforming alternative fast decoding methods (Quest, H2O, NSA) while achieving higher sparsity levels. Our kernel also achieves up to 2.15× end-to-end speedups over FlashAttention-2 at context lengths of up to 512K tokens. Finally, we introduce an offline calibration algorithm for domain-specific deployments that freezes per-head constant thresholds, cutting attention compute by an additional 27% at no quality cost.