Matrix-Mimetic Tensor Algebra: Optimal Decompositions and Equivariant Learning

Lior Horesh presents tensor-tensor algebra designed to retain key properties of matrix algebra while representing multidimensional correlations. An Eckart–Young-like tensor representation theorem underpins computationally feasible, provably optimal decompositions. Matrix-mimetic operations allow existing computational workflows to be adapted to tensors. Examples include tensorized neural-network structures and tensor graph convolutional networks for time-evolving graphs. The discussion concludes with tensor group symmetries and extensions to equivariant learning.