Computes the Hessian of
funcwith respect to the arg(s) at index
argnumvia a forward-over-reverse strategy.
The forward-over-reverse strategy (composing
jacfwd(jacrev(func))) is a good default for good performance. It is possible to compute Hessians through other compositions of
Returns a function that takes in the same inputs as
funcand returns the Hessian of
funcwith respect to the arg(s) at
You may see this API error out with “forward-mode AD not implemented for operator X”. If so, please file a bug report and we will prioritize it. An alternative is to use
jacrev(jacrev(func)), which has better operator coverage.
A basic usage with a R^N -> R^1 function gives a N x N Hessian:
>>> from torch.func import hessian >>> def f(x): >>> return x.sin().sum() >>> >>> x = torch.randn(5) >>> hess = hessian(f)(x) # equivalent to jacfwd(jacrev(f))(x) >>> assert torch.allclose(hess, torch.diag(-x.sin()))
We’ve integrated functorch into PyTorch. As the final step of the integration, functorch.hessian is deprecated as of PyTorch 2.0 and will be deleted in a future version of PyTorch >= 2.3. Please use torch.func.hessian instead; see the PyTorch 2.0 release notes and/or the torch.func migration guide for more details https://pytorch.org/docs/master/func.migrating.html