  Benford's law, also called Significant Digit Law, is observed in many
naturally occurring data-sets. For instance, the physical constants such as
Gravitational, Coulomb's Constant, etc., follow this law. In this paper, we
define a score, $MLH$, for how closely a Neural Network's Weights match
Benford's law. We show that Neural Network Weights follow Benford's Law
regardless of the initialization method. We make a striking connection between
Generalization and the $MLH$ of the network. We provide evidence that several
architectures from AlexNet to ResNeXt trained on ImageNet, Transformers (BERT,
Electra, etc.), and other pre-trained models on a wide variety of tasks have a
strong correlation between their test performance and the $MLH$. We also
investigate the influence of Data in the Weights to explain why NNs possibly
follow Benford's Law. With repeated experiments on multiple datasets using
MLPs, CNNs, and LSTMs, we provide empirical evidence that there is a connection
between $MLH$ while training, overfitting. Understanding this connection
between Benford's Law and Neural Networks promises a better comprehension of
the latter.
