Jet tagging techniques that make use of deep learning show great potential for improving physics analyses at colliders. One such method is the energy flow network (EFN)—a recently introduced neural network architecture that represents jets as permutation-invariant sets of particle momenta while maintaining infrared and collinear safety. We develop a variant of the EFN architecture based on the deep sets formalism, incorporating permutation-equivariant layers. We derive conditions under which infrared and collinear safety can be maintained, and study the performance of these networks on the canonical example of W -boson tagging. We find that equivariant EFNs have similar performance to particle flow networks, which are superior to standard EFNs. Due to convergence and generalization issues, the same improvement was not observed when extending particle flow networks with equivariant layers. Finally, we study how equivariant networks sculpt the jet mass and provide some initial results on decorrelation using planing.
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