mathematics//tensor network

A tensor network represents a high-dimensional tensor as a graph of smaller tensors whose connected indices are contracted. The factorization can expose structure that would be impossibly expensive to store in one dense array.

A tensor network represents a high-dimensional tensor as a graph of smaller tensors whose connected indices are contracted. The factorization can expose structure that would be impossibly expensive to store in one dense array.

Originally prominent in many-body physics, where they were developed to represent quantum states (the machinery many quantum-inspired algorithms borrow), tensor networks also provide tools for compressing layers and approximating large computations: in model compression a tensor factorization replaces dense weights with a smaller structured representation. Their usefulness depends on whether the target tensor has a compact low-rank structure. A beautiful factorization with the wrong rank simply moves the cost into contraction.

A tensor network replaces one enormous table with a small network of reusable relationships.