Finding a succinct multi-layer perceptron having shared weights

We present a method to find a succinct neural network having shared weights. We focus on weight sharing. Weight sharing constrains the freedom of weight values and weights are allowed to have one of common weights. A near-zero common weight can be eliminated, called weight pruning. Recently, a weight sharing method called BCW has been proposed. The BCW employs merge and split operations based on 2nd-order optimal criteria, and can escape local optima through bidirectional clustering. However, the BCW assumes a vital network parameter J, the number of hidden units, is given. This paper modifies the BCW to make the procedure faster so that the selection of J based on cross-validation can be done in reasonable cpu time. Our experiments showed that the proposed method can restore the original model for an artificial data set, and finds a small number of common weights and an interesting tendency for a real data set.