论文标题
从多方面的角度来看的通勤和解开
Commutativity and Disentanglement from the Manifold Perspective
论文作者
论文摘要
在本文中，我们将解散解释为数据歧管的局部图表的发现，并追踪该定义如何自然导致分离的等效条件：变异因素之间的交换性。我们研究了该歧管框架对两个类别问题的影响：学习矩阵指数运算符和压缩数据生成模型。在每个问题中，多种观点都会就其可行性和富有成果的解决方案产生有趣的结果。我们还将我们的多种框架与其他两个常见的分解范式联系起来：群体理论和概率的分解方法。在每种情况下，我们都会展示如何将这些框架与我们的多种观点合并。重要的是，我们在两个替代框架中都将通勤性作为中心财产恢复，进一步强调了其在解散中的重要性。
In this paper, we interpret disentanglement as the discovery of local charts of the data manifold and trace how this definition naturally leads to an equivalent condition for disentanglement: commutativity between factors of variation. We study the impact of this manifold framework to two classes of problems: learning matrix exponential operators and compressing data-generating models. In each problem, the manifold perspective yields interesting results about the feasibility and fruitful approaches their solutions. We also link our manifold framework to two other common disentanglement paradigms: group theoretic and probabilistic approaches to disentanglement. In each case, we show how these frameworks can be merged with our manifold perspective. Importantly, we recover commutativity as a central property in both alternative frameworks, further highlighting its importance in disentanglement.
