Bounding vc-dimension for neural networks: Progress and prospects

Abstract

Techniques from differential topology are used to give polynomial bounds for the VC-dimension of sigmoidal neural networks. The bounds are quadratic in ω, the dimension of the space of weights. Similar results are obtained for a wide class of Pfaffian activation functions. The obstruction (in differential topology) to improving the bound to an optimal bound O(ωlogω) is discussed, and attention is paid to the role of other parameters involved in the network architecture.