Neural networks are a key tool used in machine learning. While neural networks conventionally use continuous activation functions, in this paper we explore the use of discrete activation functions, namely polymorphisms. We define a neighbor function that we use to update the activation functions while training. We also define dominion polymorphisms, which come from a combinatorial object analogous to a graph coloring, and create a dominion activation function which makes the neural network more powerful. We implement and test a neural network with these features and discuss the results.