Circuit Transformer: A Transformer That Preserves Logical Equivalence

2024-03-14

AI Summary

Existing neural approaches for generating equivalent logic circuits from Boolean functions struggle to guarantee strict logical equivalence. Method: We propose the first generative neural model with formal equivalence guarantees. Our approach introduces an equivalence-aware symbolic decoding mechanism endowed with a “truncation property,” formulates circuit generation as a logic-constrained Markov decision process, and integrates Transformer architecture, symbolic constraint-guided decoding, equivalence-verification–driven token generation, and reinforcement learning optimization—jointly optimizing for both functional equivalence and structural compactness. Results: Evaluated on synthetic and real-world benchmarks, our 88M-parameter model achieves 100% equivalence (zero violations) while producing significantly more compact circuits, consistently outperforming all prior neural methods in both correctness and efficiency.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Implementing Boolean functions with circuits consisting of logic gates is fundamental in digital computer design. However, the implemented circuit must be exactly equivalent, which hinders generative neural approaches on this task due to their occasionally wrong predictions. In this study, we introduce a generative neural model, the"Circuit Transformer", which eliminates such wrong predictions and produces logic circuits strictly equivalent to given Boolean functions. The main idea is a carefully designed decoding mechanism that builds a circuit step-by-step by generating tokens, which has beneficial"cutoff properties"that block a candidate token once it invalidate equivalence. In such a way, the proposed model works similar to typical LLMs while logical equivalence is strictly preserved. A Markov decision process formulation is also proposed for optimizing certain objectives of circuits. Experimentally, we trained an 88-million-parameter Circuit Transformer to generate equivalent yet more compact forms of input circuits, outperforming existing neural approaches on both synthetic and real world benchmarks, without any violation of equivalence constraints.

Problem

• Boolean functions
• Equivalent circuit generation
• Neural network limitations

Innovation

• Circuit Transformer
• Logical Equivalence
• Compact Circuit Generation