Properties and Training Algorithm for RBF Networks with Concurrent Weight and Node Failure

Abstract

There exists many fault tolerant algorithms for neural networks. However, they usually only focus on one kind of weight failure or node failure. In reality, a faulty network may have different kinds of network failure concurrently. The project first studies four kinds of network failure. They are open weight fault, open node fault, weight noise, and node noise. After that, there will be a unified fault model for the concurrent fault situation, where open weight fault, open node fault, weight noise, and node noise could happen in a single network. Afterwards, I study the effect of the concurrent fault situation for radial basis function (RBF) neural networks. Moreover, I derive the training set performance when the concurrent faults happen. Next, I define the objective function for training fault tolerant networks as well as identifying a smoothing term, known as the regularization term, from the objective function. Additionally, I then develop a learning algorithm for faulty RBF networks based on the objective function. It will be shown that my approach gets a better fault tolerant ability comparing to the conventional approach. Lastly, I will sum up by developing a formula, named mean prediction error (MPE). This formula can gauge the generalization ability of faulty RBF neural networks based on the training set only. The MPE formula helps us to optimize some parameters in the RBF approach. For example, we can use it to select the RBF width. To be specific, I will verify the effectiveness of my algorithm by showing some simulations.