Invariance Measures for Neural Networks
Facundo Manuel Quiroga Jordina Torrents-Barrena Laura Cristina Lanzarini Domenec Puig-Valls
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.