Robust Hierarchical Matrix Compression of Acoustic Volume and Boundary Integral Operators

What the math gives to ML

The paper provides a practical robustness mechanism for adaptive low-rank matrix compression when the full matrix is unavailable or too expensive to inspect: augment cross approximation with structured extra entries, monitor residuals on those entries, and require sustained convergence rather than trusting a single partial error estimate. This is transferable to blockwise low-rank compression of neural-network weight matrices or attention kernels, where an incorrectly terminated approximation can silently create large task-relevant errors. The strongest initial experiment is a memory-oriented low-rank linear layer whose ACA stopping rule uses O(m+n) probes and a patience condition, comparing accuracy and memory against standard randomized SVD or fixed-rank factorization.