Constructing Large Orthogonal Minimally Aliased Response Surface Designs Through Enumeration and Combination of Weighing Designs

What the math gives to ML

The paper provides a constructive catalog of sparse ternary matrices whose exact row and column orthogonality gives norm-preserving linear maps at a fraction of dense-matrix cost. This structure can transfer to neural networks as sparse orthogonal channel mixers or as initialization and mask constraints for trainable sparse layers, supplying both cheap multiplication and a strong stability guarantee. The most promising first test is to replace selected dense MLP projections with block-diagonal weighing-design layers, while comparing fixed, trainable-on-a-fixed-support, and orthogonality-regularized variants.