Complexity depends on the representation

Choose the quantity before choosing the differentiation strategy.

Representation	What grows
Activation derivative polynomial	Arithmetic grows with derivative order
Directional Taylor jet	Coefficients grow with retained order and directions
Full mixed jet	binomial(dim + order, order) coefficients
Dense spatial Hessian	Quadratic output size in input dimension
Direct deep Laplacian	For fixed widths and depth, work and memory grow with input dimension
Deep repeated Laplacian	Exact support enumeration has a configured budget; automatic mode can report an estimator

Avoid claiming constant total cost in dimension or derivative order. Reusing a weight norm or base activation removes repeated work but does not remove all input processing or polynomial arithmetic.

Read the detailed guarantees and measured results.