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Watch a keynote presentation from POPL'18 exploring the foundational principles of differentiable programming languages with first-class differentiation operators. Delve into the semantics of a simple first-order functional programming language that incorporates reals, product types, and reverse-mode differentiation. Learn how smooth multivariate functions with open domain are employed in programming constructs like conditionals and recursion, and discover how they form complete partial orders suitable for fixed-point methods. Explore the challenges of implementing sum types and recursive types in differentiable programming, and understand the concepts of shapely datatypes and smooth functions that bridge this gap. Gain insights into the intersection of programming language foundations and real analysis, particularly relevant for deep learning applications that utilize gradient descent optimization methods for neural network weight selection. The presentation connects the historical context of automatic differentiation from the 1960s to modern applications in deep learning while highlighting opportunities for further foundational study in this emerging field.
