Constraint satisfaction problems (CSPs) are about finding values of variables that satisfy the given constraints. We show that Transformer extended with recurrence is a viable approach to learning to solve CSPs in an end-to-end manner, having clear advantages over state-of-the-art methods such as Graph Neural Networks, SATNet, and some neuro-symbolic models. With the ability of Transformer to handle visual input, the proposed Recurrent Transformer can straightforwardly be applied to visual constraint reasoning problems while successfully addressing the symbol grounding problem. We also show how to leverage deductive knowledge of discrete constraints in the Transformer's inductive learning to achieve sample-efficient learning and semi-supervised learning for CSPs.

翻译：约束满足问题（CSP）涉及找到满足给定约束的变量取值。研究表明，通过扩展递归机制的Transformer是一种可行的以端到端方式学习求解CSP的方法，相较于图神经网络、SATNet及某些神经符号模型等当前最优方法具有显著优势。凭借Transformer处理视觉输入的能力，所提出的递归Transformer可直接应用于视觉约束推理问题，同时成功解决符号接地问题。我们还展示了如何利用离散约束的演绎知识来增强Transformer的归纳学习，从而实现CSP的样本高效学习与半监督学习。