I was thinking about the issue of the GCN with respect to the permutation of the atoms.
Most GCNs (for example teh simple AXW propagation) are not invariant to permutation. Different ordering of atoms leads to other activation which could in theory produce a different output.
Most of cases this is avoided because we can use some sort of canonicalization of the molecules which makes sure that the molecule is always represented in the same manner.
However, when molecules have a similar stuctures but completely different canonicalization they will have a different ordering and thus the activation will differ greatly across the network.
Most GCNs are still performing really well on chemical datasets. Am I missing something with regards to the invariance of the models or do they perform so well despite the issue of invariance? Because despite the invariance the non-linear layers allow the model to map precisely molecules to properties.
Would,if problems of invariance/equivariance , lead to even better models?
Maybe this is complete gibberish what I am writing, but I was thinking the whole day about this issue. Could be that I am already overthinking it. But maybe someone has some thoughts to share. Or has something to point out where I went wrong.