Explore the foundations of computational mathematics, Smale's 18th problem, and potential limitations of AI in this one-hour virtual seminar talk by Anders Hansen from the University of Cambridge. Delve into the paradox of universally unstable deep learning systems despite the Universal Approximation Theorem's guarantee of stable neural networks. Examine the parallels between current AI optimism and early 20th-century mathematical optimism, and consider how AI might face similar limitations. Investigate the existence of neural networks that approximate classical scientific computing mappings, yet cannot be computed accurately by any algorithm. Analyze the inherent instability in deep learning methodologies and its implications for classification problems. Address the concerning issue of AI-generated hallucinations in medical imaging challenges and its connection to instability. Gain insights into the mathematical setup of deep learning, universal instability theorems, and the challenges of training and computing neural networks. Read more