Information-Induced Training Geometry: Exact Reduction, Canonical Completion, and Structured Expressivity
Training data constrains optimizer geometry through the covectors visible to a declared information channel. We study how such partial information determines a full positive cometric relative to a reference and which degrees of freedom remain unidentified. Our central result resolves full-column-rank positive-definite compression under affine-invariant Riemannian geometry. The compression map is a split-Hadamard metric submetry and admits an explicit unique completion that is the affine-invariant nearest full geometry realizing a visible target and yields exact full-to-visible variational reduction. When the channel moves, the completions form a gauge-invariant rank stratification of the ...
| Authors | Zavier Li |
|---|---|
| Primary category | cs.LG |
| Published | 11 July 2026 |
| Last updated at source | 11 July 2026 |
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