Talk by Pranjal Awasthi (Google) (SIMONS-TCS-ML)
38:15Talk by Katrina Ligett (Hebrew University of Jerusalem) (SIMONS-TCS-ML)
36:41Efficient Algorithms for Reliable Machine Learning (SIMONS-TCS-ML)
37:26Computational Thinking on Learning Models (SIMONS-TCS-ML)
38:30On the Komlós Conjecture (SIMONS-TCS-ML)
33:41Multi-objective Learning: An Algorithmic Toolbox for Optimal Predictions Anytime Anywhere! (SIMONS-TCS-ML)
37:40Approximately Packing Dijoins Via Nowhere-Zero Flows (SIMONS-TCS-ML)
33:46Lightning Talks! (SIMONS-TCS-ML)
56:01Venturing out into the world with AI (SIMONS-TCS-ML)
44:41Unfamiliar Terrain (SIMONS-TCS-ML)
29:51Astral Space: Convex Analysis at Infinity (SIMONS-TCS-ML)
44:01AI and Safety (SIMONS-TCS-ML)
29:26The Role of TCS in Understanding (AI) Consciousness (SIMONS-TCS-ML)
43:21The Conscious Turing Machine (CTM), a formally defined Theoretical model of Consciousness (SIMONS-TCS-ML)
45:00Theory of Modern AI: Learning Theoretic, Game Theoretic, and Algorithmic Perspectives (SIMONS-TCS-ML)
40:41An Occam's Razor Principle for Transformers? (SIMONS-TCS-ML)
39:55Red Points and Blue Points (SIMONS-TCS-ML)
38:15Latent Variable models and Subset Smoothing (SIMONS-TCS-ML)
29:26Enhanced and Efficient Reasoning in Large Language Models (SIMONS-TCS-ML)
36:16Astral Space: Convex Analysis at Infinity (SIMONS-TCS-ML)
Robert Schapire introduces 'Astral Space,' a compact extension of Euclidean space for analyzing minimizers of convex functions at infinity, developing a robust theoretical framework.
Robert Schapire (Microsoft Research)
The Role of TCS in Modern Machine Learning
Not all convex functions have finite minimizers; some can only be minimized by a sequence as it heads to infinity. In this work, we aim to develop a theory for understanding such minimizers at infinity. We study astral space, a compact extension of Euclidean space to which such points at infinity have been added. Astral space is constructed to be as small as possible while still ensuring that all linear functions can be continuously extended to the new space. Although not a vector space, nor even a metric space, astral space is nevertheless so well-structured as to allow useful and meaningful extensions of such concepts as convexity, conjugacy, and subdifferentials. We develop these concepts and analyze various properties of convex functions on astral space, including the detailed structure of their minimizers, exact characterizations of continuity, and convergence of descent algorithms.
Unfamiliar Terrain (SIMONS-TCS-ML)
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