Daniel Murfet

Deep Learning Is Singular, and That's Good

Susan Wei, Daniel Murfet, Mingming Gong, Hui Li, Jesse Gell-Redman, Thomas Quella

Journal article  |  2022  |  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS

In singular models, the optimal set of parameters forms an analytic set with singularities, and a classical statistical inference ..

Cofree coalgebras and differential linear logic

James Clift, Daniel Murfet

Journal article  |  2020  |  MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE

We prove that the semantics of intuitionistic linear logic in vector spaces which uses cofree coalgebras is also a model of differ..

Encodings of Turing machines in linear logic

James Clift, Daniel Murfet

Journal article  |  2020  |  MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE

The Sweedler semantics of intuitionistic differential linear logic takes values in the category of vector spaces, using the cofree..

Logic and the 2-Simplicial Transformer

Daniel Murfet, James Clift, Dmitry Doyrn, James Wallbridge

Conference Proceedings  |  2020  |  International Conference on Learning Representations

We introduce the 2-simplicial Transformer, an extension of the Transformer which includes a form of higher-dimensional attention g..

The cut operation on matrix factorisations

Daniel Murfet

Journal article  |  2018  |  JOURNAL OF PURE AND APPLIED ALGEBRA

The bicategory LG of Landau–Ginzburg models has polynomials as objects and matrix factorisations as 1-morphisms. The composition o..

Adjunctions and defects in Landau Ginzburg models

Nils Carqueville, Daniel Murfet

Journal article  |  2016  |  ADVANCES IN MATHEMATICS

We study the bicategory of Landau-Ginzburg models, which has polynomials as objects and matrix factorisations as 1-morphisms. Our ..

On Sweedler's cofree cocommutative coalgebra

Daniel Murfet

Journal article  |  2015  |  JOURNAL OF PURE AND APPLIED ALGEBRA

We give a direct proof of a result of Sweedler describing the cofree cocommutative coalgebra over a vector space, and use our appr..

A Toolkit for Defect Computations in Landau-Ginzburg Models

Nils Carqueville, Daniel Murfet

Conference Proceedings  |  2015  |  Proceedings of Symposia in Pure Mathematics

Computing Khovanov-Rozansky homology and defect fusion

Nils Carqueville, Daniel Murfet

Journal article  |  2014  |  ALGEBRAIC AND GEOMETRIC TOPOLOGY

Residues and duality for singularity categories of isolated Gorenstein singularities

Daniel Murfet

Journal article  |  2013  |  COMPOSITIO MATHEMATICA

We study Serre duality in the singularity category of an isolated Gorenstein singularity and find an explicit formula for the dual..