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I'm a lattice field theorist, exploring how to leverage NN in algorithms for quantum field theory that remain exact even with NNs in them, so that the NNs just
by evanb 7y ago
I'm a lattice field theorist, exploring how to leverage NN in algorithms for quantum field theory that remain exact even with NNs in them, so that the NNs just provide acceleration.
One annoying thing I've encountered is that I have some symmetries that I cannot figure out how to enforce. For example, if I have two degrees of freedom a and b and know that my physical system has a symmetry under exchange of a and b. Suppose I want to train a network to compute something in my system. For each configuration of my system I can train on (a,b) and (b,a). But the order in which I feed those as training matters, so that the network only has _approximate_ exchange symmetry, rather than exact.
Is there a way around this inexactness?
- andbberger 7y agoNot 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.
- shoyer 7y agoYou can enforce exact symmetry in neural networks with the right sort of model structure. For permutation invariance in particular, take a look at Deep Sets: https://arxiv.org/abs/1703.06114 https://arxiv.org/abs/1703.06114