Absorber-Aware Scope Classification and Post-Lowering Kernel Selection for Boolean Sparse Matrix-Vector Multiplication

This project asks why a mathematically valid optimisation does not always make sparse tensor or graph code faster. The algebra is only one part. The outcome also depends on how the data is represented and traversed, what the workload looks like, and sometimes on the machine code the compiler emits. In one experiment, GCC compiled the guarded and unguarded versions of a push kernel to identical machine code. Clang kept them distinct. That led to GAC, or algebra-gated contraction. GAC checks four things in order: whether an optimisation is correct, whether the generated loop structure can use it, whether it remains a distinct kernel after compilation, and whether it is worth the full cost once setup and representation are included. The focused paper tests GAC on Boolean sparse matrix-vector multiplication. For single-query workloads, running a dynamic selector cost more than it saved, so the frozen policy used a fixed terminal-pull kernel. On 2,807 held-out workloads evaluated separately under GCC and Clang, the policy came within 2.3% and 0.8% of the fastest available kernel for each workload on a geometric-mean basis. It also matched the best static policy chosen with hindsight, and no workload crossed the paper’s 2× catastrophic threshold. This record contains the focused research manuscript and its companion extended technical report. The focused manuscript is the main entry point. The extended report includes the broader semiring mechanism studies, cross-host evidence, resource-aware contraction planning, and the complete audit record. The source code, experiment history, hashed artefacts, public commit crosswalk, and Lean checks are available in the linked GitHub release. GitHub Release: https://github.com/000x999/GAC/releases/tag/v1.0.0