  Neuro-Symbolic (NeSy) predictive models hold the promise of improved
compliance with given constraints, systematic generalization, and
interpretability, as they allow to infer labels that are consistent with some
prior knowledge by reasoning over high-level concepts extracted from
sub-symbolic inputs. It was recently shown that NeSy predictors are affected by
reasoning shortcuts: they can attain high accuracy but by leveraging concepts
with unintended semantics, thus coming short of their promised advantages. Yet,
a systematic characterization of reasoning shortcuts and of potential
mitigation strategies is missing. This work fills this gap by characterizing
them as unintended optima of the learning objective and identifying four key
conditions behind their occurrence. Based on this, we derive several natural
mitigation strategies, and analyze their efficacy both theoretically and
empirically. Our analysis shows reasoning shortcuts are difficult to deal with,
casting doubts on the trustworthiness and interpretability of existing NeSy
solutions.
