Entropic gradient descent algorithms and wide flat minima
This work addresses the challenge of poor generalization in deep learning by targeting flat minima, offering incremental improvements through novel optimization methods.
The paper tackles the problem of finding flat minima in neural network loss landscapes to improve generalization, showing analytically that Bayes optimal estimators correspond to wide flat regions and demonstrating through experiments that algorithms like Entropy-SGD and Replicated-SGD consistently reduce generalization error for architectures such as ResNet and EfficientNet.
The properties of flat minima in the empirical risk landscape of neural networks have been debated for some time. Increasing evidence suggests they possess better generalization capabilities with respect to sharp ones. First, we discuss Gaussian mixture classification models and show analytically that there exist Bayes optimal pointwise estimators which correspond to minimizers belonging to wide flat regions. These estimators can be found by applying maximum flatness algorithms either directly on the classifier (which is norm independent) or on the differentiable loss function used in learning. Next, we extend the analysis to the deep learning scenario by extensive numerical validations. Using two algorithms, Entropy-SGD and Replicated-SGD, that explicitly include in the optimization objective a non-local flatness measure known as local entropy, we consistently improve the generalization error for common architectures (e.g. ResNet, EfficientNet). An easy to compute flatness measure shows a clear correlation with test accuracy.