Similarity of Neural Network Representations Revisited Simon - PowerPoint PPT Presentation

Similarity of Neural Network Representations Revisited Simon Kornblith, Mohammad Norouzi, Honglak Lee, Geofgrey Hinton

Motivation We need tools to understand trained neural networks ● Neural network training involves interactions between an ○ algorithm and structured data We don’t know the structure of the data ○ One way to understand trained neural networks is by comparing their ● representations Similarity of Neural Network Representations Revisited

What is a Representation? (Centered) (Centered) Net A Features Net B Features Examples Examples Similarity of Neural Network Representations Revisited

Comparing Features = Comparing Examples Sum of squared dot products Dot product between reshaped inter-example (similarities) between features similarity matrices Similarity of Neural Network Representations Revisited

Comparing Features = Comparing Examples Similarity of Neural Network Representations Revisited

Comparing Features = Comparing Examples Centered kernel alignment (CKA) (Corues et al., 2012) RV-coeffjcient (Roberu & Escoufjer, 1976) Tucker’s congruence coeffjcient (Tucker, 1951) Similarity of Neural Network Representations Revisited

The Kernel Trick H is the centering matrix Similarity of Neural Network Representations Revisited P 7

A Sanity Check for Similarity Given two architecturally identical networks A and B trained from difgerent random initializations, a layer from net A should be most similar to the architecturally corresponding layer in net B conv1 conv2 conv3 conv4 conv5 conv6 conv7 conv8 avgpool conv1 conv2 conv3 conv4 conv5 conv6 conv7 conv8 avgpool Similarity of Neural Network Representations Revisited

A Sanity Check for Similarity Similarity of Neural Network Representations Revisited

A Sanity Check for Similarity Similarity of Neural Network Representations Revisited

CKA Reveals Network Pathology 1x Depth (94.1% on CIFAR-10) 2x Depth (95.1%) 4x Depth (93.2%) 8x Depth (91.9%) Similarity of Neural Network Representations Revisited P 11

CKA Reveals Network Pathology 1x Depth (94.1%) 2x Depth (95.0%) 4x Depth (93.2%) 8x Depth (91.9%) Similarity of Neural Network Representations Revisited P 12

CKA Reveals Network Pathology 1x Depth (94.1%) 2x Depth (95.0%) 4x Depth (93.2%) 8x Depth (91.9%) Similarity of Neural Network Representations Revisited P 13

CKA Reveals Network Pathology Similarity of Neural Network Representations Revisited

CKA Reveals Network Pathology Similarity of Neural Network Representations Revisited

Thank You! cka-similarity.github.io Similarity of Neural Network Representations Revisited