High-dimensional Asymptotics of Denoising Autoencoders
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910534285131776 |
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| author | Cui, Hugo Zdeborová, Lenka |
| author_facet | Cui, Hugo Zdeborová, Lenka |
| contents | We address the problem of denoising data from a Gaussian mixture using a two-layer non-linear autoencoder with tied weights and a skip connection. We consider the high-dimensional limit where the number of training samples and the input dimension jointly tend to infinity while the number of hidden units remains bounded. We provide closed-form expressions for the denoising mean-squared test error. Building on this result, we quantitatively characterize the advantage of the considered architecture over the autoencoder without the skip connection that relates closely to principal component analysis. We further show that our results accurately capture the learning curves on a range of real data sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_11041 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | High-dimensional Asymptotics of Denoising Autoencoders Cui, Hugo Zdeborová, Lenka Machine Learning Disordered Systems and Neural Networks We address the problem of denoising data from a Gaussian mixture using a two-layer non-linear autoencoder with tied weights and a skip connection. We consider the high-dimensional limit where the number of training samples and the input dimension jointly tend to infinity while the number of hidden units remains bounded. We provide closed-form expressions for the denoising mean-squared test error. Building on this result, we quantitatively characterize the advantage of the considered architecture over the autoencoder without the skip connection that relates closely to principal component analysis. We further show that our results accurately capture the learning curves on a range of real data sets. |
| title | High-dimensional Asymptotics of Denoising Autoencoders |
| topic | Machine Learning Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2305.11041 |