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Computation of Madalines' Sensitivity to Input and Weight Perturbations

ywang802{at}vip.sina.com Department of Computer Science, Hohai University, Nanjing, China

Xiaoqin Zeng

xzeng{at}hhu.edu.cn Department of Computer Science, Hohai University, Nanjing, China

Daniel So Yeung

csdaniel{at}comp.polyu.edu.hk Department of Computing, Hong Kong Polytechnic University, Kowloon, Hong Kong

Zhihang Peng

zhihangpeng{at}hotmail.com Department of Mathematics, Hohai University, Nanjing, China

The sensitivity of a neural network's output to its input and weight perturbations is an important measure for evaluating the network's performance. In this letter, we propose an approach to quantify the sensitivity of Madalines. The sensitivity is defined as the probability of output deviation due to input and weight perturbations with respect to overall input patterns. Based on the structural characteristics of Madalines, a bottom-up strategy is followed, along which the sensitivity of single neurons, that is, Adalines, is considered first and then the sensitivity of the entire Madaline network. By means of probability theory, an analytical formula is derived for the calculation of Adalines' sensitivity, and an algorithm is designed for the computation of Madalines' sensitivity. Computer simulations are run to verify the effectiveness of the formula and algorithm. The simulation results are in good agreement with the theoretical results.