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Explore fundamental principles underlying deep learning's success through this 29-minute conference talk examining why deep networks escape the curse of dimensionality. Discover how compositionally sparse functions - a key property of all efficiently Turing computable functions - enable effective use of deep and sparse networks that power modern AI systems including large language models. Learn about the challenges of selecting optimal decompositions that exploit sparse compositionality, given that each efficiently computable function admits multiple sparse decompositions. Understand how deep networks can learn reusable sparse decompositions through curriculum learning approaches similar to chain-of-thought reasoning, where constituent functions remain common across different tasks. Gain insights into the mathematical foundations that explain deep learning's remarkable effectiveness and its implications for understanding whether mathematics is invented or discovered.
