Learning Symmetric Rules with SA TNet

SA TNet is a differentiable constraint solver with a custom backpropagation algorithm, which can be used as a layer in a deep-learning system. It is a promising proposal for bridging deep learning and logical reasoning. In fact, SA TNet has been successfully applied to learn, among others, the rules of a complex logical puzzle, such as Sudoku, just from input and output pairs where inputs are given as images. In this paper, we show how to improve the learning of SA TNet by exploiting symmetries in the target rules of a given but unknown logical puzzle or more generally a logical formula. We present SymSA TNet, a variant of SA T - Net that translates the given symmetries of the target rules to a condition on the parameters of SA TNet and requires that the parameters should have a particular parametric form that guarantees the condition. The requirement dramatically reduces the number of parameters to learn for the rules with enough symmetries, and makes the parameter learning of SymSA TNet much easier than that of SA TNet.