The training error is relatively large, High Bias
Overly simple models underfit, and overly complex models overfit.
Local KL Volume
This methodology defines a set of KL-neighbors (behaviorally similar region) around the trained model weights and efficiently estimates the probability (=Local KL Volume) that this region occupies under the initialization distribution using Monte Carlo Method + Importance sampling. Local KL Volume measures the "size" of the parameter region where the output distribution remains nearly unchanged (KL divergence ≤ ε) from the perspective of the initialization distribution.
KL volume is data-dependent, and the ratio of KL local volume between test and train datasets can be used to assess Overfitting. If the ratio of valid to train is less than 1, it indicates overfitting; if it is close to 1, it's optimal; and if greater than 1, it suggests Underfitting. Using second-moment information from optimizers like Adam Optimizer reduces directional variance, significantly decreasing the variance in volume estimation. The negative log of local volume can be interpreted as network information content (from an MDL perspective) and linked to generalization performance. As training progresses towards overfitting, local volume decreases (complexity increases).