equistore operation dot does not support gradients

[agoscinski]

Is there a reason why it is not supported? Because the error message specifically talks about the second tensor map
https://github.com/lab-cosmo/equistore/blob/e65cd07d2f0d5aefa41a7b2beade835b9b1dc03b/python/src/equistore/operations/dot.py#L49
and then the values and gradients are dotted together
https://github.com/lab-cosmo/equistore/blob/e65cd07d2f0d5aefa41a7b2beade835b9b1dc03b/python/src/equistore/operations/dot.py#L63
I cannot make sense out of it

[Luthaf]

The second tensor map is the "weights" in x = dot(A, w), so there are no gradients associated with them for now. We could add support for gradients on both sides of a dot, but that might require adding support for double gradients in equistore (to store dot(grad A, grad w))

[agoscinski]

Ah I see, I feel like this operation alone is too limiting, but I need to think about this more. Seems to be far from trivial to extend it in an understandable way.

But regarding this issue, could we just add a bit of documentation for this? like this one

    Computes the dot product of two :py:class:`TensorMap` using the values of B
    for the matrix product with A and its gradients

    .. math::
       C = A @ B
       ∇C = ∇A @ B

[Luthaf]

Adding more documentation works for me!

[agoscinski]

Should I do a separate PR for this? Seems it could be also added to #91

[Luthaf]

This is more about API documentation than user tutorials/explanation, so I would do it in a quick separate PR.

[ceriottm]

Imo adding support for gradients shouldn't be too hard. If B does not have gradients, then grad(A.B) is grad(A).B, if B also has gradients then it's grad(A).B + A.grad(B).