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SUMMARY:The manifold hypothesis in science &amp\; AI - Patrick Rubin-Delan
 chy (Edinburgh)
DTSTART:20251107T140000Z
DTEND:20251107T150000Z
UID:TALK237514@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:The manifold hypothesis is a widely accepted tenet of machine 
 learning which asserts that nominally high-dimensional data are in fact co
 ncentrated around a low-dimensional manifold. In this talk\, I will show s
 ome real examples of manifold structure occurring in science and in AI (in
 ternal representations of LLMs)\, and discuss associated research question
 s\, particularly around how observed topology and geometry might map to th
 e real world or human perceptions. I will present a statistical model and 
 associated theory which explains how complex hidden manifold structure mig
 ht emerge from simple statistical assumptions (e.g. latent variables\, cor
 relation\, stationarity)\, exposing different possible mathematical relati
 onships between the manifold and the ground truth (e.g. homeomorphism\, is
 ometry)\, and elucidating the efficacy of popular combinations of tools fo
 r data exploration (e.g. PCA followed by t-SNE).\n \nPapers:\nNick Whitele
 y\, Annie Gray\, Patrick Rubin-Delanchy. "Statistical exploration of the M
 anifold Hypothesis". JRSSB (with discussion)\, to appear.\nAlexander Model
 l\, Patrick Rubin-Delanchy\, Nick Whiteley. "The Origins of Representation
  Manifolds in Large Language Models"\, arXiv:2505.18235
LOCATION:MR12\, Centre for Mathematical Sciences
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