Explore differentiable functional programming in this Scala Days Berlin 2018 conference talk. Dive into parameterised functions, supervised learning, and gradient descent techniques. Understand deep learning as supervised learning of parameterised functions through gradient descent. Examine tensor multiplication, non-linearity, and algorithms for calculating gradients. Compare mathematician's and programmer's approaches to differentiation, including symbolic differentiation and automatic differentiation. Learn about dual numbers, forward-mode scaling, and the chain rule. Discover the importance of expressive type systems and compilation for GPU performance in implementing these concepts.