Intrinsic Green's Learning: Supervised Learning on Manifolds via Inverse PDE

arXiv:2607.07034v1 Announce Type: new Abstract: 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.

Source: arXiv cs.LG — read the full report at the original publisher.

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