Asymmetry Tunneling Beyond Adaptive Equivariance Relaxation

Overview & Synopsis

Equivariant neural networks encode prescribed symmetries as powerful inductive biases, yet real-world data may exhibit symmetry-breaking structure that these priors cannot fully capture. Prior work has largely addressed this challenge through model-side equivariance relaxation, seeking an appropriate level of equivariance for the data. This raises a complementary question: must equivariance relaxation be adaptively controlled? To investigate this question, we introduce a residual path alongside a strictly equivariant model and deliberately restrict their interface to examine the transmission of task-relevant structure. Across five benchmarks, we observe both residual collapse and survival despite these restrictions; we call the latter phenomenon asymmetry tunneling. We further characterize this phenomenon through four complementary diagnostics. Our results suggest that adaptive control of equivariance relaxation is not a prerequisite for capturing potential symmetry-breaking structure.