Hyperplane Arrangements of Trained ConvNets Are Biased
This work addresses the problem of understanding the internal geometric structures of neural networks for researchers in machine learning, though it is incremental as it builds on existing empirical studies of network properties.
The study investigated the geometric properties of trained ConvNets by analyzing hyperplane arrangements in convolutional layers, finding a significant statistical bias towards regular configurations that correlates with validation performance on datasets like CIFAR10, CIFAR100, and ImageNet.
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 performance for the architectures considered, trained on CIFAR10, CIFAR100 and ImageNet.