How should we compare neural network representations?

To understand neural networks, researchers often use similarity metrics to measure how similar or different two neural networks are to each other. For instance, they are used to compare vision transformers to convnets [1], to understand transfer learning [2], and to explain the success of standard training practices for deep models [3]. CKA (Centered Kernel Alignment) similarity between two networks trained identically except for random initialization. Lower values (darker colors) are more similar. CKA suggests that the two networks have similar representations.