Graph convolutions are not invariant under the symmetric group action

Permuting the atom order leads to different output probabilities. In this case I’ve permuted the ordering of the atoms in strychnine and a miyazaki graph about 1000 times using the following code, then ran it through deepchem in prospective mode to compare the output probabilities. For miyazaki graphs this discrepancy becomes significantly larger (you’ll also have to trust me that they’re the same graph 😃)

The code used to permute and generate the smiles:

with open("debug.csv", "w") as oh:
    writer = csv.writer(oh)
    writer.writerow(["smiles","cmpdId"])
    for k in range(10):
        ans = list(range(mol.GetNumAtoms()))
        random.shuffle(ans)
        nm = rdmolops.RenumberAtoms(mol, ans)
        newSmi = Chem.MolToSmiles(nm, isomericSmiles=True, canonical=False)
        writer.writerow([newSmi,"111"])

Note that I’ve fixed the random seed to a constant in all test runs. The results are listed as smiles, [true_proba, false_proba]. They’re supposed to be the same.

Test case 1:

Strychnine:

C12=CCO[C@H]3CC(=O)N4[C@H]5[C@H]3[C@H]1C[C@@H]1N(C2)CC[C@@]15c1ccccc14 [ 0.95647782  0.04352212]
N12C(=O)C[C@@H]3OCC=C4CN5CC[C@@]6([C@@H]1[C@H]3[C@H]4C[C@H]56)c1ccccc12 [ 0.95647794  0.04352212]

Test case 2:

