MoA-Structured Decode Attention DNF Derivation, KV-Cache Accumulation, GQA/MQA, and OpenACC Kernel

Lenore Mulin; Gaetan Hains

paper

MoA-Structured Decode Attention DNF Derivation, KV-Cache Accumulation, GQA/MQA, and OpenACC Kernel

arXiv:2607.19456

Abstract

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 $I ¨ $ -reduction eliminates the $K^{⊤}$ buffer algebraically, achieving $(d_{k} + n d_{k} + n d_{v} + d_{v}) \times 4 B$ Dynamic Random Access Memory (DRAM) traffic result numerically verified to $∥ er r ∥_{\leq} 2 \times 1 0^{- 7}$ ; (2)~a C/OpenACC Graphics Processing Unit (GPU) kernel with Operational Normal Form (ONF) stride arithmetic and hardware-coalesced memory access, verified to $∥ err ∥_{\infty} = 0$ (exact IEEE-754 floating-point arithmetic); (3)~a multi-step KV-cache with $O (d_{k} + d_{v})$ per-step append via MoA concatenation $#$ ; and (4)~Grouped-Query Attention (GQA) and Multi-Query Attention (MQA) derived via $I ¨ $ -selection, achieving a proven $\frac{h _{q}}{h _{k v}}$ reduction in KV traffic. All programs are verified against PyTorch scaled_dot_product_attention.