Fitting Multilinear Polynomials for Logic Gate Networks
📰 ArXiv cs.AI
Learn to fit multilinear polynomials for logic gate networks using vector quantization, reducing training complexity
Action Steps
- Build a 4-dimensional codebook of prototypes for 2-input Boolean gates
- Apply vector quantization to reduce training to a lower-dimensional space
- Configure a learnable logic gate network using the codebook
- Test the network using a baseline method like Soft-Mix
- Compare the performance of the proposed method with the baseline
Who Needs to Know This
Researchers and engineers working on logic gate networks and combinational circuits can benefit from this approach to simplify training and improve performance
Key Insight
💡 Multilinear polynomials can be used to reduce the dimensionality of logic gate networks, making training more efficient
Share This
🤖 Simplify logic gate network training using multilinear polynomials and vector quantization! 💻
Key Takeaways
Learn to fit multilinear polynomials for logic gate networks using vector quantization, reducing training complexity
Full Article
Title: Fitting Multilinear Polynomials for Logic Gate Networks
Abstract:
arXiv:2605.08657v1 Announce Type: cross Abstract: 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 simp
Abstract:
arXiv:2605.08657v1 Announce Type: cross Abstract: 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 simp
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