Working vocabulary

Term	Meaning
Derivative tower	Values of an activation and successive ordinary derivatives
Directional jet	Taylor coefficients along a selected direction; row k contains derivative divided by k!
Mixed jet	Coefficients D^alpha f / alpha! indexed by multi-index
Contraction	A requested aggregate such as the Hessian trace, computed without storing every tensor entry
Bias collapse	A normalized, weighted shift limit as delta tends to zero, yielding a derivative
Temperature hardening	A smooth decision becoming sharper as inverse temperature increases
Parameter autodiff	Differentiation of the training loss with respect to model parameters
Closed form	An analytic expression, whose floating-point evaluation can still have numerical error
Certificate	A checked statement about a specified quantity, domain, model, and assumptions
Release candidate	A prerelease version requiring explicit compatibility checks

See numerical scope and the learning paths.