[Submitted on 25 Aug 2026 (v1), last revised 18 Oct 2026 (this version, v2)]
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, which combines factor domains, generator-induced identifications, and position-dependent scales to distinguish topologically equivalent spaces with different factor geometries. We show that statistical independence does not imply uniform product geometry: independent hue and scale can affect observations at different, scale-dependent rates, producing anisotropy that no fixed rescaling can remove. We propose the Factor-Space Topographic Map (FactoMap), which learns interpretable prototypes indexed by a structured factor-space lattice. Topographic learning transfers the lattice’s periodicity, collapses boundaries, and non-uniform extent to the representation. Experiments show that matching this structure better preserves factor continuity and improves disentanglement of the underlying factors.
Submission history
From: Bahareh Tolooshams [view email]
[v1] Tue, 25 Aug 2026 15:59:59 UTC (2,754 KB)
[v2] Sun, 18 Oct 2026 15:34:54 UTC (13,177 KB)
