Robustness, scalability and interpretability of equivariant neural networks across different low-dimensional geometries

Mitton, Joshua (2023) Robustness, scalability and interpretability of equivariant neural networks across different low-dimensional geometries. PhD thesis, University of Glasgow.

Abstract

In this thesis we develop neural networks that exploit the symmetries of four different low-dimensional geometries, namely 1D grids, 2D grids, 3D continuous spaces and graphs, through the consideration of translational, rotational, cylindrical and permutation symmetries. We apply these models to applications across a range of scientific disciplines demonstrating the predictive ability, robustness, scalability, and interpretability.

We develop a neural network that exploits the translational symmetries on 1D grids to predict age and species of mosquitoes from high-dimensional mid-infrared spectra. We show that the model can learn to predict mosquito age and species with a higher accuracy than models that do not utilise any inductive bias. We also demonstrate that the model is sensitive to regions within the input spectra that are in agreement with regions identified by a domain expert. We present a transfer learning approach to overcome the challenge of working with small, real-world, wild collected data sets and demonstrate the benefit of the approach on a real-world application.

We demonstrate the benefit of rotation equivariant neural networks on the task of segmenting deforestation regions from satellite images through exploiting the rotational symmetry present on 2D grids. We develop a novel physics-informed architecture, exploiting the cylindrical symmetries of the group SO+ (2, 1), which can invert the transmission effects of multi-mode optical fibres (MMFs). We develop a new connection between a physics understanding of MMFs and group equivariant neural networks. We show that this novel architecture requires fewer training samples to learn, better generalises to out-of-distribution data sets, scales to higher-resolution images, is more interpretable, and reduces the parameter count of the model. We demonstrate the capability of the model on real-world data and provide an adaption to the model to handle real-world deviations from theory. We also show that the model can scale to higher resolution images than was previously possible.

We develop a novel architecture which provides a symmetry-preserving mapping between two different low-dimensional geometries and demonstrate its practical benefit for the application of 3D hand mesh generation from 2D images. This models exploits both the 2D rotational symmetries present in a 2D image and in a 3D hand mesh, and provides a mapping between the two data domains. We demonstrate that the model performs competitively on a range of benchmark data sets and justify the choice of inductive bias in the model.

We develop an architecture which is equivariant to a novel choice of automorphism group through the use of a sub-graph selection policy. We demonstrate the benefit of the architecture, theoretically through proving the improved expressivity and improved scalability, and experimentally on a range of widely studied benchmark graph classification tasks. We present a method of comparison between models that had not been previously considered in this area of research, demonstrating recent SOTA methods are statistically indistinguishable.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• Colleges/Schools: College of Science and Engineering > School of Computing Science
• Supervisor's Name: Murray-Smith, Professor Roderick
• Date of Award: 2023
• Depositing User: Theses Team
• Unique ID: glathesis:2023-83517
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 03 Apr 2023 09:58
• Last Modified: 03 Apr 2023 09:59
• Thesis DOI: 10.5525/gla.thesis.83517
• URI: https://theses.gla.ac.uk/id/eprint/83517

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