Speaker: Andrea Montanari, Stanford
Talk title: From Projection Pursuit to Interpolation Thresholds in Small Neural Networks
Time: Tuesday, April 5, 12:15pm-1:15pm (ET)
Abstract:
Given a cloud of n data points in d dimensions, consider all projections onto m-dimensional subspaces of R^d and, for each such projection, the empirical distribution of the projected points. What does this collection of probability distributions look like when n, d grow large?
I will present a new set of results on this question under the null model in which the points are i.i.d. standard Gaussian vectors, focusing on the asymptotic regime in which n, d diverge in a proportional way, while m is fixed. The previous question has application to unsupervised learning methods, such as projection pursuit and independent component analysis. I will then introduce a version of the same problem that is relevant for supervised learning, and discuss implications towards characterizing the interpolation thresholds for neural networks with m hidden neurons.
Joint work with Kangjie Zhou.
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