Towards Auditable by Construction Networks through the Elliptic Operator Lens

Alastair Poole (University of Strathclyde)

Thursday 16th July 14:00-15:00
Maths 311B

Abstract

Neural networks are notoriously difficult to audit by dint of their architecture. For high-value manufacturing this is an essential block to adoption, and one hardening through legislation such as the EU AI Act. We present a research arc that reframes learning around elliptic operator interpretations of the data, replacing dense and opaque internals with objects whose rules and behaviours are well established and open to interpretation. Building upon these, we work with sheaf Laplacians and the richer information they provide, such as domain connectivity, where a domain would fail first, and how far a new input sits from the training data. The approach has held up in practice. Our compact networks have matched standard accuracy with 64 parameters in place of 775, weld-flaw sizing trained purely on simulation has transferred to experimental inspections equipped with a label-free accuracy estimation metric, and a generalised sheaf-Laplacian operator has run unchanged on grid, graph, and curved-surface domains, competitive with tuned Fourier neural operators while returning the learned domain's intrinsic operators. The goal is a unified framework that learns well conditioned structure that humans can learn to understand, and so be more readily validated and deployed in industrial contexts. We will present the work to date, its applications to manufacturing and inspection scenarios, and the open questions we want to develop further.

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