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

arXiv:2607.19456v1 Announce Type: cross 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 psi-reduction eliminates the K^op buffer algebraically, achieving (d_k + nd_k+ nd_v+ d_v)imes4,{B} Dynamic Random Access Memory (DRAM) traffic result numerically verified to |{err}|_leq2imes10^{-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 psi-selection, achieving a proven frac {h_q} { h{kv} } reduction in KV traffic. All programs are verified against PyTorch scaled_dot_product_attention.

Source: arXiv cs.AI | 2026-07-23