Not sure I followed that, but if (a, b) is a data tuple you can enforce symmetry by ensuring that if (a, b) is in a batch, (b, a) is as well. That is, calculate

Not sure I followed that, but if (a, b) is a data tuple you can enforce symmetry by ensuring that if (a, b) is in a batch, (b, a) is as well. That is, calculate the gradient with both of them simultaneously. For generically enforcing symmetries, variational autoencoders are the best technique I'm aware of. You can impose any symmetry you like in your generative model. Of course it's still approximate though. I'd be interested to hear more about your problem, send me an email.