ELSA: Exact Linear-Scan Attention for Fast and Memory-Light Vision Transformers

This paper introduces Exact Linear Attention (ELA), a mechanism that achieves linear computational complexity for Transformer attention by exploiting the exact decomposition property of kernel functions, thereby eliminating approximation error. We identify and address two key limitations of prior linear attention -- gradient explosion and token attention dilution -- by imposing kernel constraints that ensure non-negativity, discriminability, and geometric interpretability. Several kernel functions are proposed, including the Hadamard Exp Kernel, Summation Squared Euclidean Distance Kernel, and Subtraction Squared Euclidean Distance Kernel, each tailored for specific attention behaviors. Beyond the core attention formulation, the paper presents three engineering innovations: (1) a Hyper-Link structure that replaces traditional residual connections to mitigate gradient degradation; (2) a Memory Lobe module based on bidirectional linear attention, which captures "transformation flow" across layers to implement qualitative memory and an implicit reinforcement learning paradigm; and (3) a routing-score-based bias mechanism for Mixture-of-Experts (MoE) to improve interpretability and semantic alignment. Experimental results demonstrate that ELA achieves up to 6x faster decoding speed and 75% reduction in KV cache memory usage compared to full attention, while maintaining comparable or superior training performance. The proposed memory module accelerates convergence and enhances generalization. Furthermore, we extend the linear attention principle to vision models, yielding YOLO-LAT, which attains up to 4.3x GPU inference speedup and 7.9x parameter reduction with competitive detection accuracy. These results underline the broad applicability of exact linear attention for scaling Transformer models to ultra-long sequences and efficient visual tasks.

Recent advances in sparse attention mechanisms have demonstrated strong potential for reducing the computational cost of long-context training and inference in large language models (LLMs). Native Sparse Attention (NSA), one state-of-the-art approach, introduces natively trainable, hardware-aligned sparse attention that delivers substantial system-level performance boosts while maintaining accuracy comparable to full attention. However, the kernel implementation of NSA forces a loop order that is only efficient with a relatively large number of query heads in each Grouped Query Attention (GQA) group, whereas existing LLMs widely adopt a much smaller number of query heads in each GQA group -- such an inconsistency significantly limits the applicability of this sparse algorithmic advance. In this work, we propose Flash Sparse Attention (FSA), an alternative kernel implementation that enables efficient NSA computation across a wide range of popular LLMs with a varied, smaller number of heads in each GQA group on modern GPUs. Compared to vanilla NSA kernel implementation, our empirical evaluation demonstrates that FSA achieves (i) up to 3.5x and on average 1.6x kernel-level latency reduction, (ii) up to 1.25x and 1.09x on average end-to-end training speedup on state-of-the-art LLMs, and (iii) up to 1.36x and 1.11x on average for prefill-phase speedup in LLM generative inference. The source code is open-sourced and publicly available at https://github.com/Relaxed-System-Lab/Flash-Sparse-Attention.

The quadratic $N\times N$ attention score matrix remains a central obstacle to extending Transformers to longer input lengths. Existing efficient attention methods usually reduce this bottleneck by either imposing sparsity, so that each query attends to only a small subset of keys, or by using low-rank/kernel sketches, so that global interactions are compressed into a lower-dimensional representation. We propose \emph{ELSAA}, an efficient low-rank and sparse approximation of attention. Importantly, ELSAA does \emph{not} decompose the learned projection or output matrices of the Transformer into sparse and low-rank factors. Instead, after dense projections produce $Q,K,V$, ELSAA approximates the induced attention score operator itself: a sparse branch captures selected high-similarity interactions, while a low-rank branch summarizes diffuse global interactions. Since the two branches can be normalized over supports with very different denominator mass, ELSAA introduces a denominator-aware fusion term that scales the sparse branch according to its estimated attention mass relative to the low-rank branch. This gives a practical framework for constructing low-rank and sparse attention outputs without materializing the full quadratic score matrix, aiming to enable longer-context training while preserving both sharp token-level interactions and broad contextual mixing.