Neuro-symbolic methods integrate neural architectures, knowledge representation and reasoning. However, they have been struggling at both dealing with the intrinsic uncertainty of the observations and scaling to real-world applications. This paper presents Relational Reasoning Networks (R2N), a novel end-to-end model that performs relational reasoning in the latent space of a deep learner architecture, where the representations of constants, ground atoms and their manipulations are learned in an integrated fashion. Unlike flat architectures like Knowledge Graph Embedders, which can only represent relations between entities, R2Ns define an additional computational structure, accounting for higher-level relations among the ground atoms. The considered relations can be explicitly known, like the ones defined by logic formulas, or defined as unconstrained correlations among groups of ground atoms. R2Ns can be applied to purely symbolic tasks or as a neuro-symbolic platform to integrate learning and reasoning in heterogeneous problems with both symbolic and feature-based represented entities. The proposed model overtakes the limitations of previous neuro-symbolic methods that have been either limited in terms of scalability or expressivity. The proposed methodology is shown to achieve state-of-the-art results in different experimental settings.

翻译：神经符号方法整合了神经架构、知识表示与推理。然而，它们在处理观测数据的内在不确定性以及扩展到实际应用方面一直面临挑战。本文提出关系推理网络（R2N），一种新颖的端到端模型，该模型在深度学习架构的潜在空间中进行关系推理，其中常量、基原子及其操作的表示以集成方式学习。与知识图谱嵌入器等扁平架构（仅能表示实体间关系）不同，R2N定义了一个额外的计算结构，用以解释基原子间的高层关系。所考虑的关系可以是显式已知的（如逻辑公式定义的关系），也可以定义为基原子群之间的无约束关联。R2N可应用于纯符号任务，或作为神经符号平台，在兼具符号和特征表示实体的异构问题中集成学习与推理。该模型克服了先前神经符号方法在可扩展性或表达性方面的局限。实验表明，所提方法在不同设置下均取得了最先进的结果。