程序合成的分治-对齐-征服策略
A Divide-Align-Conquer Strategy for Program Synthesis
AI总结：
针对搜索型程序合成中搜索空间指数增长的问题，提出基于结构映射理论的结构对齐与分解驱动方法，在字符串转换及ARC视觉推理任务上超越ILP基线且预测精度随示例单调增加。
摘要：
基于搜索的程序合成中的一个主要瓶颈是指数级增长的搜索空间，这使得学习大型程序变得难以处理。人类通过利用现实世界的组合性质来缓解这个问题：在结构化领域中，一个逻辑规范通常可以分解为更小的、互补的解决方案程序。我们表明，在示例编程设置中可以应用组合分割，将大型程序的搜索划分为多个较小的程序合成问题。对于每个示例，我们搜索一种将其分解为更小单元的方法，以最大化潜在任务程序下输出的重构精度。输入和输出中各组成部分的结构对齐产生了用于指导程序合成搜索的成对对应关系。为了对齐输入/输出结构，我们使用了结构映射理论（Structure-Mapping Theory, SMT），这是一种源自认知科学的人类类比推理形式模型。我们表明，具有结构对齐的分解驱动程序合成在字符串转换任务上优于归纳逻辑编程（Inductive Logic Programming, ILP）基线，即使只有最少的先验知识也是如此。与现有方法不同，我们的智能体的预测精度随着额外示例的增加而单调增加，并在字符串等高度结构化域中，对于 $m$ 个部分程序实现了平均 $\mathcal{O}(m)$ 的时间复杂度。我们将此方法扩展到 Abstraction and Reasoning Corpus (ARC) 视觉推理的复杂环境中，而在此环境中 ILP 方法以前是不可行的。
英文摘要：
A major bottleneck in search-based program synthesis is the exponentially growing search space which makes learning large programs intractable. Humans mitigate this problem by leveraging the compositional nature of the real world: In structured domains, a logical specification can often be decomposed into smaller, complementary solution programs. We show that compositional segmentation can be applied in the programming by examples setting to divide the search for large programs across multiple smaller program synthesis problems. For each example, we search for a decomposition into smaller units which maximizes the reconstruction accuracy in the output under a latent task program. A structural alignment of the constituent parts in the input and output leads to pairwise correspondences used to guide the program synthesis search. In order to align the input/output structures, we make use of the Structure-Mapping Theory (SMT), a formal model of human analogical reasoning which originated in the cognitive sciences. We show that decomposition-driven program synthesis with structural alignment outperforms Inductive Logic Programming (ILP) baselines on string transformation tasks even with minimal knowledge priors. Unlike existing methods, the predictive accuracy of our agent monotonically increases for additional examples and achieves an average time complexity of $\mathcal{O}(m)$ in the number $m$ of partial programs for highly structured domains such as strings. We extend this method to the complex setting of visual reasoning in the Abstraction and Reasoning Corpus (ARC) for which ILP methods were previously infeasible.
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。
