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.

Switching Between Discrete and Continuous Process Models to Predict Molecular Genetic Activity

Two kinds of process models have been used in programs that reason about change: Discrete and continuous models. We describe the design and implementation of a qualitative simulator, PEPTIDE, which uses both kinds of process models to predict the behavior of molecular energetic systems. The program uses a discrete process model to simulate both situations involving abrupt changes in quantities and the actions of small numbers of molecules. It uses a continuous process model to predict gradual changes in quantities. A novel technique, called aggregation, allows the simulator to switch between theses models through the recognition and summary of cycles. The flexibility of PEPTIDE's aggregator allows the program to detect cycles within cycles and predict the behavior of complex situations.