arXiv:2605.22852v1 Announce Type: cross 
Abstract: The expressive limitations of message-passing Graph Neural Networks (GNNs) have motivated a wide range of more powerful graph learning architectures. We advocate Deep Homomorphism Networks (DHNs) as a model particularly well-suited for learning over relational databases, due to their close connection to important fragments of SQL such as conjunctive queries. We study the precise expressive power of DHNs by relating them to various natural fragments and extensions of first-order logic (FO). For DHNs with max, sum, and mean aggregations, we establish connections to the unary negation fragment (UNFO) and to the extensions of UNFO with counting quantifiers and with ratio quantifiers. We further relate sum-aggregation DHNs to the unary quantifier alternation fragment of FO and to an extension of FO with expressive counting. Through the classical correspondence between FO and SQL, these results also illuminate the relation between DHNs and SQL. They also enable us to study the decidability of two fundamental static analysis problems for DHNs, the emptiness problem and the subsumption problem. Finally, we confirm through experiments that the established differences in expressive power are reflected in the performance on suitable prediction tasks.

أظهرت الأبحاث الحديثة القوة التعبيرية لشبكات التحويل العميق (DHNs) على قواعد البيانات العلائقية، موضحةً قدرتها على التعلم بفعالية من خلال الروابط مع أجزاء من SQL ومنطق الدرجة الأولى. تؤسس هذه الدراسة القدرات التعبيرية لـ DHNs، خاصةً مع التجميعات القصوى والمجموع والمتوسط، وأهميتها بالنسبة للنفي الأحادي وكمية العد.

Investigaciones recientes han destacado el poder expresivo de las Redes de Homomorfismo Profundo (DHNs) sobre bases de datos relacionales, mostrando su potencial para aprender de manera efectiva a través de conexiones con fragmentos de SQL y lógica de primer orden. Este estudio establece las capacidades expresivas de las DHNs, particularmente con agregaciones de max, sum y mean, y su relevancia para la negación unaria y los cuantificadores de conteo.

Des recherches récentes ont mis en évidence le pouvoir expressif des Réseaux d'Homomorphisme Profond (DHNs) sur les bases de données relationnelles, montrant leur potentiel d'apprentissage efficace grâce à des connexions avec des fragments de SQL et la logique du premier ordre. Cette étude établit les capacités expressives des DHNs, en particulier avec des agrégations max, sum et mean, et leur pertinence pour la négation unaire et les quantificateurs de comptage.

Recent research has highlighted the expressive power of Deep Homomorphism Networks (DHNs) over relational databases, showcasing their potential to learn effectively through connections to SQL fragments and first-order logic. This study establishes DHNs' expressive capabilities, particularly with max, sum, and mean aggregations, and their relevance to unary negation and counting quantifiers.