A Sub-linear Low-Rank Solver for Poisson's Equation using Machine Learning Frameworks for GPU Acceleration

What the math gives to ML

The paper provides a concrete cross-approximation factorization in which a matrix is reconstructed from a small set of rows, columns, and the pseudoinverse of their intersection. This is transferable to neural-network compression because a dense weight matrix or activation map can be replaced by thin factors while retaining direct access to selected entries instead of computing a full SVD. The most promising adaptation is an adaptive, warm-started CUR layer whose row and column indices are selected using residual statistical leverage scores and refreshed during fine-tuning. Its main potential is reducing parameter memory and matrix-multiplication cost for layers that are numerically low rank, although the extracted text does not provide enough detail to assess the full Cross-DEIM convergence guarantees.