Convolutional neural networks (CNNs) have undeniably been extremely successful in image classification problems. Yet, from a mathematical standpoint we do not understand why they work so well. A group of researchers recently showed that images of cats, but “painted” with an elephant’s skin, are classified as elephants with almost full certainty in state-of-the-art image recognition networks. This came as a surprise for many in the machine learning community; it was assumed that CNNs, like humans, make classifications largely based on shape rather than on small scale structures like texture. The study illustrates just how far we are from understanding the inner workings of CNNs. Indeed, it raises a substantial concern: if AI algorithms do no “see things” as we do, how can we trust them with human tasks?
The aim of this project is to use methods from the field of shape analysis to construct and rigorously analyze neural network structures for shape-based classification. Our broad aim is to extend the shape analysis framework to provide a mathematically sound theory of shape learning.