Neural Networks as Paths through the Space of Representations
This work provides a novel geometric framework for interpreting neural networks, which could aid researchers in understanding model behavior, though it is incremental in extending existing representational distance methods.
The authors tackled the problem of interpreting deep neural networks by viewing layer-wise computation as a path through a representation space, formalizing this with metric representational similarity tools like geodesics and angles, and demonstrated it by visualizing and comparing ResNet and VGG architectures on CIFAR-10.
Deep neural networks implement a sequence of layer-by-layer operations that are each relatively easy to understand, but the resulting overall computation is generally difficult to understand. We consider a simple hypothesis for interpreting the layer-by-layer construction of useful representations: perhaps the role of each layer is to reformat information to reduce the "distance" to the desired outputs. With this framework, the layer-wise computation implemented by a deep neural network can be viewed as a path through a high-dimensional representation space. We formalize this intuitive idea of a "path" by leveraging recent advances in *metric* representational similarity. We extend existing representational distance methods by computing geodesics, angles, and projections of representations, going beyond mere layer distances. We then demonstrate these tools by visualizing and comparing the paths taken by ResNet and VGG architectures on CIFAR-10. We conclude by sketching additional ways that this kind of representational geometry can be used to understand and interpret network training, and to describe novel kinds of similarities between different models.