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arXiv · 2608.24762

Beyond Uniform Local Isometry and Topology: FactoMap for Disentangled Representations

Sohini Gupta·Bahareh Tolooshams
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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.

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Sohini Gupta, Bahareh Tolooshams. 2026-08-25. Beyond Uniform Local Isometry and Topology: FactoMap for Disentangled Representations. https://arxiv.org/abs/2608.24762

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