论文标题
引理：用学习的符号抽象来引导高级数学推理
LEMMA: Bootstrapping High-Level Mathematical Reasoning with Learned Symbolic Abstractions
论文作者
论文摘要
人类通过发展抽象的层次结构来驯服数学推理的复杂性。有了适当的抽象，可以简单地表达解决严重问题的解决方案，从而使它们更有可能被发现。在本文中，我们提出了学习数学抽象（引理）：一种算法，该算法在数学领域中实现了这一想法。引理以抽象步骤增强专家迭代，在此迄今为止发现的解决方案是根据新的高级行动重新审视和重写的，然后可以解决新问题。我们以逐步的方式评估了两项数学推理任务 - 方程式解决和分数的简化。在这两个领域中，Lemma提高了现有代理的能力，既可以解决更多问题，又比在训练过程中更有效地将其推广到更困难的问题。
Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. In this paper, we propose Learning Mathematical Abstractions (LEMMA): an algorithm that implements this idea for reinforcement learning agents in mathematical domains. LEMMA augments Expert Iteration with an abstraction step, where solutions found so far are revisited and rewritten in terms of new higher-level actions, which then become available to solve new problems. We evaluate LEMMA on two mathematical reasoning tasks--equation solving and fraction simplification--in a step-by-step fashion. In these two domains, LEMMA improves the ability of an existing agent, both solving more problems and generalizing more effectively to harder problems than those seen during training.
