Understanding Neural Network Generalizability from the Perspective of Entropy*

Neural Networks (NNs) have shown remarkable success in solving a wide range of machine learning problems, ranging from image recognition to natural-language conversation (e.g., Chat-GPT). The generalizability of NNs, which measures NNs' ability to perform well on data unseen from training, is a critical evaluation metric for their usefulness in the real-world applications. However, the underlying mechanism that determines NNs' varying degrees of generalizability remains an open question. While it has been long suspected in the machine learning community that NNs at a flatter minimum of the loss-function landscape tend to generalize better, recent works suggest that the flatness itself may not be sufficient to determine the generalizability. In statistical physics, the flatness of a minimum in an energy landscape can be quantified by entropy. Therefore, we calculated the entropy of the loss-function landscape of NNs using Wang-Landau molecular dynamics and explored the potential correlation between such entropy and NNs' generalizability. By testing in both synthetic and real-world datasets, we found that the entropy-equilibrium state is better or at least comparable to the state reachable via the classical training optimizer (e.g., stochastic gradient descent).