  There is often a trade-off between building deep learning systems that are
expressive enough to capture the nuances of the reality, and having the right
inductive biases for efficient learning. We introduce Residual Pathway Priors
(RPPs) as a method for converting hard architectural constraints into soft
priors, guiding models towards structured solutions, while retaining the
ability to capture additional complexity. Using RPPs, we construct neural
network priors with inductive biases for equivariances, but without limiting
flexibility. We show that RPPs are resilient to approximate or misspecified
symmetries, and are as effective as fully constrained models even when
symmetries are exact. We showcase the broad applicability of RPPs with
dynamical systems, tabular data, and reinforcement learning. In Mujoco
locomotion tasks, where contact forces and directional rewards violate strict
equivariance assumptions, the RPP outperforms baseline model-free RL agents,
and also improves the learned transition models for model-based RL.
