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.
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