Beyond Uniform Local Isometry and Topology: FactoMap for Disentangled Representations
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Computer Science > Machine Learning
Title: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.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2608.24762 [cs.LG] |
| (or arXiv:2608.24762v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.24762
arXiv-issued DOI via DataCite (pending registration)
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Submission history
From: Bahareh Tolooshams [view email][v1] Tue, 25 Aug 2026 15:59:59 UTC (2,754 KB)
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