Fitting Multilinear Polynomials for Logic Gate Networks
We study learnable logic gate networks that stack layers of 2-input Boolean gates to build combinational circuits. Every 2-input gate has a unique multilinear polynomial with 4 coefficients, so the 16 Boolean gates form a codebook of prototypes in a 4-dimensional space, reducing training to a vector-quantization problem. The baseline method, Soft-Mix, learns a 16-dimensional softmax over gate identities, but the codebook has rank~4: 11 of 15 simplex directions carry nullspace gradient, and at uniform initialization the backward signal vanishes exactly. We prove that no affine product reparameterization fixes the resulting interaction-coefficient starvation under STE, and show that the cov...
| Authors | Youngsung Kim |
|---|---|
| Primary category | cs.LG |
| Published | 9 May 2026 |
| Last updated at source | 9 May 2026 |
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