神经关系程序：统一结构化数据上的查询与神经计算
Neuro-Relational Programs: Unifying Queries and Neural Computation over Structured Data
AI总结：
提出神经关系程序（NRP），一种扩展Datalog规则的声明式查询语言，通过嵌入操作融合关系推理与可学习神经组件，实现关系数据上的通用神经计算。
摘要：
在关系数据库上进行深度学习的传统方法是将图神经网络（GNN）等神经模型应用于数据库的图表示。最近的方法则直接操作数据库，将元组与嵌入关联，并扩展查询机制以联合处理嵌入和关系内容。受这些发展的启发，我们引入了神经关系程序（NRP），这是一种针对关系数据库的声明式查询语言，其事实携带数值向量嵌入。NRP扩展了Datalog风格的规则，增加了组合、聚合和转换嵌入的操作，从而在单一形式主义中交错关系推理和可学习神经组件。这产生了一种对关系数据进行神经计算的通用方法：NRP既可以看作带有可训练组件的查询计划，也可以看作内置关系结构的神经架构。NRP的自然语法片段恢复了现有架构和查询形式主义。零元NRP对应于非自适应查询算法；一元NRP推广了GNN风格的消息传递，并精确捕捉了深度同态网络，我们将这一联系扩展到带有行ID的数据库上的前沿保护NRP。我们通过FOCQ（一阶逻辑在实权重结构上的计数扩展）刻画了带有ReLU-FFN变换的无限制NRP的表达能力，从而建立了与有序数据库上的均匀TC$^0$的精确联系。这些结果共同确立了NRP作为关系数据上查询和神经计算的广泛声明式框架。
英文摘要：
The conventional approach to deep learning over relational databases applies neural models, such as Graph Neural Networks (GNNs), to a graph representation of the database. Recent approaches instead operate on databases directly, associating tuples with embeddings and extending query mechanisms to jointly process embeddings and relational content. Inspired by these developments, we introduce Neuro-Relational Programs (NRPs), a declarative query language for relational databases whose facts carry numeric vector embeddings. NRPs extend Datalog-style rules with operations that combine, aggregate, and transform embeddings, thereby interleaving relational reasoning and learnable neural components within a single formalism. This yields a general approach to neural computation over relational data: an NRP can be read both as a query plan with trainable components and as a neural architecture with relational structure built in. Natural syntactic fragments of NRPs recover existing architectures and query formalisms. Zero-ary NRPs correspond to non-adaptive query algorithms; monadic NRPs generalize GNN-style message passing and precisely capture Deep Homomorphism Networks, a connection that we extend to frontier-guarded NRPs over databases with row-ids. We characterize the expressive power of unrestricted NRPs with ReLU-FFN transformations by FOCQ, an extension of first-order logic with counting interpreted over real-weighted structures, yielding a precise connection with uniform TC$^0$ over ordered databases. Together, these results establish NRPs as a broad declarative framework for querying and neural computation over relational data.
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