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Hyperplane Arrangements of Trained ConvNets Are Biased. (arXiv:2003.07797v2 [cs.CV] UPDATED)
cs.LG updates on arXiv.org arxiv.org
We investigate the geometric properties of the functions learned by trained
ConvNets in the preactivation space of their convolutional layers, by
performing an empirical study of hyperplane arrangements induced by a
convolutional layer. We introduce statistics over the weights of a trained
network to study local arrangements and relate them to the training dynamics.
We observe that trained ConvNets show a significant statistical bias towards
regular hyperplane configurations. Furthermore, we find that layers showing
biased configurations are critical to validation …
architectures arxiv bias dynamics hyperplane network observe performance space statistical statistics study training validation