Correlation between entropy and generalizability in a neural network

Although neural networks can solve very complex machine-learning problems, the theoretical reason for their generalizability is still not fully understood. Here we use Wang-Landau Mote Carlo algorithm to calculate the entropy (logarithm of the volume of a part of the parameter space) at a given test accuracy, and a given training loss function value or training accuracy. Our results show that entropical forces help generalizability. Although our study is on a very simple application of neural networks (a spiral dataset and a small, fully-connected neural network), our approach should be useful in explaining the generalizability of more complicated neural networks in future works.

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