Tensorn

Tensorn is a term used in some mathematical and computational discussions to denote a generalized tensor-like object. It is not a standardized concept, and definitions vary across sources. In broad terms, a tensorn extends ordinary tensors by allowing additional indexing structures, such as dynamic or context-dependent modes, which can change with the problem setting or over time.

Conceptually, a tensorn can be described as a multi-dimensional array augmented with extra structural data that specifies how its modes interact or evolve. One common view is to represent a tensorn as either a standard multi-way array together with a meta-structure that governs mode configurations, or as a network of smaller tensorns connected by contraction operations. This flexibility aims to capture data or models where the dimensionality or alignment of modes is not fixed.

Core operations associated with tensorns resemble those of tensors and tensor networks. Contraction reduces the order by summing over shared indices, while tensorn products generalize outer products to accommodate the additional mode structure. Other operations, such as reshaping, splitting, and decompositions, may be defined in ways that respect the dynamic or context-specific aspects of the tensorn. In practice, variants may emphasize symmetry, sparsity, or specific transformation rules for certain modes.

Applications attributed to tensorns appear mainly in theoretical discussions of multilinear algebra and in exploratory work on high-order data representations, tensor networks in physics, and machine learning models that seek to generalize fixed-dimension tensors. Because the term is loosely used, concrete definitions and implementations are source-dependent.

See also: tensor, tensor network, hypermatrix, multilinear algebra.