Toward a computational theory of manifold untangling: from global embedding to local flattening

Xin Li, Shuo Wang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

It has been hypothesized that the ventral stream processing for object recognition is based on a mechanism called cortically local subspace untangling. A mathematical abstraction of object recognition by the visual cortex is how to untangle the manifolds associated with different object categories. Such a manifold untangling problem is closely related to the celebrated kernel trick in metric space. In this paper, we conjecture that there is a more general solution to manifold untangling in the topological space without artificially defining any distance metric. Geometrically, we can either embed a manifold in a higher-dimensional space to promote selectivity or flatten a manifold to promote tolerance. General strategies of both global manifold embedding and local manifold flattening are presented and connected with existing work on the untangling of image, audio, and language data. We also discuss the implications of untangling the manifold into motor control and internal representations.

Original languageEnglish
Article number1197031
JournalFrontiers in Computational Neuroscience
Volume17
DOIs
StatePublished - 2023

Keywords

  • blessing of dimensionality
  • manifold embedding
  • manifold flattening
  • motor control
  • object recognition

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