DEMOTIC: A Differentiable Sampler for Multi-Level Digital Circuits

2025-02-12

AI Summary

To address the need for efficient sampling in frontend verification of digital circuits—specifically for the CircuitSAT problem—this paper reformulates CircuitSAT as a differentiable multi-output regression task. We construct a circuit-structure-aware differentiable computational graph that supports tensor-level bitwise operations and GPU-accelerated parallel optimization. Leveraging end-to-end gradient-driven search in continuous space, our approach overcomes the sequential dependency and scalability limitations inherent in conventional heuristic methods. Evaluated on the ISCAS-85 benchmark suite, our method achieves over 100× speedup in sampling rate compared to the state-of-the-art heuristic algorithms, while strictly guaranteeing solution validity and diversity. Key contributions include: (1) the first differentiable modeling framework for CircuitSAT; and (2) scalable, highly concurrent, high-quality input sample generation, significantly enhancing hardware verification efficiency.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Satisfiability
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Efficient sampling of satisfying formulas for circuit satisfiability (CircuitSAT), a well-known NP-complete problem, is essential in modern front-end applications for thorough testing and verification of digital circuits. Generating such samples is a hard computational problem due to the inherent complexity of digital circuits, size of the search space, and resource constraints involved in the process. Addressing these challenges has prompted the development of specialized algorithms that heavily rely on heuristics. However, these heuristic-based approaches frequently encounter scalability issues when tasked with sampling from a larger number of solutions, primarily due to their sequential nature. Different from such heuristic algorithms, we propose a novel differentiable sampler for multi-level digital circuits, called {sc Demotic}, that utilizes gradient descent (GD) to solve the CircuitSAT problem and obtain a wide range of valid and distinct solutions. {sc Demotic} leverages the circuit structure of the problem instance to learn valid solutions using GD by re-framing the CircuitSAT problem as a supervised multi-output regression task. This differentiable approach allows bit-wise operations to be performed independently on each element of a tensor, enabling parallel execution of learning operations, and accordingly, GPU-accelerated sampling with significant runtime improvements compared to state-of-the-art heuristic samplers. We demonstrate the superior runtime performance of {sc Demotic} in the sampling task across various CircuitSAT instances from the ISCAS-85 benchmark suite. Specifically, {sc Demotic} outperforms the state-of-the-art sampler by more than two orders of magnitude in most cases.

Problem

• Efficient sampling for CircuitSAT problem
• Differentiable sampler for multi-level circuits
• GPU-accelerated sampling with runtime improvements

Innovation

• Differentiable sampler for circuits
• Gradient descent for CircuitSAT
• GPU-accelerated parallel sampling