There are currently many applications of Topology to AI, primarily to ML, particularly applications of Algebraic Topology.
But in the case of (General) Topology in finite spaces applied to AI: are there any current problems rigorous enough for a doctoral thesis?
Isaiah Oluwasegun Owolabi
Yes—finite topological spaces like Alexandrov topology can model explainability in Graph Neural Networks, using closure and continuity to analyze learning behavior. It’s a rigorous and novel path linking topology with interpretable AI.
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Rey Segundo Guerrero-Proenza
Isaiah Oluwasegun Owolabi Do you know any example of that kind of application, or you have some reference related to this topic?
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Isaiah Oluwasegun Owolabi
“An Alexandrov Topology on Graphs” – Shows how Alexandrov spaces can be applied to graph structures, relevant for connecting finite topology to GNNs. 🔗 https://www.researchgate.net/publication/288410055_An_alexandroff_topology_on_graphs “A Survey on Explainability of Graph Neural Networks” – Offers a broad overview of GNN explainability methods that can be extended with topological tools. 🔗 https://arxiv.org/abs/2306.01958
Yes, here are two useful references:
Both should provide a good foundation if you're exploring this topic further.
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