Saturday, March 31, 2018

Saturday Morning Video: On Characterizing the Capacity of Neural Networks using Algebraic Topology by William Guss

Here is a video from Microsoft Research by William Guss. I love it because it seems to connect to some of the earlier work we have seen in compressive sensing and related field. ( recently here, or earlier here  or here)

Much like one of the commenter on YouTube, I would have loved less questions during the presentation but it is a fascinating subject. From Guss' website:

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 region 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. This observation allowed us to connect existing theory to empirically driven conjectures on the choice of architectures for fully-connected neural networks.

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