Block-Wise Differentiable Sinkhorn Attention: Tail-Refinement Gradients with a Gap-Aware Dustbin Bridge

ArXi:2605.08123v1 Announce Type: new 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 production $R=2$ case, 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.