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Explore the emerging field of Topological Data Analysis (TDA) and its intersection with machine learning in this 30-minute conference talk by Jens Agerberg. Discover how teaching neural networks elements of geometry and topology can enhance their ability to reason about data shapes. Learn about the surprising applications of these methods beyond computer vision, including evaluating and improving embedding learning and sample distribution in generative models. Gain insights into the potential of geometrical recognition and reasoning for developing more powerful AI systems. Examine the challenges and results of expanding machine learning's mathematical toolkit to include computational geometry and topology. Recorded at the 2023 GAIA Conference, this talk offers a fascinating look into the future of AI and data analysis.