  Neuro-Symbolic (NeSy) integration combines symbolic reasoning with Neural
Networks (NNs) for tasks requiring perception and reasoning. Most NeSy systems
rely on continuous relaxation of logical knowledge, and no discrete decisions
are made within the model pipeline. Furthermore, these methods assume that the
symbolic rules are given. In this paper, we propose Deep Symbolic Learning
(DSL), a NeSy system that learns NeSy-functions, i.e., the composition of a
(set of) perception functions which map continuous data to discrete symbols,
and a symbolic function over the set of symbols. DSL learns simultaneously the
perception and symbolic functions while being trained only on their composition
(NeSy-function). The key novelty of DSL is that it can create internal
(interpretable) symbolic representations and map them to perception inputs
within a differentiable NN learning pipeline. The created symbols are
automatically selected to generate symbolic functions that best explain the
data. We provide experimental analysis to substantiate the efficacy of DSL in
simultaneously learning perception and symbolic functions.
