
TL;DR
This paper explores the categorical structures underlying deep learning, connecting gradient descent and backpropagation to polynomial functors and dynamical systems, and discusses their logical and theoretical implications.
Contribution
It demonstrates that categories of learners relate to polynomial functors and dynamical systems, providing a new categorical perspective on deep learning mechanisms.
Findings
Slens is a full subcategory of Poly, linking lenses to polynomial functors.
Maps in Para(Slens) correspond to generalized Moore machines.
The category p-Coalg forms a topos, enabling logical reasoning about dynamical systems.
Abstract
In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)Learn from the category of parameterized Euclidean spaces to that of learners, a category developed explicitly to capture parameter update and backpropagation. It was soon realized that there is an isomorphism LearnPara(Slens), where Slens is the symmetric monoidal category of simple lenses as used in functional programming. In this note, we observe that Slens is a full subcategory of Poly, the category of polynomial functors in one variable, via the functor . Using the fact that (Poly,) is monoidal closed, we show that a map in Para(Slens) has a natural interpretation in terms of dynamical systems (more precisely, generalized Moore machines) whose…
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