Papers › Neural Anisotropy Directions

Neural Anisotropy Directions

17 Jun 2020NeurIPS 2020 12arXiv:2006.09717archive 2025-07-28

Guillermo Ortiz-Jimenez, Apostolos Modas, Seyed-Mohsen Moosavi-Dezfooli, Pascal Frossard

In this work, we analyze the role of the network architecture in shaping the inductive bias of deep classifiers. To that end, we start by focusing on a very simple problem, i.e., classifying a class of linearly separable distributions, and show that, depending on the direction of the discriminative feature of the distribution, many state-of-the-art deep convolutional neural networks (CNNs) have a surprisingly hard time solving this simple task. We then define as neural anisotropy directions (NADs) the vectors that encapsulate the directional inductive bias of an architecture. These vectors, which are specific for each architecture and hence act as a signature, encode the preference of a network to separate the input data based on some particular features. We provide an efficient method to identify NADs for several CNN architectures and thus reveal their directional inductive biases. Furthermore, we show that, for the CIFAR-10 dataset, NADs characterize the features used by CNNs to discriminate between different classes.

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GradientCovarianceAnisotropyFinder LTS4/neural-anisotropy-directions/nad_computation.py official repository ran Apache-2.0 (permissive) · 39c01bcce404741c · report
input_numerical_jacobian LTS4/neural-anisotropy-directions/nad_computation.py official repository ran · fixture could not drive it Apache-2.0 (permissive) · 1a7c50021e79245d · report
NADs VahidZee/nads/nads/compute/gradient_covariance.py community (archive-listed) ran · metamorphic tier: deterministic MIT (permissive) · 0f838c9168e36b16 · report
numerical_jacobian VahidZee/nads/nads/compute/gradient_covariance.py community (archive-listed) ran · fixture could not drive it MIT (permissive) · dc61272119b0560e · report
GradientCovariance VahidZee/nads/nads/compute/gradient_covariance.py community (archive-listed) unverified MIT (permissive) · ede6d5b4a5394294 · report
make_subdirectories VahidZee/nads/nads/compute/gradient_covariance.py community (archive-listed) unverified MIT (permissive) · f36de828f2999ceb · report
visualize_image VahidZee/nads/nads/compute/gradient_covariance.py community (archive-listed) unverified MIT (permissive) · 9118a1c9f6fc8c15 · report
visualize_nads VahidZee/nads/nads/compute/gradient_covariance.py community (archive-listed) unverified MIT (permissive) · 9ca12e126bfb8d93 · report
visualize_spectrum VahidZee/nads/nads/compute/gradient_covariance.py community (archive-listed) unverified MIT (permissive) · a840a0cfb6a71e5e · report

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