Algebraic Operations on Tensor Trains (opens in new tab)

The tensor train (TT) model is widely used to approximate high-dimensional tensors, enabling efficient handling of data that may exceed available memory. TT helps address the curse of dimensionality in applications such as system identification and dynamic programming. In some applications, TT is known as a ``matrix product state" (MPS). This paper introduces algorithms that facilitate the summation, Hadamard (elementwise) product, and matrix--v...