Matthew Scott Gibson

Deterministic Integer Topologies: Bypassing the Matrix-Multiplication Bottleneck via Cache-Resident Graph Traversal

A 6-regular integer lattice of order N = T112 = 6328 occupies 74.16 KiB and fits in a 256 KiB Kaby Lake L2. Two-socket telemetry: 9.76 ns/hop on an i7-7700 (102 M hops/s) and 5.75 ns/hop on an i7-14700F (174 M hops/s). Fail-closed halt 1.5 µs / 800 ns. One 1024×1024 float32 GEMM...

Metric Tensor Folding and Discrete Structural Alignment: Bypassing GEMM via T112 Lattice Geometry and Inversion Transduction Grammars

Abstract:State-of-the-art natural language processing architectures remain constrained by continuous floating-point matrix multiplications (GEMM) and quadratic attention scaling, imposing severe memory bandwidth and thermal taxes on silicon substrates. We present a unified framew...

Metric Tensor Folding and Discrete Structural Alignment: Bypassing GEMM via T112 Lattice Geometry and Inversion Transduction Grammars

Abstract:State-of-the-art natural language processing architectures remain constrained by continuous floating-point matrix multiplications (GEMM) and quadratic attention scaling, imposing severe memory bandwidth and thermal taxes on silicon substrates. We present a unified framew...