Learning of depth two neural nets with constant fan-in at the hidden nodes

P. Auer, S. Kwek, W. Maass, and M. K. Warmuth

Abstract:

We present algorithms for learning depth two neural networks where the hidden nodes are threshold gates with constant fan-in. The transfer function of the output node might be more general: we have results for the cases when the threshold function, the logistic function or the identity function is used as the transfer function at the output node. We give batch and on-line learning algorithms for these classes of neural networks and prove bounds on the performance of our algorithms. The batch algoritms work for real valued inputs whereas the on-line algorithms assume that the inputs are discretized. The hypotheses of our algorithms are essentially also neural networks of depth two. However, their number of hidden nodes might be much larger than the number of hidden nodes of the neural network that has to be learned. Our algorithms can handle such a large number of hidden nodes since they rely on multiplicative weight updates at the output node, and the performance of these algorithms scales only logarithmically with the number of hidden nodes used.

Reference: P. Auer, S. Kwek, W. Maass, and M. K. Warmuth. Learning of depth two neural nets with constant fan-in at the hidden nodes. In Proc. of the 9th Conference on Computational Learning Theory 1996, pages 333-343. ACM-Press (New York), 1996.