[cgreerrun]

You can use the straight through operator!

During the forward pass you sample a discrete outcome given your NN weights to get an error for backprop. During the backward pass you directly propogate through the weights.

This GradTree paper[1] does a good job covering how to do discrete gradient-based optimization (i.e. NNs w/ discrete representations).

Another option is to use a GFlowNet[2]. Then you have a NN policy that takes discrete actions like you're playing an RL game. You're not back-propogating through something that isn't continuous, but you're utilizing a NN to make informed decisions about a problem with a discrete representation.

[1] GradTree (https://arxiv.org/pdf/2305.03515.pdf) [2] GFlowNet (https://arxiv.org/abs/2111.09266)

[smaddox]

It might also be possible to solve a corresponding convex optimization problem, similar to https://arxiv.org/pdf/2303.03382.pdf

[ubj]

If an appropriate dual problem is found this could be possible.

I'm baffled why Mert Pilanci's work in this area hasn't received more attention. His proofs of a zero duality gap for neural networks are impressive.

[lucidrains]

gradtree is cool! thanks for the share!

[cgreerrun]

You're welcome! If you're interested, there is a follow up paper about a method that extends GradTree to a boosted tree as well called GRANDE[1].

[1]https://arxiv.org/abs/2309.17130