Conceptual Tensors

Documentation status: reference — see Maturity and evidence.

A conceptual tensor connects tensor-like computation to explicit conceptual axes and sparse semantic structure.

Key idea

Instead of treating every position as an anonymous numeric coordinate, a conceptual tensor can associate dimensions or entries with conceptual identities.

Compared with dense tensors

Dense tensor
  regular numerical layout
  efficient vectorized operations

Conceptual tensor
  semantic/sparse structure
  explicit conceptual coordinates

Training and computation

Conceptual tensors can participate in computation when the supported operation can preserve or project their structure. When a dense kernel is required, materialize an explicit dense projection rather than silently dropping semantic axes.

Preferred uses

• sparse feature spaces;
• graph/hypergraph structures;
• conceptual adjacency or incidence representations;
• models where provenance of tensor coordinates matters;
• hybrid symbolic/neural computation.