学习满足逻辑约束的人工神经网络
Artificial Neural Networks that Learn to Satisfy Logic Constraints
摘要：
基于逻辑的问题，如规划、定理证明或谜题，通常涉及组合搜索和结构化知识表示。人工神经网络是非常成功的统计学习器，然而，多年来，它们在表示和处理复杂结构知识方面的弱点一直受到批评，而复杂结构知识对于组合搜索和符号操作至关重要。提出了两种神经网络结构，在神经网络的激活过程中对结构化的关系知识进行编码，在连接权值中存储有界一阶逻辑约束。两种架构都学习搜索满足约束的解决方案。学习是通过对来自同一领域的问题实例进行无监督练习来完成的，以提高网络解决速度的方式。不存在为训练集和测试集的问题实例提供答案的教师。然而，域约束作为先验知识提供给测量约束违反程度的损失函数。执行激活计算和学习的迭代，直到在输出单元上出现最大限度地满足约束的解。作为测试案例，块世界规划问题用于训练学习在该域中规划的网络，但是所提出的技术可以更普遍地用于将先验符号知识与统计学习相结合
英文摘要：
Logic-based problems such as planning, theorem proving, or puzzles, typically involve combinatoric search and structured knowledge representation. Artificial neural networks are very successful statistical learners, however, for many years, they have been criticized for their weaknesses in representing and in processing complex structured knowledge which is crucial for combinatoric search and symbol manipulation. Two neural architectures are presented, which can encode structured relational knowledge in neural activation, and store bounded First Order Logic constraints in connection weights. Both architectures learn to search for a solution that satisfies the constraints. Learning is done by unsupervised practicing on problem instances from the same domain, in a way that improves the network-solving speed. No teacher exists to provide answers for the problem instances of the training and test sets. However, the domain constraints are provided as prior knowledge to a loss function that measures the degree of constraint violations. Iterations of activation calculation and learning are executed until a solution that maximally satisfies the constraints emerges on the output units. As a test case, block-world planning problems are used to train networks that learn to plan in that domain, but the techniques proposed could be used more generally as in integrating prior symbolic knowledge with statistical learning
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
