The University of Sussex

Bayesian regularisation and pruning using a Laplace prior

Peter M. Williams

Standard techniques for improved generalisation from neural networks include weight decay and pruning. Weight decay has a Bayesian interpretation with the decay function corresponding to a prior over weights. The method of transformation groups and maximum entropy indicates a Laplace rather than a Gaussian prior. After training, the weights then arrange themselves into two classes: (1) those with a common sensitivity to the data error (2) those failing to achieve this sensitivity and which therefore vanish. Since the critical value is determined adaptively during training, pruning - in the sense of setting weights to exact zeros - becomes a consequence of regularisation alone. The count of free parameters is also reduced automatically as weights are pruned. A comparison is made with results of MacKay using the evidence framework and a Gaussian regulariser.


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