Presenter:     Dr. Christopher Cornwell, Department of Mathematics, Towson University

Abstract:      Associated to the parameters of a neural network with a ReLU activation function is a number called the functional dimension.  Roughly speaking, the functional dimension measures the number of degrees of freedom for determining a new network function by perturbing the parameters, as is done during network training.  For a choice of network and parameters, a tight upper bound on the functional dimension is known – one that is strictly less than the number of parameters; conditions under which the functional dimension is strictly less than that upper bound have been explored, and it is an active area of research.  In this talk, after an introduction to the ideas above, I will discuss contributions of me and collaborators to this area.  Several recent works by others have focused on the existence of a positive measure subset of parameters that achieve the upper bound.  Our work explores the probability of getting initial parameters that fail to achieve the upper bound, using standard assumptions on initial parameters as random variables.