A Connection Between GRBF and MLP

Both multilayer perceptrons (MLP) and Generalized Radial Basis Functions (GRBF) have good approximation properties, theoretically and experimentally. Are they related? The main point of this paper is to show that for normalized inputs, multilayer perceptron networks are radial function networks (albeit with a non-standard radial function). This provides an interpretation of the weights w as centers t of the radial function network, and therefore as equivalent to templates. This insight may be useful for practical applications, including better initialization procedures for MLP. In the remainder of the paper, we discuss the relation between the radial functions that correspond to the sigmoid for normalized inputs and well-behaved radial basis functions, such as the Gaussian. In particular, we observe that the radial function associated with the sigmoid is an activation function that is good approximation to Gaussian basis functions for a range of values of the bias parameter. The implication is that a MLP network can always simulate a Gaussian GRBF network (with the same number of units but less parameters); the converse is true only for certain values of the bias parameter. Numerical experiments indicate that this constraint is not always satisfied in practice by MLP networks trained with backpropagation. Multiscale GRBF networks, on the other hand, can approximate MLP networks with a similar number of parameters.

Intelligence Without Reason

Computers and Thought are the two categories that together define Artificial Intelligence as a discipline. It is generally accepted that work in Artificial Intelligence over the last thirty years has had a strong influence on aspects of computer architectures. In this paper we also make the converse claim; that the state of computer architecture has been a strong influence on our models of thought. The Von Neumann model of computation has lead Artificial Intelligence in particular directions. Intelligence in biological systems is completely different. Recent work in behavior-based Artificial Intelligenge has produced new models of intelligence that are much closer in spirit to biological systems. The non-Von Neumann computational models they use share many characteristics with biological computation.