论文标题
与卫星学习对称规则
Learning Symmetric Rules with SATNet
论文作者
论文摘要
卫星是具有自定义反向传播算法的可区分约束求解器，可以用作深度学习系统中的层。这是弥合深度学习和逻辑推理的有前途的建议。实际上，卫星已成功地用于学习复杂的逻辑难题的规则，例如sudoku，仅来自输入和输出对，其中输入以图像为图像。在本文中，我们通过在给定但未知的逻辑难题的目标规则中利用对称性或更通常是逻辑公式来展示如何改善卫星的学习。我们提出Symsatnet，这是卫星的一种变体，将目标规则的给定对称性转换为卫星参数的条件，并要求参数应具有保证条件的特定参数形式。需求大大减少了用足够的对称性学习规则的参数数量，并使Symsatnet的参数学习比卫星更容易。我们还描述了一种从示例中自动发现目标规则对称的技术。我们对Sudoku和Rubik的立方体进行的实验表明，在基线卫星上，Symsatnet的大幅改进。
SATNet 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, SATNet 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 SATNet by exploiting symmetries in the target rules of a given but unknown logical puzzle or more generally a logical formula. We present SymSATNet, a variant of SATNet that translates the given symmetries of the target rules to a condition on the parameters of SATNet 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 SymSATNet much easier than that of SATNet. We also describe a technique for automatically discovering symmetries of the target rules from examples. Our experiments with Sudoku and Rubik's cube show the substantial improvement of SymSATNet over the baseline SATNet.
