Shared Representational Geometry Across Neural Networks
This provides insight into the geometry of learned representations in neural networks, which is incremental as it extends known linear results to non-linear cases.
The paper tackled the problem of whether different neural networks trained on the same dataset share underlying representational structures, showing that both standard and residual networks encode inputs as orthogonal transformations of a shared representation on CIFAR10 and CIFAR100.
Different neural networks trained on the same dataset often learn similar input-output mappings with very different weights. Is there some correspondence between these neural network solutions? For linear networks, it has been shown that different instances of the same network architecture encode the same representational similarity matrix, and their neural activity patterns are connected by orthogonal transformations. However, it is unclear if this holds for non-linear networks. Using a shared response model, we show that different neural networks encode the same input examples as different orthogonal transformations of an underlying shared representation. We test this claim using both standard convolutional neural networks and residual networks on CIFAR10 and CIFAR100.