Ml Knowledge Artifacts Algebra

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, \(R^2 = 0.95\)), 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.