Invariance measures for neural networks

Invariances in neural networks are useful and necessary for many tasks. However, the representation of the invariance of most neural network models has not been characterized. We propose measures to quantify the invariance of neural networks in terms of their internal representation. The measures are efficient and interpretable, and can be applied to any neural network model. They are also more sensitive to invariance than previously defined measures. We validate the measures and their properties in the domain of affine transformations and the CIFAR10 and MNIST datasets, including their stability and interpretability. Using the measures, we perform a first analysis of CNN models and show that their internal invariance is remarkably stable to random weight initializations, but not to changes in dataset or transformation. We believe the measures will enable new avenues of research in invariance representation.