PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Manfred Denker, Anna Mazzucato, Mari Royer, Victor Nistor, Alexei Novikov.

Title:Distributions represented by restricted Boltzmann machines
Seminar:Probability and Financial Mathematics Seminar
Speaker:Jason Morton, Penn State University
Abstract:
We derive relations between theoretical properties of restricted Boltzmann machines (RBMs), popular neuroscience and machine learning models which form the building blocks of deep learning models, and several natural notions from discrete mathematics and convex geometry. We give implications and equivalences relating RBM-representable probability distributions, perfectly reconstructibe inputs, Hamming modes, zonotopes and zonosets, point configurations in hyperplane arrangements, linear threshold codes, and multi-covering numbers of hypercubes. As a motivating application, we prove results on the relative representational power of mixtures of product distributions and products of mixtures of pairs of product distributions (RBMs) that formally justify widely held intuitions about distributed representations. In particular, we show that an exponentially larger mixture of products, requiring an exponentially larger number of parameters, is required to represent the probability distributions represented as products of mixtures.

Room Reservation Information

Room Number:MB106
Date:03 / 21 / 2014
Time:03:35pm - 04:35pm