My PhD student Erwei Wang, various collaborators and I have recently published a detailed survey article on this topic: Deep Neural Network Approximation for Custom Hardware: Where We've Been, Where We're Going, to appear in ACM CSUR. In this post, I will informally explain my personal view of the role of approximation in supervised learning (classification), and how this links to the very active topic of DNN accelerator design in hardware. We can think of a DNN as a graph, where nodes perform computations and edges carry data. This graph can be interpreted (executed) as a function mapping input data to output data. The quality of this DNN is typically judged by a loss function .