SEAL - A Symmetry Encouraging Loss for High Energy Physics

Physical symmetries provide a powerful inductive bias for machine learning models in science, improving robustness, data efficiency, and interpretability. However, building models that explicitly enforce symmetries requires specialized architectures, and real-world experiments often break these symmetries through finite detector granularity and energy thresholds. We introduce SEAL (Symmetry Encouraging Loss), a family of soft-constraint loss terms that encourage equivariance, requiring no architectural modifications. We present two complementary variants: GSEAL, which penalizes output differences under random group transformations of the input, and $\delta$SEAL, which penalizes the model's gradients along directions corresponding to infinitesimal symmetry transformations. We focus on Lorentz invariance, which is highly relevant to High Energy Physics and rarely encountered in other domains, but the formulation is general and applicable to any Lie group. Using top quark tagging as a case study, we observe that the addition of the soft constraints leads to more robust performance while requiring minimal computational costs.