TR00-055 Authors: Peter Auer, Stephen Kwek, Manfred K. Warmuth

Publication: 14th July 2000 17:56

Downloads: 2045

Keywords:

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 algorithms 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.