{
  "abstract": "Symbols can provide compact representations of complex sensory information. Mathematically, chaotic attractors can provide a basis for such representations, with object identity encoded in the topological organization of the attractor. In three-dimensional phase space, this organization can be characterized by the linking matrix of unstable periodic orbits, which serves as a topological fingerprint. Because the linking matrix has no closed-form dependence on the learnable parameters, we learn the chaotic series generating the target attractors rather than optimizing the invariant directly; the reconstructed attractor then determines its unstable periodic orbits and linking matrix through its topology. In this paper, we propose a third-order tensor that maps inputs to connection matrices that generate the corresponding chaotic series. Exploiting the duality between a vector and its sequential representation as a series, we lift inputs into a higher-dimensional space and reorder their components, allowing the input to be presented sequentially rather than simultaneously. We first demonstrate that this representation can discriminate between classes in the \\href{https://archive.ics.uci.edu/dataset/151/connectionist+bench+sonar+mines+vs+rocks}{Sonar} dataset. We then examine perceptual constancy using the \\href{https://www.csc.kth.se/cvap/databases/kth-tips/index.html}{KTH-TIPS2-a} dataset, where variations in color and texture within a class are mapped to distinct chaotic series associated with the same topological attractor class. The results demonstrate that the proposed tensor-based mapping can preserve attractor class while accommodating variations in the sensory realization of an object.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13278",
  "author_total": 1,
  "authors": [
    {
      "name": "Amir M. Majd"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/drm2yrjez2rjw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13278",
  "fulltext_url": null,
  "id": "drm2yrjez2rjw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13278",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "nlin.CD"
    ],
    [
      "openalex",
      "1702|Neural Networks and Applications"
    ]
  ],
  "openalex": "W7213278679",
  "pdf_url": "https://arxiv.org/pdf/2609.13278",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/drm2yrjez2rjw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.13278",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13278"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Tensor-Based Chaotic Perception",
  "title_text": "Tensor-Based Chaotic Perception",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/drm2yrjez2rjw",
  "venue": "arXiv",
  "versions": []
}