Symmetry-Preserving Pruning of Group Equivariant Convolutional Networks via Representation Theory

Group equivariant convolutional neural networks (G-CNNs) achieve superior sample efficiency by encoding symmetry into network architecture, yet their computational overhead (up to 3.78× slower inference and 4.63× more multiply–accumulate operations) hinders deployment on resource-constrained edge devices. Existing pruning methods cannot be applied directly: arbitrarily removing weights breaks the group representation structure and degrades equivariance. We characterize the complete design space of equivariance-preserving compression, proving that exactly two axes leave a convolutional layer equivariant: irrep-bundle pruning, which reduces irreducible-representation multiplicities, and orbit-wise pruning, which removes complete spatial orbits from kernel supports; via Schur’s lemma, no third structure-preserving axis exists. This completeness result, rather than the use of representation theory itself, is our central contribution. We turn it into practice through direct sub-filter extraction, which yields real convolutional parameter reduction (up to 83%) and 1.4–2.9× measured inference speedup, unlike masking, which gives no real speedup. Across three datasets (MNIST, CIFAR-10, EuroSAT) and three symmetry groups (C4, D4, SO(2)), compression is nearly lossless on strongly symmetric data: the 4-layer EuroSAT model drops only 1.07% at 83% reduction. On weakly symmetric data (CIFAR-10), the pruned model can even gain 2.6 points, but our analysis attributes this to relaxing a mismatched equivariance constraint rather than to pruning itself; the value of pruning over from-scratch training scales with the data’s symmetry strength.