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Partially Linear Autoencoders for Manifold Learning and Dimensionality Reduction — arXiv:2608.29867

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.29867
License (as archived): CC0-1.0
Archived: 2026-10-17T08:36:56.785Z
SHA-256 of the archived text: 5a0278960df6e317322b856b4195386ab17ffb16f58751cbd98255458c86fe19
Stable URL of this page: https://metraipolis.com/documento/dc_f51ec769e793

How to cite

Partially Linear Autoencoders for Manifold Learning and Dimensionality Reduction — arXiv:2608.29867 — arXiv (en), https://arxiv.org/abs/2608.29867 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f51ec769e793 (Metraipolis archive dc_f51ec769e793, sha256 5a0278960df6e317322b856b4195386ab17ffb16f58751cbd98255458c86fe19)

BibTeX

@misc{dcf51ec769e793,
  title = {Partially Linear Autoencoders for Manifold Learning and Dimensionality Reduction — arXiv:2608.29867},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.29867},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f51ec769e793; sha256 5a0278960df6e317322b856b4195386ab17ffb16f58751cbd98255458c86fe19},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.29867. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Autoencoders are widely used for nonlinear dimensionality reduction and manifold learning. While most common implementations rely on both nonlinear encoders and decoders, we investigate the specific role of the encoder and the extent to which it can be constrained to be linear without reducing accuracy. We conduct a comparative study on four autoencoder architectures: standard fully nonlinear autoencoders (AE), linear-encoder autoencoders (Lenc-AE), linear-decoder autoencoders (Ldec-AE), and fully linear autoencoders (LAE), evaluated on synthetic manifolds, computational mechanics data sets, and real-world image data sets including MNIST. We demonstrate that imposing a linear encoder preserves most of the representational capacity of the autoencoder, provided the decoder remains nonlinear. In particular, Lenc-AE consistently outperforms both Ldec-AE and LAE, and achieves reconstruction quality comparable to fully nonlinear AE, while offering advantages in terms of parsimony and interpretability of the latent representation. These results suggest that the nonlinear decoder is the critical component for manifold learning, rather than the encoder. A geometric interpretation of this finding is developed, which identifies the precise conditions under which a linear encoder is sufficient, and the specific manifold configurations that expose its limitations.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-01 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2608.29867 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T08:13:26.771Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).