Question on eSCN

[liangzhixin-202169]

Hello, I have a question about eSCN.
I have read the section "A.3 ESCN CONVOLUTION" of your paper, and I wonder is there an implicit condition for the summation running the irreps order L_i and L_f? More specifically, assuming tensor product "1ox(0e+1o+2e)", I want to consider "1o" as output irreps. So, how does equiformerv2 distinguish the odd irreps "1o" that comes from "1ox(0e+2e)" and even irreps "1e" that comes from "1ox1o"?

[yilunliao]

Hi @liangzhixin-202169

Please see my responses below.

1. I have read the section "A.3 ESCN CONVOLUTION" of your paper, and I wonder is there an implicit condition for the summation running the irreps order L_i and L_f?

Yes, your understanding is right. The paper/implementation of EquiformerV2 only consider the case of SE(3). So if you need parity or E(3), you would need to restrict how L_i and L_f interact.

2. So, how does equiformerv2 distinguish the odd irreps "1o" that comes from "1ox(0e+2e)" and even irreps "1e" that comes from "1ox1o"?

In this implementation (as well as the implementation of eSCN), we do not consider the parity and the irreps would be like 1x0e+1x1e+1x2e... (no "o"). You would have to keep two copies of irreps (one for even and one for odd) so that you can use something like 1x0e+1x0o...
It should be straightforward to do that, and I think the idea of rotating features holds for both even and odd irreps.

Feel free to let me know if you have any other question.

[liangzhixin-202169]

Thank you for your reply!
Do you mean to use even parity irreps for node feature, and "0e+1o+2e+..." for relative position projection?

[yilunliao]

The node features can have both even and odd irreps like (1x0e+1x0o+1x1e+1x1o...) while the relative positions are of 1x0e+1x1o+1x2e... if E(3) is considered.

[liangzhixin-202169]

I am sorry to reply so late, but I am still confusion about the implementation of so(2) convolution. The type-L irreps_out from so(3)'s tensor product is a mixture of type-(L,e) and type-(L,o) irreps from the perspective of o(3), right? Therefore equilformerV2 considering se(3) only do not need to distinguish parity?

[yilunliao]

Yes, I think what you said are correct.