Successive Schur-Riesz Analysis for Approximation

What the math gives to ML

The paper's transferable asset is a representation-stable way to enlarge nested approximation spaces when coefficient blocks are redundant or strongly correlated. It first quotients coefficient vectors that produce the same function, then measures each new block only through the component orthogonal to the previously generated space; the corresponding block Schur complement gives the intrinsic new dimension and approximation gain. This suggests an adaptive neural architecture that adds feature, adapter, or expert blocks only after removing directions already represented by existing blocks, while using singular-value thresholds to eliminate parameter redundancy. The extracted material does not include the paper's full Riesz-bound theorem, so the most defensible transfer is an implementable empirical orthogonal-innovation module rather than a claimed convergence guarantee.