A0181
Title: The manifold hypothesis in science and AI
Authors: Patrick Rubin-Delanchy - University of Edinburgh (United Kingdom) [presenting]
Abstract: The manifold hypothesis is a widely accepted tenet of machine learning, which asserts that nominally high-dimensional data are in fact concentrated around a low-dimensional manifold. Some real examples of manifold structure occurring in science and in AI (internal representations of LLMs) are shown, and associated questions are discussed, particularly around how observed topology and geometry might map to the real world (science) or a human-understandable concept (AI). Statistical models and embedding theory are presented, which help explain the efficacy of popular combinations of tools for manifold learning, such as PCA followed by t-SNE. Finally, a vast array of unexplored possibilities in representation learning and potential implications for the future role of AI in science are pointed out.
