Validating Memory-Optimal Transformer Kernels on Real Hardware: From Formal Derivation to Measured Performance Across Two HPC Clusters

arXiv:2609.33916 · cs.DC, cs.AI · Submitted 2026-09-27 · Read on arXiv

cs.DC, cs.AI

Submitted: 2026-09-27

Updated: 2026-09-27

Terminology

• Decode — 31× in this paper · explained in 2 episodes
• Core — 24× in this paper · explained in 2 episodes
• Benchmark — 10× in this paper · explained in 2 episodes
• Transformer — 10× in this paper · explained in 2 episodes
• Verification — 5× in this paper · explained in 2 episodes
• Mathematics of Arrays — 3× in this paper
• Denotational Normal Form — 2× in this paper
• Trace — 2× in this paper · explained in 2 episodes
• Benchmarking — 1× in this paper · explained in 3 episodes
• Non-Uniform Memory Access — 1× in this paper
• Operational Normal Form — 1× in this paper

Sources

• Attention at the Theoretical Minimum: A Mathematics of Arrays Framework for Memory-Optimal Transformer Kernels
• MoA-Structured Decode Attention DNF Derivation, KV-Cache Accumulation, GQA/MQA, and OpenACC Kernel

Related papers

• iScheduler: Reinforcement Learning-Driven Continual Optimization for Large-Scale Resource Investment Problems
• SAMM: Sharded Automated Market Maker
• InferScale: GPU-Native KV Injection for Personalized LLM Serving
• Vigil: Accountable Liveness against Selective Silence
• Steelhead: Interleaving Partially Synchronous and Asynchronous Commit Rules on a Shared DAG
• Pushing CPU Speech Synthesis to the Wall: Extreme Inference Tuning under Serverless Architecture and Billing