Beyond Uniform Local Isometry and Topology: FactoMap for Disentangled Representations

2026-08-25

AI Summary

研究解决了使用欧氏坐标表示生成因素时的几何不匹配问题，提出Factor-Space Topographic Map (FactoMap)方法来学习与因素空间结构相匹配的表示，从而实现因素解耦。

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.

Problem

• disentanglement
• factor space
• geometry
• topology
• generative factors

Innovation

• Factor-Space Topographic Map
• disentanglement
• geometric separability
• topological equivalence
• factor continuity