  The appearance of the double-descent risk phenomenon has received growing
interest in the machine learning and statistics community, as it challenges
well-understood notions behind the U-shaped train-test curves. Motivated
through Rissanen's minimum description length (MDL), Balasubramanian's Occam's
Razor, and Amari's information geometry, we investigate how the logarithm of
the model volume: $\log V$, works to extend intuition behind the AIC and BIC
model selection criteria. We find that for the particular model classes of
isotropic linear regression and statistical lattices, the $\log V$ term may be
decomposed into a sum of distinct components, each of which assist in their
explanations of the appearance of this phenomenon. In particular they suggest
why generalization error does not necessarily continue to grow with increasing
model dimensionality.
