AI 中文总结
该研究提出将自编码器参数矩阵的谱特性作为样本的向量表示，经理论分析和CIFAR-10、FashionMNIST实验验证，该表示可高精度区分不同子集训练的模型，证实自编码器参数可作为样本表示。
AI 中文摘要
本文研究自编码器模型的参数与其训练数据统计特性之间的关系。自编码器被定义为具有编码器-解码器架构的模型，其训练目标是通过压缩的潜在表示重构输入数据。本文提出，模型参数可被视为对应样本的稠密向量表示。为验证该假设，开展了理论与实验研究，其中基于自编码器参数矩阵的谱特性构建向量表示。理论分析表明，模型参数矩阵的奇异值与训练数据协方差矩阵的特征值相关，确保了数据空间与参数空间之间的信息传递。在CIFAR-10和FashionMNIST数据集上的实验结果证实，所得向量表示无需借助复杂的向量生成算法或使用原始样本，即可在区分在不同数据子集上训练的模型时达到较高准确率。这些结果表明，训练后的自编码器参数可被视为样本表示。
英文摘要
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.
Comments13 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
Journal refBishuk 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
