Midpoint Projection Theory (MPT) - Sampokilis 2025

Summary: The draft proposes Midpoint Projection Theory (MPT), a framework that leverages group symmetries in neural representations. MPT defines a projection operator PGPG that maps any feature vector onto the “midpoint” (group-orbit average) of its symmetry orbit. Iterating PGPG across layers – the folding principle – collapses symmetric modes so that only one representative per orbit remains. The author lists key contributions: a formal definition of the projection operator and folding principle, a notion of latent symmetry, a theorem (“Sampokilis Theorem”) showing that projecting at the midpoint does not alter network outputs, and example applications to Transformers, VAEs, and edge inference. An appendix gives preliminary bounds on distributional divergence and parameter savings.