tensorach

Tensorach is a term used in mathematical and computational literature to denote a generalized tensor object that extends conventional tensors with an auxiliary annotation channel. The annotation channel, abbreviated ach, stores metadata, contextual weights, or alignment information associated with each tensor element. A tensorach of order n is indexed by n tensor indices together with an annotation index, effectively forming a tensor of shape I1 × I2 × ... × In × A, where A is the size of the annotation axis.

Formally, a tensorach behaves as a multilinear object in the original vector spaces and supports standard tensor operations such as contraction and outer product. In addition, it admits specialized projection or fusion operations that collapse the annotation axis or project it into a fixed vector, enabling compatibility with conventional tensor libraries.

Applications for tensoraches are discussed in speculative or experimental contexts, including multi-modal data fusion, relational reasoning in neural networks, and physics-inspired models where metadata and context play a central role. Proponents argue that the annotation channel can improve interpretability by exposing auxiliary information alongside numeric values, though it also adds computational overhead.

History and status: The term tensorach emerged in the 2020s in exploratory literature on generalized tensor representations. It has not achieved standardization or widespread consensus and remains mainly a topic of theoretical investigation and early-stage prototypes.

Related concepts include tensors, multilinear algebra, tensor networks, and tensor augmentations.