MoA-Structured Decode Attention DNF Derivation, KV-Cache Accumulation, GQA/MQA, and OpenACC Kernel
We derive four memory-optimal inference artifacts for transformer attention using the Mathematics of Arrays (MoA), each following directly from the forward-pass Denotational Normal Form (DNF) of with the query-row index fixed to the current decode step. The artifacts are: (1)~a single-query decode DNF in which the $ψ$-reduction eliminates the $K^\top$ buffer algebraically, achieving $(d_k + nd_k+ nd_v+ d_v)\times4\,{B}$ Dynamic Random Access Memory (DRAM) traffic result numerically verified to $\|{err}\|_\leq2\times10^{-7}$; (2)~a C/OpenACC Graphics Processing Unit (GPU) kernel with Operational Normal Form (ONF) stride arithmetic and hardware-coalesced memory access, verified to $\|\mathr...
| Authors | Lenore Mulin, Gaetan Hains |
|---|---|
| Primary category | cs.LG |
| Published | 21 July 2026 |
| Last updated at source | 21 July 2026 |
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