Functional Rule Extraction Method for Artificial Neural Networks
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The idea I propose in this paper is a method that is based on comprehensive functions for directed and undirected rule extraction from artificial neural network operations. Firstly, I defined comprehensive functions, then constructed a comprehensive multilayer network (denoted as 𝛮). Each activation function of 𝛮 is parametrized to a comprehensive function. Following 𝛮 construction, I extracted rules from the network by observing that the network output depends on probabilities of composite functions that are comprehensive functions. This functional rule extraction method applies to the perceptron and multilayer neural network. For any 𝛮 model that is trained to predict some outcome given some event, that model behaviour can be expressed – using the functional rule extraction method – as a formal rule or informal rule obeyed by the network to predict that outcome. As example, figure 1 consist of a comprehensive physics function that is parameter for one of the network hidden activation functions. Using the functional rule extraction method, I deduced that the comprehensive multilayer network prediction depends on probability of that physics function and probabilities of other composite comprehensive functions in 𝛮. Additionally, functional rule extraction method can aid in applied settings for generation of equations of learned phenomena. This generation can be achieved by first training an 𝛮 model toward predicting outcome of a phenomenon, then extracting the rules and assuming that probability values of the network comprehensive functions are constants. Finally, to simplify the generated equation, comprehensive functions with probability 𝑝 = 0 can be omitted.
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