172 citations · 796 across the 66 of their papers we have counts for
9 papers · 1 filter
Functorial aggregation
David I. Spivak, Richard Garner, Aaron David Fairbanks
We study polynomial comonads and polynomial bicomodules. Polynomial comonads amount to categories. Polynomial bicomodules between categories amount to parametric right adjoint func…
Deep neural networks as nested dynamical systems
David I. Spivak, Timothy Hosgood
There is an analogy that is often made between deep neural networks and actual brains, suggested by the nomenclature itself: the "neurons" in deep neural networks should correspond…
Regular Calculi I: Graphical Regular Logic
Tslil Clingman, Brendan Fong, David I. Spivak
What is ergonomic syntax for relations? In this first paper in a series of two, to answer the question we define regular calculi: a suitably structured functor from a category repr…
Dirichlet polynomials and entropy
David I. Spivak, Timothy Hosgood
A Dirichlet polynomial in one variable is a function of the form $d({\mathcal{y}})=a_n n^{\mathcal{y}}+\cdots+a_22^{\mathcal{y}}+a_11^{\mathcal{y}}+a_00^{\mathc…
Learners' Languages
David I. Spivak
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 func…
Wiring diagrams as normal forms for computing in symmetric monoidal categories
Evan Patterson, David I. Spivak, Dmitry Vagner
Applications of category theory often involve symmetric monoidal categories (SMCs), in which abstract processes or operations can be composed in series and parallel. However, in 20…