  Compositional generalization is one of the main properties which
differentiates lexical learning in humans from state-of-art neural networks. We
propose a general framework for building models that can generalize
compositionally using the concept of Generalized Grammar Rules (GGRs), a class
of symmetry-based compositional constraints for transduction tasks, which we
view as a transduction analogue of equivariance constraints in physics-inspired
tasks. Besides formalizing generalized notions of symmetry for language
transduction, our framework is general enough to contain many existing works as
special cases. We present ideas on how GGRs might be implemented, and in the
process draw connections to reinforcement learning and other areas of research.
