Learning Stable Group Invariant Representations with Convolutional Networks
This provides a theoretical framework for interpreting network architectures in machine learning, but it is incremental as it builds on existing group theory concepts.
The paper tackles the problem of understanding how deep convolutional networks achieve invariance to transformations by showing that their invariance properties can be described as stable group invariance, where network architecture determines the invariance group and filters characterize the group action.
Transformation groups, such as translations or rotations, effectively express part of the variability observed in many recognition problems. The group structure enables the construction of invariant signal representations with appealing mathematical properties, where convolutions, together with pooling operators, bring stability to additive and geometric perturbations of the input. Whereas physical transformation groups are ubiquitous in image and audio applications, they do not account for all the variability of complex signal classes. We show that the invariance properties built by deep convolutional networks can be cast as a form of stable group invariance. The network wiring architecture determines the invariance group, while the trainable filter coefficients characterize the group action. We give explanatory examples which illustrate how the network architecture controls the resulting invariance group. We also explore the principle by which additional convolutional layers induce a group factorization enabling more abstract, powerful invariant representations.