16 citations · 32 across the 9 of their papers we have counts for
10 papers
Metacat: a categorical framework for formal systems
Paul Wilson
We present a categorical framework for formal systems in which inference rules with metavariables over a category of syntax , taken to be a cartesian PROP, are rep…
Convergence for Discrete Parameter Update Schemes
Paul Wilson, Fabio Zanasi, George Constantinides
Modern deep learning models require immense computational resources, motivating research into low-precision training. Quantised training addresses this by representing training com…
Deep Learning with Parametric Lenses
Geoffrey S. H. Cruttwell, Bruno Gavranovic, Neil Ghani +2
We propose a categorical semantics for machine learning algorithms in terms of lenses, parametric maps, and reverse derivative categories. This foundation provides a powerful expla…
Data-Parallel Algorithms for String Diagrams
Paul Wilson, Fabio Zanasi
We give parallel algorithms for string diagrams represented as structured cospans of ACSets. Specifically, we give linear (sequential) and logarithmic (parallel) time algorithms fo…
Categories of Differentiable Polynomial Circuits for Machine Learning
Paul Wilson, Fabio Zanasi
Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on trainin…
String diagrams for Strictification and Coherence
Paul Wilson, Dan Ghica, Fabio Zanasi
Whereas string diagrams for strict monoidal categories are well understood, and have found application in several fields of Computer Science, graphical formalisms for non-strict mo…
Category Theory in Machine Learning
Dan Shiebler, Bruno Gavranović, Paul Wilson
Over the past two decades machine learning has permeated almost every realm of technology. At the same time, many researchers have begun using category theory as a unifying languag…
The Cost of Compositionality: A High-Performance Implementation of String Diagram Composition
Paul Wilson, Fabio Zanasi
String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have b…
Categorical Foundations of Gradient-Based Learning
G. S. H. Cruttwell, Bruno Gavranović, Neil Ghani +2
We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides…
Reverse Derivative Ascent: A Categorical Approach to Learning Boolean Circuits
Paul Wilson, Fabio Zanasi
We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differenti…