On the equivalence of Hopfield Networks and Boltzmann Machines

Details On the equivalence of Hopfield Networks and Boltzmann Machines On the equivalence of Hopfield Networks and Boltzmann Machines

2011-05-13

arxiv.org/abs/1105.2790v3

Physics

Condensed Matter

Disordered Systems and Neural Networks

15 pages, 2 figures

Scientific paper

A specific type of neural network, the Restricted Boltzmann Machine (RBM), is implemented for classification and feature detection in machine learning. RBM is characterized by separate layers of visible and hidden units, which are able to learn efficiently a generative model of the observed data. We study a "hybrid" version of RBM's, in which hidden units are analog and visible units are binary, and we show that thermodynamics of visible units are equivalent to those of a Hopfield network, in which the N visible units are the neurons and the P hidden units are the learned patterns. We apply the method of stochastic stability to derive the thermodynamics of the model, by considering a formal extension of this technique to the case of multiple sets of stored patterns, which may act as a benchmark for the study of correlated sets. Our results imply that simulating the dynamics of a Hopfield network, requiring the update of N neurons and the storage of N(N-1)/2 synapses, can be accomplished by a hybrid Boltzmann Machine, requiring the update of N+P neurons but the storage of only NP synapses. In addition, the well known glass transition of the Hopfield network has a counterpart in the Boltzmann Machine: It corresponds to an optimum criterion for selecting the relative sizes of the hidden and visible layers, resolving the trade-off between flexibility and generality of the model. The low storage phase of the Hopfield model corresponds to few hidden units and hence a overly constrained RBM, while the spin-glass phase (too many hidden units) corresponds to unconstrained RBM prone to overfitting of the observed data.

Affiliated with

Also associated with

No associations

Rating

On the equivalence of Hopfield Networks and Boltzmann Machines does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the equivalence of Hopfield Networks and Boltzmann Machines, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the equivalence of Hopfield Networks and Boltzmann Machines will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-27960