Small equivariant example

[DeNeutoy]

Hi @yilunliao,

Thanks for the nice codebase - I am adapting it for another purpose, and I was running into some issues when checking the outputs are actually equivariant. Are there any init flags that must be set in a certain way to guarantee equivariance?

I have a snippet equivalent to this:

import torch_geometric
import torch
from e3nn import o3
from torch_geometric.data import Data
from nets.equiformer_v2.equiformer_v2_oc20 import EquiformerV2_OC20

edge_index = torch.tensor([[0, 1, 1, 2],
                           [1, 0, 2, 1]], dtype=torch.long)
pos = torch.randn(10, 3)
data = Data(pos=pos, edge_index=edge_index)

R = torch.tensor(o3.rand_matrix())

model = EquiformerV2_OC20(
        num_layers=2,
        attn_hidden_channels=16,
        ffn_hidden_channels=16,
        sphere_channels=16,
        edge_channels=16,
        alpha_drop=0.0, # Turn off dropout for eq
        drop_path_rate=0.0, # Turn off drop path for eq
    )

energy1, forces1 = model(data)
rotated_pos = torch.matmul(pos, R)
data.pos = rotated_pos
energy2, forces2 = model(data)

assert energy1 == energy2
assert torch.allclose(forces1, torch.matmul(forces2, R), atol=1.0e-3)

and the energies are equal, but the forces do not obey equality under rotation. I've turned off all dropout and set the model to eval - just wondering if there are any other tricks to retain the genuine eq behaviour. Thanks!

[yilunliao]

Hi @DeNeutoy

Can you let me know how large the difference is?
After scanning over the code, can you also make sure you should compare this:

 assert torch.allclose(torch.matmul(forces1, R), forces2, atol=1.0e-3)

not this:

 assert torch.allclose(forces1, torch.matmul(forces2, R), atol=1.0e-3)

I think it is because force2 has input positions rotated, and therefore you have to rotate force2 back or rotate the output force1 before comparing the two force outputs.

Best

[DeNeutoy]

Thanks for the response @yilunliao - sorry, I was rotating the forces1 and comparing as you suggested - this was a bug in my snippet, but not my actual code. I dug into this a little and when I look at the nodes which are not correct, I see this:

print((forces1 == forces2).all(-1).all(-1))
tensor([False, False, False,  True,  True,  True,  True,  True,  True,  True])

indicating that it is only nodes which have edges that are affected. I then confirmed this by modifying the input graph, and only the receivers changes this, e.g:

senders = torch.tensor([0, 1, 2, 1, 2, 0])
receivers = torch.tensor([1, 0, 1, 2, 0, 4])
# Rerun, get:
tensor([False, False, False,  True, **False**,  True,  True,  True,  True,  True])

but changing the senders doesn't:

senders = torch.tensor([0, 1, 2, 1, 2, 4])
receivers = torch.tensor([1, 0, 1, 2, 0, 0])
# Rerun, get:
tensor([False, False, False,  True, True,  True,  True,  True,  True,  True])

I was wondering if this might alert you to something? I then started stepping through the code, and the embeddings are equal up until the edge degree embedding, but if I remove this, they are then unequal again after the TransBlockV2 stack.

For the node indices which don't match, the absolute difference is large:

print(torch.abs(forces1, forces2)[:3, :, :].mean())
1.0051

This is with a completely untrained model, although I wouldn't expect that to make a difference.

Any help is much appreciated!

[yilunliao]

@DeNeutoy

I see.

Can you make sure the results of edge-degree embeddings satisfy equivariance constraint?
Since this embedding only uses rotation and applies linear layers to m = 0 components, this is strictly equivariant and can be easily tested.

I have limited bandwidth until the weekend or next week but will look at this and provide another example. (Ping me if you have not heard from me)

[yilunliao]

@DeNeutoy

Sorry for the late reply.

Have you figured out the issue?
If no, can you please update me on what you think is the problem?

I have an incoming deadline, so I would be late to response, but I will make sure we can find the reason.

Best

[DeNeutoy]

Hi @yilunliao ,

I haven't, unfortunately. I tried looking into the edge degree embeddings, but it's not as simple as looking at a rotation of the input vectors - the edge_embedding outputs a SO3_embedding object, which internally has a _rotate method which is defined by the SO3_rotations + wigner matrices defined by the model's forward pass. So it was kind of unclear to me how to "unrotate" the embeddings.

If you had a small example, that would be helpful - but I understand if this is difficult to produce. These things are quite complex!

[yilunliao]

Hi @DeNeutoy .

Here is how we rotate the embedding back to the original coordinate after SO(2) linear layers:
https://github.com/atomicarchitects/equiformer_v2/blob/main/nets/equiformer_v2/so3.py#L452

Sure. I can provide a simple example to test that, but I will do that next weekend due to an incoming deadline.

Best

[BurgerAndreas]

Hi @yilunliao,

A small example would be extremely useful to build on your codebase!
Could you help us out?