Dihedral group (D_inf)

Why weight-space perception fails when networks train independently

The symmetry story in weight-space learning finally has the hard numbers it needed. This study, built on roughly 1.8 million fitted SIRENs, shows that randomizing only the exact symmetry group destroys 79.1 of the 80.4 accuracy points separating shared-init from random-init networks. That is sufficiency, cleanly demonstrated. The deeper insight, though, is computational. If a complete invariant matches function access informationally, then weight-space's real edge must be efficiency, not insight. That reframing deserves attention.