Block-Wise Differentiable Sinkhorn Attention: Tail-Refinement Gradients with a Gap-Aware Dustbin Bridge
We study long-context balanced entropic optimal transport (OT) attention on TPU hardware through a stopped-base, fixed-depth tail-refinement surrogate. After a stopped $T$-step Sinkhorn solve, we unroll a short refinement tail and differentiate that surrogate exactly. For the reported $R=2$ TPU path, the backward pass contains four staircase plan factors. We prove an exact one-reference-tile schedule: the $R=2$ score cotangent is a single reference plan tile times an explicit modifier field built from vector cotangents and dual differences. This yields block-wise cost $O((T+R)LW)$, $O(Ld)$ input storage, and $O(L)$ additional HBM usage for fixed head dimension $d$ and band width $W$ on th...
| Authors | Dylan Forde |
|---|---|
| Primary category | cs.LG |
| Published | 28 April 2026 |
| Last updated at source | 7 September 2026 |
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