👉 Tensor Networks (TN) is a mathematical framework used to represent and manipulate high-dimensional tensors, which are multi-dimensional arrays often encountered in physics, machine learning, and signal processing. By decomposing these tensors into a network of interconnected, lower-dimensional tensors (called "blocks"), TN provides an efficient way to store and compute complex multi-linear relationships. This decomposition reduces computational complexity, making it feasible to handle problems that would otherwise be intractable due to the sheer size of the tensors. Tensor Networks are particularly useful in quantum information theory for modeling quantum states and operations, in deep learning for capturing hierarchical features in data, and in numerical simulations for solving partial differential equations. The key idea is to exploit the structure of tensors to perform operations like contraction and tensor multiplication more efficiently, often leading to significant reductions in computational resources and time.
