这篇论文提出了一个名为FactoMap的新方法，它通过引入因素空间结构来改进解耦表示，这对于需要从数据中提取独立因素的应用来说是一个重要的进展。与传统的解耦方法相比，FactoMap能够更好地处理因素空间中的复杂几何形状，从而提高解耦的准确性。
许多解耦方法使用欧几里得乘积坐标表示生成因素，尽管潜在的因素空间可能缠绕、折叠或具有位置相关的几何形状。我们引入了因素空间结构，结合因素域、生成器诱导的识别和位置相关的尺度，以区分具有不同因素几何形状的拓扑等价空间。我们表明，统计上独立的因素不必在几何上可分离：色调和尺度产生的影响以不同的速率增长，导致无法通过固定缩放消除的各向异性。我们提出了因素空间拓扑图（FactoMap），它通过因素空间晶格学习可解释的原型。拓扑学习将晶格的周期性、折叠和非均匀范围转移到表示中。实验表明，匹配这种结构可以保持因素连续性并实现潜在因素的解耦。
Beyond Uniform Local Isometry and Topology: FactoMap for Disentangled Representations
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.