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, tensor networks also provide tools for compressing layers and approximating large computations. 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.

Think of it as replacing one enormous table with a small network of reusable relationships.