Miyazaki graph

C1~C234~C5~C~26~C2~C7~C8~C9~C%10~C%11~C~7~C7(~C%12~C(~C%13~C%14~C~9%15%16~C9%17~C~%15~C%15~C%18(~C%19~C%20~C~9~C9~C%21~C%22~C~%20~C%20~C%23%24%25~C~C~C~%22%26(~C%22~C~%26%27~C%26~C%28~C%29~C%30~C%31%32%33~C%34~C%35~C%36(~C~%35%37(~C~C~%31)~C~%29~C%29~C%31~C~%27~C%27~C(~C~%26~C~%30~C~%37~C~%27~C~%32~%29)~C~%23(~C~%28~%31)~C~%24~%22)~C%22~C%23~C%24~C~%33~%34~C%26~C~%22~C%22~C%27~C%28%29%30~C~C~C%31%32(~C%33%34~C%35~C%37~C%38~C%39~C%40~C%41~C%42%43%44~C%45%46~C%47~C%48~C%49~C%50~C~%45~C%45~C%51~C%52~C%53%54%55~C~C~C%56%57(~C(~C~%48~C~%53~C~%50~C~%51~%56)~C~%52~C~%47~C~%45~C~%49%45~C(~C~%45%47(~C~%40~C%40~C(~C~%39~%33)~C(~C~%35~C(~C~%40~%42)~C~%47~C~%41~%37)~C~%28~%38~C~%29~C~%31~%34)~C~C~%43)~C~%46~%44)~C%28~C~%57%29~C%31~C%33~C%34~C%35~C%37~C%38~C~%33~C%33~C%39~C~%31~C(~C(~C~%35~%29)~C%29~C~%37~C~%33%31%35~C%33~C%37~C%40(~C%41~C%42~C%43~C%44~C~%40~C~%44~C(~C~%33~%31~%43)~C~%41~%42)~C~%38~%37(~C~C~%35)~C~%39~%29)~C~%54~%34~C~%55~%28)~C(~C%28~C~%30~C(~C~%26~C~%36~C~%28~%24)~C~%32~%22)~C~%23~%27)~C%22~C~%20~C~%19~C~%17~C(~C~9~%18)~C~%22~C~%25~%21)~C~%15(~C~8~C~%14~C~2~%12)(~C~%10~%13)~C~C~%16)~C~%11~6)~C2(~C6~C8~C~3~C3~C9~C%10~C%11%12~C%13~C%14~C%15(~C%16~C(~C~6~C~4~C(~C~%10~%16)~C~3~2)~C~%11~C~8~C~9~%15)~C~%1423~C4~C6~C8~C9~C~2~C2~C(~C~4~C4~C%10~C~6~C6~C~9~C9~C~2~C~4~C~62~C46%11~C%14~C%15~C~%14~C%14~C%16~C~4~C~%16~C~%15~C~%144(~C~C~6)~C(~C~%10~4~9)~C~%11~2)~C~8~%12~%13~C~C~3)(~C~5~7)~C~1 [ 0.96809512  0.03190488]
C12~C3~C4~C5~C6~C7~C89~C%10%11%12~C%13~C%14~C%15~C%16~C%17~C%18~C%19%20~C%21%22%23~C%24~C%25~C%26~C~%25~C~%21~C%21~C(~C~%26%25(~C(~C~%25%26~C(~C%25~C~%19~C(~C(~C(~C~%15%19(~C(~C~5~%19~C5~C(~C~4~8)~C4~C8~C(~C(~C%15%19(~C%27%28~C%29~C%30~C%31~C%32~C%33~C%34~C%35%36%37~C%38%39~C~%35~C%35~C%40(~C~C~%36)(~C(~C%36~C~%29~C(~C(~C(~C~%36~%37)~C~%33~%40)~C~%32~%27)~C~%31%27~C(~C~%28~%15)~C~1~8~%27~C~C~%19)~C~%30~%34)~C~%351~C8~C%15~C~%38~C%19~C%27~C%28~C%29~C%30~C(~C%31~C~%28%32%33~C~C~C~%30%28(~C%30%34~C%35~C%36~C%37~C%38~C%40~C%41~C~%36~C~%32(~C%32~C(~C%36~C%42~C(~C~%37~C%37%43(~C%44~C%45~C%46(~C%47~C%48~C%49~C~%44~%37~C%37~C%44~C~%46~C~%49~C%46~C%49~C%50%51%52~C%53~C(~C(~C%54(~C%55~C~%54%56~C%54~C%57~C%58~C~%50(~C~%55~%51)~C%50~C%51~C~%56~C~%58~C%55~C%56~C~%57~C%57~C%58%59%60~C~C~C~%56%61(~C(~C~%57~C~%54~%50)~C~%51~C~%58~%55)~C%50~C~%59~C~%60%51~C%54~C%55~C%56~C%57~C%58~C%59~C~%55~C%55~C%60%62%63~C~C~C~%59%64(~C%59~C(~C(~C(~C~%54~C~%59~%55)~C~%56~%61~%50)~C~%57~%51)~C~%60~%58)~C%50~C~%62~C~%63%51~C%54~C%55~C%56~C%57~C%58%59%60~C%61%62~C%63~C%65~C%66~C%67~C~%61~C~%67~C(~C~%65~%63)~C~%66%61~C(~C~%61%63(~C%61~C%65~C~%58~C(~C~%54~C%54~C~%50~%64~C~%55~C(~C~%51~C~%54~%65)~C~%57~%61)~C~%56~%63)~C~C~%59)~C~%62~%60)(~C~C~%52)~C~%46~C~%53~%48)~C~%49~%44)~C~%47~%37)~C~%45~%42~%38~C~C~%43)~C~%36~%40)~C~%32~%35)~C~%41~%30)~C~%33~C~%28~%34)~C~%27~C~%15~%31)~C~8~C~%39~C~%29~C~%19~1)~C~3~4)~C~2~6)~C~7~5)~C~%10~9)~C~C~%11)~C~%25~%13)~C~%16~%12)~C~%17~%26)~C~%14~%18)~C~%22~%20)~C~C~%23)~C~%24~%21 [ 0.95993292  0.04006705]

[proteneer]

This is only temporarily alleviated by #428 - maybe we should leave this open for now?

[rbharath]

I’ve marked this issue as a Research Question. If you’re a deep learning researcher, this might be a good topic to investigate.