“…Works in this direction include [45,46,11,47,52,32,36] and earlier works for Boolean circuits and sum-product networks [20,21,10]. The number of linear regions of the functions represented by networks with piecewise linear activations has sparked substantial interest in the study of neural networks, with works including [34,47,33,5,40,23]. Recent works have explored approaches based on tropical geometry [55,9,3] and power diagram subdivisions [6], while others have studied the expectated number of linear regions for typical choices of the parameters in the case of ReLU networks [18,19], empirical enumeration [39], and the relations between linear regions and the behavior of algorithms that are used to select the parameters of neural networks based on data, such as speed of convergence and implicit biases of gradient descent [44,56,26].…”