提出FactoMap，让生成因素在非均匀几何空间中更好解耦。
Beyond Uniform Local Isometry and Topology: FactoMap for Disentangled Representations
- 用因子空间结构建模位置相关几何，突破传统欧氏坐标限制。
- 实验表明匹配该结构可保持因子连续性并实现真正解耦。
- 适合研究生成模型几何本质或需要精确控制生成因素的场景。
许多解耦方法使用欧几里得乘积坐标表示生成因素，但底层因子空间可能具有缠绕、坍缩或位置依赖几何。本文引入因子空间结构，结合因子域、生成器诱导的等价关系和位置依赖尺度，以区分拓扑等价但几何不同的空间。我们证明统计独立的因素未必几何可分：色相与尺度的影响增长速率不同，导致各向异性，固定重缩放无法消除。为此提出因子空间拓扑图（FactoMap），学习由因子空间格点索引的可解释原型。拓扑学习将格点周期性、坍缩和非均匀范围迁移至表征中。实验显示，匹配该结构能保持因子连续性，并实现对底层因子的有效解耦。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。