Beyond Uniform Local Isometry and Topology: FactoMap for Disentangled Representations

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, yielding anisotropy that no fixed rescaling removes. We propose the Factor-Space Topographic Map (FactoMap), which learns interpretable prototypes indexed by a factor-space lattice. Topographic learning transfers the lattice's periodicity, collapses, and non-uniform extent to the representation. Experiments show that matching this structure preserves factor continuity and enables disentanglement of the underlying factors.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2608.24762 [cs.LG]

(or arXiv:2608.24762v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.24762 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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