Learnability of Learned Neural Networks

This paper explores the simplicity of learned neural networks under various settings: learned on real vs random data, varying size/architecture and using large minibatch size vs small minibatch size. The notion of simplicity used here is that of learnability i.e., how accurately can the prediction function of a neural network be learned from labeled samples from it. While learnability is different from (in fact often higher than) test accuracy, the results herein suggest that there is a strong correlation between small generalization errors and high learnability. This work also shows that there exist significant qualitative differences in shallow networks as compared to popular deep networks. More broadly, this paper extends in a new direction, previous work on understanding the properties of learned neural networks. Our hope is that such an empirical study of understanding learned neural networks might shed light on the right assumptions that can be made for a theoretical study of deep learning.