7 papers
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…
Disconnection Rules are Complete for Chemical Reactions
Ella Gale, Leo Lobski, Fabio Zanasi
We provide a category theoretical framework capturing two approaches to graph-based models of chemistry: formal reactions and disconnection rules. We model a translation from the l…
Quantitative Monoidal Algebra: Axiomatising Distance with String Diagrams
Gabriele Lobbia, Wojciech Różowski, Ralph Sarkis +1
String diagrammatic calculi have become increasingly popular in fields such as quantum theory, circuit theory, probabilistic programming, and machine learning, where they enable re…
A Fibrational Theory of First Order Differential Structures
Matteo Capucci, Geoffrey S. H. Cruttwell, Neil Ghani +1
We develop a categorical framework for reasoning about abstract properties of differentiation, based on the theory of fibrations. Our work encompasses the first-order fragments of…
Learning Closed Signal Flow Graphs
Ekaterina Piotrovskaya, Leo Lobski, Fabio Zanasi
We develop a learning algorithm for closed signal flow graphs - a graphical model of signal transducers. The algorithm relies on the correspondence between closed signal flow graph…
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…
A Categorical Model for Retrosynthetic Reaction Analysis
Ella Gale, Leo Lobski, Fabio Zanasi
We introduce a mathematical framework for retrosynthetic analysis, an important research method in synthetic chemistry. Our approach represents molecules and their interaction usin…