Multi-agent systems are increasingly deployed autonomously in complex, real-world environments. Yet the black-box nature of deep policy learning approaches — despite their universal approximation power enabling coordinated, emergent behaviors — poses significant hurdles for ensuring scalability and safety. How can learned robot policies respect the underlying physics and geometry of the systems they control ? A promising direction is to structurally enforce intrinsic properties of the system as inductive biases. Symmetries are a particularly natural choice: in robotics, behavioral and geometric symmetries manifest as equivalences among state-action pairs under predictable group transformations, meaning a policy need only learn one mapping per equivalence class rather than redundantly re-learning the same behavior across all related instances. Embedding such structure directly into learned policies improves sample efficiency, generalization, and interpretability. This raises several fundamental questions we will explore in this talk: How can symmetry be embedded into deep distributed policies? What happens when a system exhibits only partial or broken symmetries? How can symmetry-enhanced parameterizations better capture safety certificates? And how can symmetries be exploited to enhance distribution-agnostic uncertainty quantification of pre-trained models?