TFExpression

TFExpression is a conceptual abstraction used in TensorFlow-inspired machine learning workflows to represent a computable mathematical expression whose operands are tensors or other expressions. It enables building, manipulating, and evaluating expressions within a dataflow graph or eager execution context.

Structure: A TFExpression typically comprises a root operator and a tree of operands. Leaves can be literal constants, input tensors, or parameter variables. Internal nodes represent operations such as arithmetic, linear algebra, or activation-like functions. Expressions may carry metadata for shapes, dtypes, and broadcasting rules.

Evaluation and differentiation: TFExpression expressions can be evaluated by supplying concrete tensor values for the leaves, producing a result tensor. They can be compiled into executable graphs for optimized runtime. If the framework supports automatic differentiation, TFExpression graphs can propagate gradients to enable backpropagation and training.

Optimization and transformation: TFExpression can be subjected to algebraic simplifications, common-subexpression elimination, or operator fusion to improve performance. They also allow symbolic transformations, such as rewriting expressions for numerical stability or implementing different backends.

Relation and usage: TFExpression sits alongside other concepts such as computational graphs, symbolic math, and autodiff engines. It is used by model builders to express computations in a modular, composable way and to facilitate portability across devices and backends.