Usage of geotorch in Hypernetwork about geotorch HOT 9 CLOSED

I do not think I fully understand the problem here. Can you provide a minimal working example of this behaviour?

from geotorch.

Hope this example explains what I am trying to do https://colab.research.google.com/drive/16hiNR8TO1M5uJvw_nTChGjWVtx6OsB3Y?usp=sharing

from geotorch.

Could you make the colab public?

from geotorch.

Sorry, does it work for you now?

from geotorch.

It does now, thanks. I'll take a look at it in a bit.

from geotorch.

Thought about the problem a bit more and it might be the best idea to just add the parameterization of the orthogonal matrix as part of the hyperparameter instead of doing as part of geotorch, (added it to the notebook). If you want you can close the Issue, Thank you for your quick help.
Ps:
Is the cayley or the matrix exponential representation more efficient?

from geotorch.

Hi, sorry, I have not had time to look into this today.
I just had a look, and it turns out that what's happening is that every time that you put the constraint, the constraint is initialised. Therefore the randomness. If you put an orthogonal constraint on a linear layer nn.Linear(3,3), the default weight from this layer is not orthogonal, and it is not clear which orthogonal weight it should be initialised to. As such, when you do geotorch.orthogonal(layer, "weight"), it initialises layer.weight to a randomly sampled orthogonal matrix. See:
https://geotorch.readthedocs.io/en/latest/orthogonal/stiefel.html#geotorch.Stiefel.sample
The sampling happens here (see line 22)
https://github.com/Lezcano/geotorch/blob/55a91ca973ddeeb12d193d464af4b23da93d5ab4/geotorch/constraints.py#L18-L23
I hope this helps you understanding a bit better the inner workings of GeoTorch! I think I should make this a bit more explicit somewhere.

If you do not like this behaviour, you can always initialise your layer to whichever orthogonal matrix you like by doing

layer = nn.Linear(3, 3)
geotorch.orthogonal(layer, "weight")
X = my_sampling_method(3, 3)
layer.weight = X

About the Cayley vs Exponential, the exponential map, as it is implemented in PyTorch, is more efficient than the Cayley map. That being said, I'd suggest you time them for the sizes that you are going to use with timit on a Jupyter notebook, just to be on the safe side.

from geotorch.

As a separate minor point, I would recommend you to use geotorch's methods over implementing them yourself, as they have a number of small optimisations and little quirks that you can benefit from at zero cost. It also has the advantage that it's more explicit with the intentions of what you want to do, but that's another story :)

from geotorch.

Thank you for your help, I thought that it was a problem like this with geotorch but I did not see how to fix it, now I should be able to bring it back into the code

from geotorch.