Entropic Symmetrization Resistance

What the math gives to ML

The paper develops a distribution-level notion of symmetrization in which an independent noise variable is chosen so that convolution with the input distribution becomes invariant under inversion, while minimizing the entropy of that noise. This is a transferable design principle for discrete latent representations: enforce a desired group symmetry with the least-random augmentation rather than using uniform random transformations. The explicit cyclic-group construction is especially useful because it gives a closed-form, sparse symmetrizer for an asymmetric two-point distribution, and the boundary-simplex results suggest that entropy-efficient symmetrizers should have sparse support. A practical first test is a categorical latent or classifier-head regularizer that samples additive group noise from this sparse construction and compares it with uniform symmetry augmentation.