Does tutorial 2 use the Theseus derivatives through the NLLS? (Or just through the objective?)

This tutorial parameterizes a quadratic ax^2+b with a optimized by PyTorch autograd and b optimized with the Theseus NLLS for a given a. The key piece that enables a to be learned is that we pass it back into the same cost function the NLLS optimizer uses except we take a gradient step of the cost function w.r.t. a, which doesn’t use the derivative information of how b was computed through the NLLS optimizer:

Thus if I understand correctly, this tutorial isn’t using the derivatives through the NLLS optimization process. To try to understand this better, I added a torch.no_grad call around the NLLS optimizer to block the gradients through it and it didn’t change the output and it was still able to fit the quadratics:

\cc @vshobha @mhmukadam @luisenp

[mhmukadam]

Thanks for flagging @bamos and everyone for the discussion. Let’s follow @vshobha’s proposal, we’ll merge the edits to T2 that clarify the language, and add new tutorials to demonstrate the ideas above before closing this issue. Later we can see if it makes sense to consolidate any if they flow well together.

[vshobha]

The goal of Tutorial 2 is to show the user how you can differentiate through the TheseusLayer abstraction. Since this example does not differentiate through the optimization itself, I’d suggest we just change the intro/title to simplify. As it is, it makes the point that we can create a TheseusLayer and differentiate through it. What actually gets ends up getting differentiated is under the hood from the user’s perspective – in this case, it turns out that differentiation through the optimization is not needed.

As for showcasing how to differentiate through the optimization, maybe we could do the following:

• A new tutorial showing what @bamos and @luisenp have in mind (it is still difficult to understand the details of why Theseus is necessary for this example through the comments)
• A separate new tutorial showing how a computation with multiple optimizations use the NLLS.