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This research proposes a novel method where autoencoder parameters serve as dense vector representations of training data, linked theoretically via singular values and covariance eigenvalues. Experimental validation on standard datasets confirms that these spectral characteristics can accurately distinguish between models trained on different subsets without requiring access to the original samples. The findings offer a significant advancement in model interpretability and potential applications for efficient data fingerprinting or compression within deep learning pipelines.
Spectral characteristics of autoencoder parameters as a vector representation of data
arXiv:2609.03495v1 Announce Type: new Abstract: This paper examines the relationship between the parameters of autoencoder models and the statistical properties of the data on which they are trained. Autoencoders are defined as models with an encoder-decoder architecture, trained to reconstruct input data through a compressed latent representation. It is proposed that the model parameters can be viewed as a dense vector representation of the corresponding sample. To test this hypothesis, a theoretical and experimental study is conducted in which a vector representation is formed based on the spectral characteristics of the autoencoder parameter matrices. Theoretical analysis shows that the singular values of the model parameter matrices are related to the eigenvalues of the covariance matrix of the training data, ensuring the transfer of information between the data space and the parameter space. Experimental results on the CIFAR-10 and FashionMNIST datasets confirm that the resulting vector representations allow for a high degree of accuracy in distinguishing between models trained on different data subsets, without resorting to complex vector generation algorithms or using the original samples. These results suggest that the parameters of trained autoencoders can be viewed as sample representations.
Abstract:This paper examines the relationship between the parameters of autoencoder models and the statistical properties of the data on which they are trained. Autoencoders are defined as models with an encoder-decoder architecture, trained to reconstruct input data through a compressed latent representation. It is proposed that the model parameters can be viewed as a dense vector representation of the corresponding sample. To test this hypothesis, a theoretical and experimental study is conducted in which a vector representation is formed based on the spectral characteristics of the autoencoder parameter matrices. Theoretical analysis shows that the singular values of the model parameter matrices are related to the eigenvalues of the covariance matrix of the training data, ensuring the transfer of information between the data space and the parameter space. Experimental results on the CIFAR-10 and FashionMNIST datasets confirm that the resulting vector representations allow for a high degree of accuracy in distinguishing between models trained on different data subsets, without resorting to complex vector generation algorithms or using the original samples. These results suggest that the parameters of trained autoencoders can be viewed as sample representations.
13 pages, 6 figures. This is a shortened (theorem proofs are skipped) and translated version of the paper published in a Russian-language peer-reviewed journal, the citation is in the paper footnote
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2609.03495 [cs.LG]
(or arXiv:2609.03495v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.03495 arXiv-issued DOI via DataCite (pending registration)
Bishuk A., Nikitina M., Bakhteev O. "Spectral characteristics of autoencoder parameters as a vector representation of data." Upravlenie bolsimi sistemami. 2026. Vol. 120. P. 51-83
https://doi.org/10.25728/ubs.2026.120.3 DOI(s) linking to related resources
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