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SUMMARY:Boltzmann Machines [Confirmed]
DTSTART:20250407T193000Z
DTEND:20250407T210000Z
DTSTAMP:20260608T083100Z
UID:indico-event-1120@events.perimeterinstitute.ca
DESCRIPTION:Speakers: Geoffrey Hinton (University Professor Emeritus (Univ
 ersity of Toronto))\n\nTo train a neural net efficiently we need to comput
 e the gradient of some measure of the performance of the net with respect 
 to each of the connection weights. The standard way to do this is to use t
 he chain rule to backpropagate gradients through layers of neurons. I shal
 l briefly review a few of the engineering successes of backpropagation and
  then describe a very different way of getting the gradients that\, for a 
 while\, seemed a lot more plausible as a model of how the brain gets gradi
 ents.\n \nConsider a system composed of binary neurons that can be active
  or inactive with weighted pairwise couplings between pairs of neurons\, i
 ncluding long range couplings. If the neurons represent pixels in a binary
  image\, we can store a set of binary training images by adjusting the cou
 pling weights so that the images are local minima of a Hopfield energy fun
 ction which is minus the sum over all pairs of active neurons of their cou
 pling weights. But this energy function can only capture pairwise correlat
 ions. It cannot represent the kinds of complicated higher-order correlatio
 ns that occur in images. Now suppose that in addition to the "visible" neu
 rons that represent the pixel intensities\, we also have a large set of hi
 dden neurons that have weighted couplings with each other and with the vis
 ible neurons. Suppose also that all of the neurons are asynchronous and st
 ochastic: They adopt the active state with a log odds that is equal to the
  difference in the energy function when the neuron is inactive versus acti
 ve. Given a set of training images\, is there a simple way to set the weig
 hts on all of the couplings so that the training images are local minima o
 f the free energy function obtained by integrating out the states of the h
 idden neurons? The Boltzmann machine learning algorithm solved this proble
 m in an elegant way. It was proof of principle that learning in neural net
 works with hidden neurons was possible using only locally available inform
 ation\, contrary to what was generally believed at the time.\n\nhttps://ev
 ents.perimeterinstitute.ca/event/1120/
LOCATION:PI/1-100 - Theatre (Perimeter Institute for Theoretical Physics)
URL:https://events.perimeterinstitute.ca/event/1120/
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