12 papers
Mutation-acyclicity in rank four is decidable but not semialgebraic
Kymani T. K. Armstrong-Williams, Edward Hirst, Blake Jackson +1
We prove that mutation-acyclicity of quivers on four vertices is decidable. If a four-vertex quiver is mutation-acyclic, then some sequence of mutations takes it to an acyclic…
Optimal Pruning for Neural Architectures using Fisher Information Distances
David S. Berman, Yen-Yu Fu, Edward Hirst +1
A new scheme for parameter pruning is introduced, derived from the differential-geometric distance in model space. Pruning a parameter sets its value to zero, representing a displa…
Black Hole Black Boxes: Numerical Black Hole Metrics via AInstein Neural Networks
Tancredi Schettini Gherardini, Edward Hirst, Alexander George Stapleton
The AInstein architecture introduced an unsupervised neural method for solving the Riemannian Einstein equations on arbitrary manifolds. This Physics Informed Neural Network approa…
PINNs in More General Geometry
Edward Hirst
Neural architectures trained with losses inspired by differential conditions are the basis for PINN models. Since many constructions in differential geometry may be framed as minim…
Minimising Willmore Energy via Neural Flow
Edward Hirst, Henrique N. Sá Earp, Tomás S. R. Silva
The neural Willmore flow of a closed oriented -surface in is introduced as a natural evolution process to minimise the Willmore energy, which is the squared …
Versor: A Geometric Sequence Architecture
Truong Minh Huy, Edward Hirst
A novel sequence architecture is introduced, Versor, which uses Conformal Geometric Algebra (CGA) in place of traditional linear operations to achieve structural generalization and…
A Machine Learning Approach to the Nirenberg Problem
Gianfranco Cortés, Maria Esteban-Casadevall, Yueqing Feng +4
This work introduces the Nirenberg Neural Network: a numerical approach to the Nirenberg problem of prescribing Gaussian curvature on for metrics that are pointwise conformal…
Approximate Gaussianity Beyond Initialisation in Neural Networks
Edward Hirst, Sanjaye Ramgoolam
Ensembles of neural network weight matrices are studied through the training process for the MNIST classification problem, testing the efficacy of matrix models for representing th…
Grokking vs. Learning: Same Features, Different Encodings
Dmitry Manning-Coe, Jacopo Gliozzi, Alexander G. Stapleton +4
Grokking typically achieves similar loss to ordinary, "steady", learning. We ask whether these different learning paths - grokking versus ordinary training - lead to fundamental di…
AInstein: Numerical Einstein Metrics via Machine Learning
Edward Hirst, Tancredi Schettini Gherardini, Alexander G. Stapleton
A new semi-supervised machine learning package is introduced which successfully solves the Euclidean vacuum Einstein equations with a cosmological constant, without any symmetry as…
Machine Learning Mutation-Acyclicity of Quivers
Kymani T. K. Armstrong-Williams, Edward Hirst, Blake Jackson +1
Machine learning (ML) has emerged as a powerful tool in mathematical research in recent years. This paper applies ML techniques to the study of quivers -- a type of directed multig…
Calabi-Yau Links and Machine Learning
Edward Hirst
Calabi-Yau links are specific -fibrations over Calabi-Yau manifolds, when the link is 7-dimensional they exhibit both Sasakian and G2 structures. In this invited contribution…