Standard Graph Neural Networks need curved semantic manifolds
Standard Graph Neural Networks are structurally constrained when mapping complex text attribution: linear aggregation in flat Euclidean space inevitably forces semantic drift. To map high-dimensional knowledge faithfully you have to transition to curved semantic manifolds, where the geometry itself carries the relational structure.
Across thirty years of building scientific analysis pipelines — genetics, satellite imagery, multi-continent high-resiliency financial applications — the through-line has been the same: representations must remain mathematically faithful to their underlying geometry, or they stop being interpretable the moment the data leaves your dev set.
I've recently open-sourced a framework that discovers emergent knowledge-graph relations in high-order semantic vector spaces through manifold learning and spectral analysis. Initial proofs, a small teaser, and the Python codebase live at paudley/nonlinear-semantic-graphs; the working paper that motivates the design is in Publications.
I'm looking to connect with researchers and applied scientists specialising in Topological Data Analysis, Geometric Deep Learning, and Knowledge Representation — especially anyone working on geodesic aggregation or spectral graph theory — to push these ideas into robust enterprise deployments. Comment on the LinkedIn original or drop me a line directly.
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