SVCCA: Singular Vector Canonical Correlation Analysis for Deep Understanding and Improvement

By Maithra Raghu, Justin Gilmer, Jason Yosinski, Jascha Narain Sohl-Dickstein. 2017

36 citations recorded by the source corpus.

With the continuing empirical successes of deep networks, it becomes increasingly important to develop better methods for understanding training of models and the representations learned within. In this paper we propose Singular Vector Canonical Correlation Analysis (SVCCA), a tool for quickly comparing two representations in a way that is both invariant to affine transform (allowing comparison between different layers and networks) and fast to compute (allowing more comparisons to be calculated than with previous methods). We deploy this tool to measure the intrinsic dimensionality of layers, showing in some cases needless over-parameterization; to probe learning dynamics throughout training, finding that networks converge to final representations from the bottom up; to show where class-specific information in networks is formed; and to suggest new training regimes that simultaneously save computation and overfit less.

Subfields: Artificial Intelligence, Ecology, Genetics

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Citations in the corpus

Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV) (2017, methodology): “This simple approach is supported by recent work using local linearity (Alain & Bengio, 2016; Raghu et al., 2017; Bau et al., 2017; Szegedy et al., 2013).”
Understanding intermediate layers using linear classifier probes (2016, background): “Refer to Figure 6 of Raghu et al. (2017b) for more details.”
Training Deeper Neural Machine Translation Models with Transparent Attention (2018, background): “Second, when a network is properly trained the lowest layers usually converge quickly, whereas the topmost layers take longer (Raghu et al., 2017).”
On the importance of single directions for generalization (2018, methodology): “…the model pruning literature, many studies have removed units with the goal of generating smaller models with similar performance (Li et al., 2017, Anwar et al., 2015, Molchanov et al., 2017), and recent work has explored methods for discovering maximally important directions (Raghu et al. (2017)).”
TCAV: R ELATIVE CONCEPT IMPORTANCE TESTING WITH L INEAR C ONCEPT A CTIVATION V ECTORS (2017, background): “It has also been shown that representations are not necessarily contained in individual neurons but more generally in linear combinations of neurons (19; 27).”
FreezeOut: Accelerate Training by Progressively Freezing Layers (2017, background): “The same idea has been proposed by [9], where it is motivated by the observation that the representations learned by deep nets can be analytically shown to converge from the bottom up.”
The Case for Full-Matrix Adaptive Regularization (2018, background): “In the spirit of recent empirical lenses of this ﬂavor [RGYSD17, LXTG17], we leave this as a way to visualize deep learning dynamics, possibly of independent exploratory interest.”
On the Learning Dynamics of Deep Neural Networks (2018, background): “Theoretic explanations of that phenomenon exist in the case of regression on linear neural networks (Saxe, 2015) but extensions to the nonlinear case (Heskes & Kappen, 1993; Raghu et al., 2017; Arora et al., 2018) fail to provide analytical solutions.”