{
  "id": "2309.08247",
  "version": "v1",
  "published": "2023-09-15T08:41:12.000Z",
  "updated": "2023-09-15T08:41:12.000Z",
  "title": "A Geometric Perspective on Autoencoders",
  "authors": [
    "Yonghyeon Lee"
  ],
  "comment": "10 pages, 13 figures, a summary of the contents presented in publications from NeurIPS 2021, ICLR 2022, and TAG-ML at ICML 2023",
  "categories": [
    "cs.LG",
    "cs.AI",
    "cs.CG"
  ],
  "abstract": "This paper presents the geometric aspect of the autoencoder framework, which, despite its importance, has been relatively less recognized. Given a set of high-dimensional data points that approximately lie on some lower-dimensional manifold, an autoencoder learns the \\textit{manifold} and its \\textit{coordinate chart}, simultaneously. This geometric perspective naturally raises inquiries like \"Does a finite set of data points correspond to a single manifold?\" or \"Is there only one coordinate chart that can represent the manifold?\". The responses to these questions are negative, implying that there are multiple solution autoencoders given a dataset. Consequently, they sometimes produce incorrect manifolds with severely distorted latent space representations. In this paper, we introduce recent geometric approaches that address these issues.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-15T08:41:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric perspective",
      "multiple solution autoencoders",
      "high-dimensional data points",
      "severely distorted latent space representations",
      "produce incorrect manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}