Papers › The Intrinsic Dimension of Images and Its Impact on Learning

The Intrinsic Dimension of Images and Its Impact on Learning

18 Apr 2021ICLR 2021 1arXiv:2104.08894archive 2025-07-28

Phillip Pope, Chen Zhu, Ahmed Abdelkader, Micah Goldblum, Tom Goldstein

It is widely believed that natural image data exhibits low-dimensional structure despite the high dimensionality of conventional pixel representations. This idea underlies a common intuition for the remarkable success of deep learning in computer vision. In this work, we apply dimension estimation tools to popular datasets and investigate the role of low-dimensional structure in deep learning. We find that common natural image datasets indeed have very low intrinsic dimension relative to the high number of pixels in the images. Additionally, we find that low dimensional datasets are easier for neural networks to learn, and models solving these tasks generalize better from training to test data. Along the way, we develop a technique for validating our dimension estimation tools on synthetic data generated by GANs allowing us to actively manipulate the intrinsic dimension by controlling the image generation process. Code for our experiments may be found here https://github.com/ppope/dimensions.

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1ran · honoured contract
2ran · our draft was wrong
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KNNComputerNoCheck ppope/dimensions/estimators/geomle.py official repository ran · metamorphic tier: deterministic MIT (permissive) · 5a9384c8c8db2afa · report
fit_poly_reg ppope/dimensions/estimators/geomle.py official repository ran · fixture could not drive it fingerprinted MIT (permissive) · df7da5b2892df07a · report
intrinsic_dim_sample_wise ppope/dimensions/estimators/mle.py official repository ran · our draft was wrong fingerprinted MIT (permissive) · df91d00c39eb470a · report
intrinsic_dim_scale_interval ppope/dimensions/estimators/mle.py official repository ran · our draft was wrong fingerprinted MIT (permissive) · 71f28a5a636fea5e · report
mle_center ppope/dimensions/estimators/geomle.py official repository ran MIT (permissive) · aee171526745aa8a · report
_func ppope/dimensions/estimators/geomle.py official repository unverified MIT (permissive) · 8f89b37d9005aa30 · report
geomle ppope/dimensions/estimators/geomle.py official repository unverified MIT (permissive) · d52066bee0e04253 · report
update_nn ppope/dimensions/estimators/geomle.py official repository unverified MIT (permissive) · 7b18db6c52e2a536 · report
drop_zero_values identical code first harvested elsewhere ran · fixture could not drive it fingerprinted licence of this copy not recorded · c3e52574ec7f8090 · report
tolist identical code first harvested elsewhere ran · honoured contract fingerprinted licence of this copy not recorded · a67a7b23ea7331c5 · report

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