On Characterizing the Capacity of Neural Networks Using Algebraic Topology

Anonymous

Nov 07, 2017 (modified: Nov 07, 2017) ICLR 2018 Conference Blind Submission readers: everyone Show Bibtex
  • Abstract: The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most expressive and generalizable architectures suited to that data, beyond inductive bias. After suggesting algebraic topology as a measure for data complexity, we show that the power of a network to express the topological complexity of a dataset in its decision boundary is a strictly limiting factor in its ability to generalize. We then provide the first empirical characterization of the topological capacity of neural networks. Our empirical analysis shows that at every level of dataset complexity, neural networks exhibit topological phase transitions and stratification. This observation allowed us to connect existing theory to empirically driven conjectures on the choice of architectures for a single hidden layer neural networks.
  • TL;DR: We show that the learnability of different neural architectures can be characterized directly by computable measures of data complexity.
  • Keywords: deep learning theory, architecture selection, algebraic topology

Loading