Unifying singular value decompositions of tensors via aligned orthogonality

What the math gives to ML

The paper develops a higher-order analogue of SVD in which tensor rank-one terms are simultaneously aligned with singular-vector bases of tensor flattenings. Its transferable asset is the combination of mode-wise orthogonality, shared indexing across tensor factors, identifiable structured decompositions, and truncation as a critical low-complexity approximation. This suggests tensorized neural layers whose factors remain aligned and orthogonal, enabling principled rank pruning rather than arbitrary CP or Tucker compression. The most practical first test is replacing a dense linear or convolutional layer with an aligned orthogonal tensor factorization and measuring accuracy at equal parameter count and inference FLOPs.