  The classical Clarke subdifferential alone is inadequate for understanding
automatic differentiation in nonsmooth contexts. Instead, we can sometimes rely
on enlarged generalized gradients called "conservative fields", defined through
the natural path-wise chain rule: one application is the convergence analysis
of gradient-based deep learning algorithms. In the semi-algebraic case, we show
that all conservative fields are in fact just Clarke subdifferentials plus
normals of manifolds in underlying Whitney stratifications.
