Intrinsic Green's Learning: Supervised Learning on Manifolds via Inverse PDE
We introduce Intrinsic Green's Learning (IGL), a framework that models a target function on a manifold as the solution to a linear PDE whose source term is learned from data. Rather than approximating the target directly, IGL learns a source and integrates it against a Green's kernel. An encoder discovers a low-dimensional coordinate chart on the manifold where both the source and the kernel decompose as low-rank tensors, collapsing a high-dimensional integral into independent one-dimensional integrals with cost linear in the intrinsic dimension. A two-stage algorithm separates coordinate discovery from source fitting, a near-convex linear solve, preventing the dimensional collapse of joi...
| Authors | Alexandre Quemy |
|---|---|
| Primary category | cs.LG |
| Published | 8 July 2026 |
| Last updated at source | 8 July 2026 |
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