Huh, that's an interesting idea. If you get sick of MILPs, maybe you could use a representation of your finite field instead of the field itself? That way you

Huh, that's an interesting idea. If you get sick of MILPs, maybe you could use a representation of your finite field instead of the field itself? That way you could do everything in C^n, and preserve differentiability to use SGD or something like it.