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Depth-Staggered Fibonacci Spacing for Sparse Attention: Static Schedules Beat Learned Dilation and Extrapolate Where Dense Attention Fails

We study sparse self-attention in which each query attends to a dense local window plus a set of Fibonacci-spaced offsets, with a per-layer scalar alpha that compresses or expands the spacing. Across 21 language models trained under one matched recipe (60M parameters, 512 hidden, 16 layers, 426M tokens), we compare four ways of setting alpha across depth: fixed, per-layer learned, a static linear stagger, and a coprime (anti-gridding) reassignment of that stagger, together with a reach-matched power-of-2 control. Three results stand out. First, a static per-layer stagger improves perplexity over both fixed and learned alpha, and the gain is base-agnostic: applying the same stagger to a power-of-2 base lifts it above fixed Fibonacci and to parity with learned Fibonacci attention. Second, learning per layer is inert: it does not beat the static schedule and costs roughly five times the inference latency. Third, and most consequential, all sparse variants extrapolate to four times their training length with little or no degradation, whereas a recipe-matched dense baseline collapses (perplexity rises by 201% at 4x length); we attribute this to fixed-offset attention only ever querying relative positions seen during training. We also report two honest negatives: at training length the best sparse model has about 26% higher perplexity than the dense baseline, and the staggering gain is uniform across context positions rather than concentrated at long range.

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