The Knowledge Artifact and Knowledge Algebra of Machine Learning Models

A 200-tree Random Forest has 126,074 parameters. Its knowledge? Three numbers and a basis.
We introduce the Knowledge Artifact — a portable representation of what any ML model has
learned — and the Knowledge Algebra — provably exact arithmetic on these artifacts. Any
model with a predict method is decomposed into spectral coefficients via kernel eigendecomposition.
The resulting vector supports addition (combine models: 5x error reduction), subtraction (remove
bias: 10x correlation reduction; remove dangerous capabilities: 38x), averaging (federated learning:
21% improvement, zero data sharing), distance (model comparison), differencing (structural audit,
R2 =0.95), and continual extension (zero catastrophic forgetting). Function-space arithmetic is
19.2x more accurate than weight-space arithmetic (Task Arithmetic) — provably, by Eckart
Young. All artifacts are portable, composable, and predictable via one matrix multiplication in any
language.