Stats, Optimization, and Machine Learning Seminar - Colton Grainger and Claire Savard

Colton Grainger, Department of Mathematics, University of Colorado Boulder

On Characterizing the Capacity of Neural Networks using Algebraic Topology

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.
 

Claire Savard, Department of Physics, University of Colorado Boulder

Applying Topological Data Analysis Techniques to Music Information Retreiva

Abstract unavailable

Tuesday, November 27, 2018 at 3:30pm to 4:30pm


Engineering Center, ECCR 257
1111 Engineering Drive, Boulder, CO 80309

Event Type

Colloquium/Seminar

Interests

Science & Technology, Research & Innovation

Audience

Faculty, Students, Graduate Students, Postdoc

College, School & Unit

Engineering & Applied Science

Tags

statistics, optimization, machine learning

Group
Applied Mathematics
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