SVCCA: Singular Vector Canonical Correlation Analysis for Deep Learning Dynamics and Interpretability

Raghu, Maithra; Gilmer, Justin; Yosinski, Jason; Sohl-Dickstein, Jascha

doi:10.48550/arxiv.1706.05806

Cited by 17 publications

(29 citation statements)

References 13 publications

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“…In both of the experimental settings there is a one-to-one correspondence between points in the point clouds. We compared these point clouds by calculating: RTD (proposed), CKA (Kornblith et al, 2019), IMD (Tsitsulin et al, 2020) and SVCCA (Raghu et al, 2017). We calculated linear CKA since (Kornblith et al, 2019) concluded that it provides the same performance as with RBF kernel but doesn't require to select a kernel width.…”

Section: Experiments With Synthetic Point Cloudsmentioning

confidence: 99%

“…We calculated linear CKA since (Kornblith et al, 2019) concluded that it provides the same performance as with RBF kernel but doesn't require to select a kernel width. For SVCCA, we calculated average correlation ρ for the truncation threshold 0.99, as recommended by the authors (Raghu et al, 2017). The IMD score (Tsitsulin et al, 2020) was very noisy and we averaged it over 100 runs.…”

Section: Experiments With Synthetic Point Cloudsmentioning

confidence: 99%

“…Comparison of representations is an ill-posed problem without a "ground truth" answer. Early studies were based on variants of Canonical Correlation Analysis (CCA): SVCCA, (Raghu et al, 2017), PWCCA (Morcos et al, 2018). However, CCA-like measures define similarity too loosely since they are invariant to any invertible linear transformation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Representation Topology Divergence: A Method for Comparing Neural Network Representations

Barannikov¹,

Трофимов²,

Balabin³

et al. 2022

Preprint

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Comparison of data representations is a complex multi-aspect problem that has not enjoyed a complete solution yet. We propose a method for comparing two data representations. We introduce the Representation Topology Divergence (RTD), measuring the dissimilarity in multi-scale topology between two point clouds of equal size with a one-to-one correspondence between points. The data point clouds are allowed to lie in different ambient spaces. The RTD is one of the few TDA-based practical methods applicable to real machine learning datasets. Experiments show the proposed RTD agrees with the intuitive assessment of data representation similarity and is sensitive to its topological structure. We apply RTD to gain insights on neural networks representations in computer vision and NLP domains for various problems: training dynamics analysis, data distribution shift, transfer learning, ensemble learning, disentanglement assessment.

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Section: Experiments With Synthetic Point Cloudsmentioning

confidence: 99%

Section: Experiments With Synthetic Point Cloudsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Representation Topology Divergence: A Method for Comparing Neural Network Representations

Barannikov¹,

Трофимов²,

Balabin³

et al. 2022

Preprint

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show abstract

“…For example, one approach is to investigate what certain units are looking for by generating artificial inputs that maximizes an individual neuron's activation (Erhan et al, 2009). Alternatively, it is possible to study the activations of each neuron after passing certain data through the model, whose results can reflect on the input data and allows for further unsupervised investigation (Simonyan et al, 2013;Raghu et al, 2017).…”

Section: Representation Analysismentioning

confidence: 99%

Interactive Visualization and Representation Analysis Applied to Glacier Segmentation

Zheng¹,

Miao²,

Sankaran³

2021

Preprint

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Interpretability has attracted increasing attention in earth observation problems. We apply interactive visualization and representation analysis to guide interpretation of glacier segmentation models. We visualize the activations from a U-Net to understand and evaluate the model performance. We build an online interface using the Shiny R package to provide comprehensive error analysis of the predictions.Users can interact with the panels and discover model failure modes. Further, we discuss how visualization can provide sanity checks during data preprocessing and model training.

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“…Raghu et al [30] proposed Singular Vector Canonical Correlation Analysis (SVCCA) for comparing two representations. They defined a neuron as a vector in R m over a dataset with m examples.…”

Section: Similarity Indexmentioning

confidence: 99%

Graph-Based Similarity of Neural Network Representations

Chen¹,

Lu²,

Yang³

et al. 2021

Preprint

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Understanding the black-box representations in Deep Neural Networks (DNN) is an essential problem in deep learning. In this work, we propose Graph-Based Similarity (GBS) to measure the similarity of layer features. Contrary to previous works that compute the similarity directly on the feature maps, GBS measures the correlation based on the graph constructed with hidden layer outputs. By treating each input sample as a node and the corresponding layer output similarity as edges, we construct the graph of DNN representations for each layer. The similarity between graphs of layers identifies the correspondences between representations of models trained in different datasets and initializations. We demonstrate and prove the invariance property of GBS, including invariance to orthogonal transformation and invariance to isotropic scaling, and compare GBS with CKA. GBS shows state-of-the-art performance in reflecting the similarity and provides insights on explaining the adversarial sample behavior on the hidden layer space. 1 .

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SVCCA: Singular Vector Canonical Correlation Analysis for Deep Learning Dynamics and Interpretability

Cited by 17 publications

References 13 publications

Representation Topology Divergence: A Method for Comparing Neural Network Representations

Representation Topology Divergence: A Method for Comparing Neural Network Representations

Interactive Visualization and Representation Analysis Applied to Glacier Segmentation

Graph-Based Similarity of Neural Network Representations

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