Convert a Binary GumbelSoftmax output to BCE

I am trying to calculate the loss between a feature GAN output and the labels produced by an auxiliary classifier (AC). For the GAN, I am using tanh activations for numerical features and gumbel softmax for categorical features. The AC can calculate the MSE for numerical features, cross entropy for categorical features and binary cross entropy (BCE) for binary features.

Since my GAN uses gumbel softmax for all non-numerical features, I am unable to compute the loss between the GAN gumbel softmax output (2 units) and the AC BCE output (1 unit, similar to using a single output node with sigmoid activation). Is there a way that I can convert my gumbel softmax output to a single probability vector that can be used by the AC.

The AC is built using an external library (LightGBM), so I am trying to modify pytorch’s output to fit there. Also, using the CE for binary features is not recommended as stated in the LightGBM documentation.