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 $\|\mathrm{err}\|_\infty=0$ (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 $ψ$-selection, achieving a proven $\frac {h_q} { h_{kv} }$ reduction in KV traffic. All programs are verified against PyTorch scaled_dot_product_attention.
Conditional computation can decouple language model quality from per-token inference cost, yet leading techniques act on a single axis in isolation: Mixture-of-Experts (MoE) sparsifies the FFN, Mixture-of-Depths (MoD) skips whole transformer blocks, and KV-cache quantization comp…
Long-context large language model inference relies on the KV cache to avoid redundant attention computation, but incurs high memory and bandwidth overheads. Low-bit KV-cache quantization reduces this cost, yet it severely degrade quality; particularly, one-bit quantization reduce…
Deterministic KV-cache eviction keeps the top-$k$ tokens under an importance score and deletes the rest. We prove that this design cannot know what it destroyed: evicted values can be altered so that everything the serving system retains is unchanged while the true attention-outp…
KV-cache compression methods are predominantly evaluated with the query appended to the context before compression -- a query-aware protocol. Yet the economic case for a compressed KV cache is reuse: compress a document once, answer many future questions against it. In that deplo…
We report a way to make a frozen small language model both more capable and dramatically cheaper at once, without changing any weights. Verified knowledge is deposited once as a byte-exact key-value (KV) state artifact and later restored, by graft, into a fresh inference context.…
Attention-based KV cache eviction (H2O and its descendants) compresses the memory-constrained state of a long-context model by ranking tokens on accumulated attention mass, treated here as signal energy, and keeping the heaviest. On schema-dense input streams such as nested JSON,…