  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.
