Beyond Uniform Local Isometry and Topology: FactoMap for Disentangled Representations

Key takeaways

• arXiv:2608.24762v1 Announce Type: cross Abstract: Many disentanglement methods represent generative factors using Euclidean product coordinates, although the underlying factor spaces may wrap, collapse, or have position-dependent geometry.
• We introduce factor-space structure, combining factor domains, generator-induced identifications, and position-dependent scales to distinguish topologically equivalent spaces with different factor geometries.
• We show that statistically independent factors need not be geometrically separable: hue and scale produce effects that grow at different rates, yieldin