ELSAA: Efficient Low-Rank and Sparse Attention Approximation for Training Transformers

Long contexts have become standard in pretrained LLMs, yet they remain expensive to run: prefill compute grows quadratically with sequence length, and every decode step re-reads a key-value cache that grows linearly with it. Sparse attention cuts these costs by attending only to a relevant subset of past tokens, but selecting that subset is itself expensive. We present SpotAttention, a lightweight selector that attaches to a frozen pretrained transformer and learns by KL distillation to estimate its attention distribution. The selector picks the top-K keys each query attends to, and because its estimate is a calibrated distribution, a dual top-p rule reads the per-query, per-layer budget directly from it. Across Qwen3 (dense, 4B-32B) and Qwen3.5 (hybrid linear/full attention, 4B-9B), SpotAttention matches dense accuracy at contexts up to 128K tokens, eight times the training length. Decode at L=128K runs 3.9x faster than FlashAttention and 1.8x faster than Twilight, the strongest training-free baseline. Quantizing the selector's K-cache to INT4 or FP4 microscale shrinks it 3.5x at no accuracy cost.

Sparse attention offers a promising strategy to extend long-context capabilities in Transformer LLMs, yet its efficiency-accuracy trade-offs remain unclear due to the lack of comprehensive evaluation. We address this gap with the largest-scale empirical analysis to date of training-free sparse attention, evaluating six methods across multiple model families and sizes, sequences up to 128K tokens, and sparsity levels up to 0.95 (i.e., $1/20$ attention budget) on nine diverse tasks. We first organise the rapidly evolving landscape of sparse attention methods into a taxonomy along four design axes. Our analysis then yields actionable insights: 1) sparse attention is effective: larger sparse models outperform smaller dense ones at equivalent cost, improving the Pareto frontier; 2) for the training-free methods we study, fine-grained per-query importance estimation during prefilling remains impractical-due to both the cost of estimation and the lack of sparse kernels that translate fine-grained sparsity into wall-clock gains-forcing a task-dependent choice between global-to-token and block-to-block selection. Instead, during decoding, token-to-page selection becomes feasible, enabling better generalisation and higher sparsity tolerance; 3) longer sequences tolerate higher sparsity, suggesting that fixed-budget methods in production are suboptimal. Together, these findings provide practical guidance for deploying sparse attention and methodological recommendations for future evaluations. Our code is available at https://github.com/PiotrNawrot/sparse-frontier.

Sparse attention has been proposed as a way to alleviate the quadratic cost of transformers, a central bottleneck in long-context training. A promising line of work is $α$-entmax attention, a differentiable sparse alternative to softmax that enables input-dependent sparsity yet has lagged behind softmax due to the computational overhead necessary to compute the normalizer $τ$. In this paper, we introduce AdaSplash-2, which addresses this limitation through a novel histogram-based initialization that reduces the number of iterations needed to compute $τ$ to typically 1--2. The key idea is to compute a coarse histogram of attention scores on the fly and store it in on-chip SRAM, yielding a more accurate initialization that enables fast forward and backward computation. Combined with a sparsity-aware GPU implementation that skips zero blocks with low overhead, AdaSplash-2 matches or improves per-step training time relative to FlashAttention-2 when block sparsity is moderate-to-high (e.g., $>$60%), which often occurs at long-context lengths. On downstream tasks, models trained with our efficient $α$-entmax attention match softmax baselines at short-context lengths and achieve substantial gains in long-context settings.