VSAONLINE. SEASON 11. December 22, 20:00GMT. Tony Shaska.

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Dec 16, 2025, 6:51:34 AM12/16/25

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Dear all,

Welcome to the next talk of Season 11 on VSAONLINE. Tony Shaska, Oakland University , USA will give a talk

”Artificial Neural Networks on Graded Vector Spaces.”

Date: December 22, 2025

Time: 20:00 GMT

Zoom: https://ltu-se.zoom.us/j/65564790287

WEB: https://bit.ly/vsaonline

Abstract: This talk presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic properties of graded vector spaces, where features carry distinct weights, we extend classical neural networks with graded neurons, layers, and activation functions that preserve structural integrity. Grounded in group actions, representation theory, and graded algebra, our approach combines theoretical rigor with practical utility.

We introduce graded neural architectures, loss functions prioritizing graded components, and equivariant extensions adaptable to diverse gradings. Case studies validate the framework's effectiveness, outperforming standard neural networks in tasks such as predicting invariants in weighted projective spaces and modeling supersymmetric systems.

This work establishes a new frontier in machine learning, merging mathematical sophistication with interdisciplinary applications. Future challenges, including computational scalability and finite field extensions, offer rich opportunities for advancing this paradigm.