The following technical report is available online at
http://cogsci.ucsd.edu (follow links to Tech Reports & Software )
Physical copies are also available (see the site for information).
A Learning Theorem for Networks
at Detailed Stochastic Equilibrium.
Javier R. Movellan
Department of Cognitive Science
University of California San Diego
The paper studies a stochastic extension of continuous
recurrent neural networks and analyzes gradient descent learning
rules to train their equilibrium solutions. A theorem is given that
specifies sufficient conditions for the gradient descent learning
rules to be local covariance statistics between two random
variables: 1) an evaluator which is the same for all the network
parameters, and 2) a system variable which is independent of the
learning objective. The generality of the theorem suggests that
instead of suppressing noise present in physical devices, a natural
alternative is to use it to simplify the credit assignment problem.
In deterministic networks credit assignment requires an evaluation
signal which is different for each node in the
network. Surprisingly, when noise is not suppressed, all is needed
is an evaluator which is the same for the entire network, and a
local Hebbian signal. This modularization of signals greatly
simplifies hardware and software implementations. The paper shows
how the theorem applies to four different learning objectives which
span supervised, reinforcement and unsupervised problems: 1)
regression, 2) density estimation, 3) risk minimization, 4)
information maximization. Simulations, implementation issues and
implications for computational neuroscience are discussed.