  Benford's Law (BL) or the Significant Digit Law defines the probability
distribution of the first digit of numerical values in a data sample. This Law
is observed in many naturally occurring datasets. It can be seen as a measure
of naturalness of a given distribution and finds its application in areas like
anomaly and fraud detection. In this work, we address the following question:
Is the distribution of the Neural Network parameters related to the network's
generalization capability? To that end, we first define a metric, MLH (Model
Enthalpy), that measures the closeness of a set of numbers to Benford's Law and
we show empirically that it is a strong predictor of Validation Accuracy.
Second, we use MLH as an alternative to Validation Accuracy for Early Stopping,
removing the need for a Validation set. We provide experimental evidence that
even if the optimal size of the validation set is known before-hand, the peak
test accuracy attained is lower than not using a validation set at all.
Finally, we investigate the connection of BL to Free Energy Principle and First
Law of Thermodynamics, showing that MLH is a component of the internal energy
of the learning system and optimization as an analogy to minimizing the total
energy to attain equilibrium.
