A Symmetry-Preserving Tensor $\star_{\mathbf{M}}$-SVD

What the math gives to ML

The paper gives a constructive tensor factorization that preserves bilateral reflection symmetry while retaining the matrix-SVD-like decomposition and Frobenius error behavior. Its transferable asset is the ability to constrain a learned low-rank basis to a symmetry subspace and remove redundant parameters without flattening spatial or temporal modes. A practical neural-network adaptation is a symmetry-preserving low-rank feature layer or adapter: transform a tensor along its third mode, project each frontal slice into the reflection-invariant subspace, compute truncated SVD factors, and reconstruct the full basis on demand. This is most promising for image, video, medical-imaging, and object-recognition models with bilateral symmetry.