使用描述复杂性和SMT求解器保证的机器学习
Machine Learning with Guarantees using Descriptive Complexity and SMT Solvers
摘要：
机器学习是计算机科学的一个蓬勃发展的部分。有许多有效的机器学习方法并没有提供强有力的理论保证，以及一个漂亮的通用学习理论。不幸的是，提供强有力的理论保证的机器学习方法还不够有效，无法应用。在本文中，我们介绍了一种逻辑方法来机器学习。模型由逻辑公式的元组表示，输入和输出都是逻辑结构。我们提出了我们的框架与几个应用程序，我们使用SAT和SMT求解器进行评估。我们认为这种机器学习方法特别适合于弥合效率和理论合理性之间的差距。我们利用描述性复杂性理论的结果来证明我们的方法的强有力的理论保证。为了证明其适用性，我们提出了实验结果，包括学习棋盘游戏的复杂性理论的减少规则。我们还解释了神经网络如何适应我们的框架，尽管目前的实现不能扩展到为现实世界的神经网络提供保证。
英文摘要：
Machine learning is a thriving part of computer science. There are many efficient approaches to machine learning that do not provide strong theoretical guarantees, and a beautiful general learning theory. Unfortunately, machine learning approaches that give strong theoretical guarantees have not been efficient enough to be applicable. In this paper we introduce a logical approach to machine learning. Models are represented by tuples of logical formulas and inputs and outputs are logical structures. We present our framework together with several applications where we evaluate it using SAT and SMT solvers. We argue that this approach to machine learning is particularly suited to bridge the gap between efficiency and theoretical soundness. We exploit results from descriptive complexity theory to prove strong theoretical guarantees for our approach. To show its applicability, we present experimental results including learning complexity-theoretic reductions rules for board games. We also explain how neural networks fit into our framework, although the current implementation does not scale to provide guarantees for real-world neural networks.
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。
