  The volume of the distribution of weight sets associated with a loss value
may be the source of implicit regularization from overparameterization due to
the phenomenon of contracting volume with increasing dimensions for geometric
figures demonstrated by hyperspheres. We introduce the geometric regularization
conjecture and extract to an explanation for the double descent phenomenon by
considering a similar property resulting from shrinking intrinsic
dimensionality of the distribution of potential weight set updates available
along training path, where if that distribution retracts across a volume verses
dimensionality curve peak when approaching the global minima we could expect
geometric regularization to re-emerge. We illustrate how data fidelity
representational complexity may influence model capacity double descent
interpolation thresholds. The existence of epoch and model capacity double
descent curves originating from different geometric forms may imply
universality of closed n-manifolds having dimensionally adjusted n-sphere
volumetric correspondence.
