Tensor Operations

Documentation status: reference — see Maturity and evidence.

The tensor API exposes a common computation model over supported tensor representations.

Representation

• DenseTensor-style representations favor compact numerical layout.
• ConceptualTensor-style representations retain conceptual/sparse coordinates.

Conversions between them should be explicit.

Operation families

Typical operation families include:

• element-wise arithmetic;
• matrix and tensor products;
• reductions and statistics;
• activation functions;
• softmax and loss functions;
• normalization;
• slicing and concatenation;
• convolution-like operations;
• graph-oriented aggregation;
• forward/backward computation and gradient handling.

Computation graph

Operations can form a directed computation graph. Training-oriented execution records the information required for backward propagation where the operation and tensor types support it.

Mixed conceptual/dense execution

Use conceptual representations for semantic structure and dense representations for efficient numerical kernels. The boundary should be deliberate so that model meaning and performance choices remain distinguishable.