When Parameter Gradient Flows Close in Representation Space
The represented gradient flow of a parameterized model depends on a mobility that can retain hidden parameter information. We study when one entire represented mobility map works for every autonomous loss from one fixed initialization. For two-factor matrix representations wider than both output dimensions, with individually full-row-rank factors, we classify all admissible joint ranks: closure occurs precisely at effective scalar-balanced minimal joint rank or a two-value signed spectral family at full joint rank. All intermediate ranks are excluded; positive represented flows belong to known square-root families. For general representations with constant ambient representation and gradi...
| Authors | Shengye Tao |
|---|---|
| Primary category | cs.LG |
| Published | 20 October 2026 |
| Last updated at source | 20 October 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 21 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.