[
  "MFVI underestimates posterior variance in parameter space but can overestimate predictive variance relative to the exact posterior, with Theorem 3.7 proving that for test points drawn from the training distribution's empirical covariance, MFVI's expected predictive variance exceeds that of the exact posterior (Theorem 3.7).",
  "Lemma 3.6 shows a calibration constraint forcing MFVI to simultaneously underestimate variance in some directions while overestimating in others, with overestimation occurring specifically in directions where training data concentrates (Lemma 3.6).",
  "In a pathological rank-1 training-data subspace scenario, as dimensionality increases the MFVI posterior's predictive variance converges to the prior variance, effectively discarding training information (Section 5.1).",
  "Temperature-scaled posteriors (cold posteriors, T<1) correct the predictive-variance overestimation and improve in-distribution predictions, while T>1 benefits out-of-distribution performance, offering a novel explanation for the Cold Posterior Effect.",
  "Experiments on basis function regression and UCI datasets show optimal temperatures below 1 for in-distribution test points and above 1 for out-of-distribution test points, consistent with the theoretical predictions (Section 6, UCI experiments)."
]