Inside Every Calculus Is A Little Algebra Waiting To Get Out
Because of deep learning, there has been a surge in interest in automatic differentiation, especially from the functional programming community. As a result, there are many recent papers that look at automatic differentiation from a Category Theory perspective. However, Category Theorists have already been looking at differentiation and calculus in general since the late ’60s in the context of Synthetic Differential Geometry, but it seems that this work is largely ignored by those interested in AD. In this talk, we will provide a gentle introduction to the ideas behind SDG, by relating them to dual numbers, and show how it provides a simple axiomatic and purely algebraic approach to (automatic) differentiation and integration. And no worries if you suffer from arithmophobia, there will be plenty of Kotlin code that turns the math into something fun you can play with for real.
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