log-likelihood of order/connectivity-agnostic training

[wangleiphy]

Here you simply average over the logits. However, did I understand correctly that the order/connectivity-agnostic training amounts to a mixture model with $p(x) = \sum_{o} p(x, o)$ ? If so, it appears that one needs to compute log-likelihood for each mask and then perform logsumexp to obtain the mixture log-likelihood.