Title: Neural networks interpretability through Taylor series and polynomial regression coefficients
Authors: Pablo Morala - Universidad Carlos III de Madrid (Spain) [presenting]
Rosa Lillo - Universidad Carlos III de Madrid (Spain)
Jenny Alexandra Cifuentes - Universidad Pontificia Comillas (Spain)
Inaki Ucar - uc3m-Santander Big Data Institute (Spain)
Abstract: Despite being used widely, neural networks are still regarded as black boxes and are used and built through trial and error. A new approach to these problems is proposed here, by finding a relationship between a trained neural network and its weights and the coefficients of a polynomial regression that performs almost equivalently as the original neural network. To do so, Taylor expansion is used at the activation functions of each neuron. Then the resulting expressions are joint in order to obtain a combination of the original network weights that are associated with each term of a polynomial regression. The order of this polynomial regression is determined by the order used in the Taylor expansion and the number of layers in the neural network. The proposal has been empirically tested covering a wide range of different situations, showing its effectiveness and opening the door to extending this methodology. This kind of relationship between modern machine learning techniques and more traditional statistical approaches can help solve interpretability concerns. In this case, polynomial regression coefficients have a much easier interpretation than neural network weights and reduce significantly the number of parameters.