Search papers, labs, and topics across Lattice.
This paper introduces Intrinsic Green's Learning (IGL), a novel framework that learns a target function on a manifold by modeling it as the solution to a linear partial differential equation (PDE) with a learned source term. IGL effectively reduces the complexity of high-dimensional integrals by leveraging low-rank tensor decompositions and a two-stage algorithm that separates coordinate discovery from source fitting. The approach not only achieves near-optimal classification performance on the MNIST dataset but also automatically recovers the intrinsic dimension of the manifold, showcasing its efficiency and effectiveness in supervised learning tasks.
IGL achieves near-optimal classification while automatically uncovering the intrinsic dimension of the manifold, challenging traditional approaches to supervised learning on complex data structures.
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 joint training. Learnable gates on each coordinate automatically discover the intrinsic dimension of the manifold. We validate IGL on synthetic manifolds and on MNIST, where it simultaneously achieves near-optimal classification and automatic recovery of the intrinsic dimension.
