论文标题
通过子空间扩散解开
Disentangling by Subspace Diffusion
论文作者
论文摘要
我们提出了一种新型的非参数算法，用于基于对称性的数据歧管（几何歧管成分估计器（Geomancer））的分离。 Geomancer对Higgins等人提出的问题提供了部分答案。 （2018年）：是否可以仅从对其作用的物体轨道的观察结果中学习如何分解谎言组？我们表明，如果已知歧管的真实度量，并且每个因子歧管都具有非平凡的载体（例如，例如3D中的旋转），则可以完全无监督的数据歧管分解。我们的算法是通过估计在随机行走扩散下不变的子空间来起作用的，从而使DE RHAM分解与差分几何形状具有近似值。我们证明了地貌对几种复杂的合成歧管的功效。我们的工作减少了一个问题，即是否有可能进行无监督的解剖学，即是否有可能进行无监督的度量学习，从而提供了对代表学习的几何性质的统一见解。
We present a novel nonparametric algorithm for symmetry-based disentangling of data manifolds, the Geometric Manifold Component Estimator (GEOMANCER). GEOMANCER provides a partial answer to the question posed by Higgins et al. (2018): is it possible to learn how to factorize a Lie group solely from observations of the orbit of an object it acts on? We show that fully unsupervised factorization of a data manifold is possible if the true metric of the manifold is known and each factor manifold has nontrivial holonomy -- for example, rotation in 3D. Our algorithm works by estimating the subspaces that are invariant under random walk diffusion, giving an approximation to the de Rham decomposition from differential geometry. We demonstrate the efficacy of GEOMANCER on several complex synthetic manifolds. Our work reduces the question of whether unsupervised disentangling is possible to the question of whether unsupervised metric learning is possible, providing a unifying insight into the geometric nature of representation learning.
