Modern ML is primarily data-driven, with scale often outperforming specially engineered architectures. In the physical sciences, however, theoretical principles such as symmetries can provide inductive biases that improve the robustness and data efficiency of ML models. While symmetries are ubiquitous in particle physics, fully symmetric models can be difficult to train and implement. Moreover, real-world experiments often exhibit broken symmetries due to imperfections and finite detector resolution. We introduce a method for building symmetry-aware ML models through soft constraints. We investigate two complementary approaches: one that encourages invariance to sampled group transformations, and one that encourages invariance to infinitesimal symmetry actions. We apply these ideas to Lorentz invariance, and find that incorporating soft constraints can improve the invariance and the performance of state-of-the-art models without changing their architecture.