Tensor Product

Tensor products are mathematical operations combining multiple vectors or matrices into higher-dimensional tensors, enabling efficient representation and manipulation of multiway data. Current research focuses on developing computationally efficient tensor-tensor products, improving tensor decompositions for various applications (e.g., image alignment, multimodal data fusion), and leveraging tensor products within neural network architectures (e.g., Tensor Product Representations, MIONet) to enhance model expressiveness and systematic generalization. These advancements are significantly impacting fields like signal processing, machine learning, and scientific computing by providing improved methods for data analysis, model building, and algorithm design.