Demonstrating a new evaluation method on ReLU based Neural Networks for classification problems

Abstract

Deep neural networks, which have proven to be effective methods to solve complex problems, can even be applied in decision systems controlling critical processes. However, in such applications the outcomes of the neural network must be checked if it we have a clear understanding regarding the operation of network at given input intervals. The most straightforward, though often computationally expensive approach for this checking process evaluates the network at discrete input points and estimates the expected outputs at the given interval. The present research aims to develop a novel approach that can identify in the case of specific input intervals whether the operation process and the output of a neural network can be considered as known or unknown. During the presented case study, we investigated the ReLU (Rectified Linear Unit) and Sigmoid activation functions, using the double moon and the Banknote Authentication classification problems for demonstration.Our method can be applied to identify certain input intervals where the given neural network cannot support critical decisions. The evaluation is performed based on a nonlinear system of equations and inequalities built on arbitrary continuous activation functions. To define the critical intervals of the input variables (i.e. where the decision-making system should not be relied on), those input variable combinations are identified which result in a non-expected output value. This inverse logic is intended to identify intervals of the input variables where the response of the system and the correct decision are not identical. The presented demonstration examples supported our assumption that the number of the neurons and the dimension of the decision space have a significant impact on the complexity of the evaluation process.