# Keeping Neural Networks Simple by Minimizing the
Description Length of the Weights

Geoffrey E. Hinton and Drew van Camp

Department of Computer Science

University of Toronto

**Abstract**

Supervised neural networks generalize well if there is much less
information in the weights than there is in the output vectors of the training cases.
So during learning, it is important to keep the weights simple by penalizing the
amount of information they contain. The amount of information in a weight can
be controlled by adding Gaussian noise and the noise level can be adapted during learning
to optimize the trade-off between the expected squared error of the network and the amount
of information in the weights. We describe a method of computing the derivatives of
the expected squared error and of the amount of information in the noisy weights in a
network that contains a layer of non-linear hidden units. Provided the output units
are linear, the exact derivatives can be computed efficiently without time-consuming Monte
Carlo simulations. The idea of minimizing the amount of information that is required
to communicate the weights of a neural network leads to a number of interesting schemes
for encoding the weights

Download: [postscript] [pdf]

*Sixth ACM Conference on Computational Learning Theory,
Santa Cruz, July 1993.*

[home page] [publications]