Systolic Linear Attention: Co-Designing Tile-Grouped Gated Delta Attention for TPUs

Abstract

Gated-delta linear attention layers such as Gated DeltaNet (GDN), Kimi Delta Attention (KDA), and GDN-2 are tuned for GPUs, where small tensor-core tiles and fast vector registers make per-channel decay rescaling and sequential in-block solves cheap. On Google TPUs, which concentrate compute in wide $256 \times 256$ systolic matrix units backed by a slower vector unit, porting these layers directly leaves half of each matrix tile empty and bottlenecks on vector operations. We present \textbf{Systolic Linear Attention (SLA)}, which reshapes gated delta attention around the matrix unit by widening keys to $256$ with grouped value heads, grouping decay gates into four $64$-channel tiles, and computing the chunk solve entirely with block matrix products in a single fused kernel. On TPU v7x, a full \texttt{SLA-R4} layer runs $1.6\times$--$2.5\times$ faster than the open-source Tokamax KDA kernel ($1.4\times$--$2.4\times$ with exact chunk inversion), driven primarily by head sharing and kernel fusion. Across a $2{,}048$-chip TPU v7x pre-training study of sparse Mixture-of-Experts (MoE) models from $6.5\text{B}$ to $63.1\text{B}$ parameters, SLA trains $11\%$--$24\%$ faster than KDA at similar perplexity, and reaches slightly lower perplexity than KDA in smaller matched-seed runs.