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Grounding Representation Similarity Through Statistical Testing
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CKA rather than PWCCA to measure representation dissimilarity | BERT base layer representations · QNLI probe, varying pretraining seed and layer depth | Spearman ρ with probe accuracy difference: 0.763 -> 0.876 | Helped |
| Use CKA rather than PWCCA to measure representation dissimilarity | BERT base layer representations · SST-2 probe, varying pretraining seed and layer depth | Spearman ρ with probe accuracy difference: 0.829 -> 0.905 | Helped |
| Use PWCCA rather than CKA to measure representation dissimilarity | BERT base representations with principal-component deletion · SST-2 probe | Spearman ρ with probe accuracy difference: 0.751 -> 0.870 | Helped |
| Use PWCCA rather than CKA to measure representation dissimilarity | BERT base layer representations · HANS lexical non-entailment | Spearman ρ with OOD accuracy difference: 0.462 -> 0.568 | Helped |
| Use Procrustes rather than CKA to measure representation dissimilarity | BERT medium layer representations · Antonymy stress test | Spearman ρ with OOD accuracy difference: 0.227 -> 0.243 | Helped |
| Use CKA rather than PWCCA to measure representation dissimilarity | BERT medium layer representations · Numerical stress test | Spearman ρ with OOD accuracy difference: 0.031 -> 0.122 | Mixed |
| Use CKA rather than Procrustes to measure representation dissimilarity | ResNet-14 layer representations · CIFAR-100 probe | Spearman ρ with probe accuracy difference: 0.485 -> 0.507 | Helped |
| Use CKA rather than Procrustes to measure representation dissimilarity | ResNet-14 layer representations · SVHN probe | Spearman ρ with probe accuracy difference: 0.363 -> 0.372 | Helped |
| Use Procrustes rather than CKA to measure representation dissimilarity | ResNet-14 layer representations · CIFAR-10C OOD corruptions | Spearman ρ with OOD accuracy difference: 0.041 -> 0.060 | Helped |
| Delete principal components from the BERT representation (ablation) | BERT base layer 12 · SST-2 probe | probing accuracy: 80\% to 63\% | Hurt |
| Use CKA as the dissimilarity measure instead of Procrustes or PWCCA | BERT base layer 12 under principal-component deletion · SST-2 probe | detectability of representation change: 97\% | Hurt |
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