Understanding deep neural networks from the perspective of piecewise linear property

In recent years, deep learning models have been widely used and are behind major breakthroughs across many fields. Deep learning models are usually considered to be black boxes due to their large model structures and complicated hierarchical nonlinear transformations. As deep learning technology continues to develop, the understanding of deep learning models is raising concerns, such as the understanding of the training and prediction behaviors and the internal mechanism of models. In this thesis, we study the model understanding problem of deep neural networks from the perspective of piecewise linear property. First, we introduce the piecewise linear property. Next, we review the role and progress of deep learning understanding from the perspective of the piecewise linear property. The piecewise linear property reveals that deep neural networks with piecewise linear activation functions can generally divide the input space into a number of small disjointed regions that correspond to a local linear function within each region. Next, we investigate two typical understanding problems, namely model interpretation, and model complexity. In particular, we provide a series of derivations and analyses of the piecewise linear property of deep neural networks with piecewise linear activation functions. We propose an approach for interpreting the predictions given by such models based on the piecewise linear property. Next, we propose a method to provide local interpretation to a black box deep model by mimicking a piecewise linear approximation from the deep model. Then, we study deep neural networks with curve activation functions with the aim of providing piecewise linear approximations for these networks that would let them benefit from the piecewise linear property. After proposing a piecewise linear approximation framework, we investigate model complexity and model interpretation using the approximation. The thesis concludes by discussing future directions for understanding deep neural networks from the perspective of the piecewise linear property.