arXiv:2601. 19179v2 Announce Type: replace Abstract: Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA).
By Qipeng Zhan, Zhuoping Zhou, Zexuan Wang, Li Shen
arXiv:2606. 03553v1 Announce Type: cross Abstract: While principal component analysis (PCA) is a fundamental tool for dimensionality reduction, its dense representations make it ill-suited for high-dimensional data.
By David V\"avinggren, Francis Bach, Andr\'e M. H. Teixeira, Dave Zachariah, Ant\^onio H. Ribeiro
arXiv:2602. 10680v2 Announce Type: replace-cross Abstract: Many real-world datasets contain hidden structure that cannot be detected by simple linear correlations between input features.
By Vicente Conde Mendes, Lorenzo Bardone, C\'edric Koller, Jorge Medina Moreira, Vittorio Erba, Emanuele Troiani, Lenka Zdeborov\'a
arXiv:2608.29867v1 Announce Type: new
Abstract: Autoencoders are widely used for nonlinear dimensionality reduction and manifold learning. While most common implementations rely on both nonlinear enc...
By Louen Pottier, Louis Lesueur, Anders Thorin
The paper presents a theoretical analysis of symmetric autoencoders, a class of deep learning architectures frequently used in machine learning tasks. It distinguishes between different symmetric designs and shows that the reconstruction error of orthonormal symmetric autoencoders can be interpreted via the Eckart‑Young‑Schmidt theorem. Building on this insight, the authors propose an EYS‑based initialization strategy using repeated SVD, and validate its effectiveness through numerical experiments comparing it to conventional deep autoencoders.
By Simone Brivio, Nicola Rares Franco
arXiv:2501. 09876v3 Announce Type: replace-cross Abstract: Generative modeling aims to generate new data samples that resemble a given dataset.
By Wonjun Lee, Riley C. W. O'Neill, Dongmian Zou, Jeff Calder, Gilad Lerman