PolarGate: Breaking the Functionality Representation Bottleneck of And-Inverter Graph Neural Network

Understanding the functionality of Boolean networks is crucial for processes such as functional equivalence checking, logic synthesis and malicious logic identification. With the proliferation of deep learning in electronic design automation (EDA), graph neural networks (GNNs) are widely used for embedding the and-inverter graphs (AIGs), a standard form of Boolean networks, into vectorized representation. A key challenge in the use of GNN for Boolean representation is that although GNNs can well encapsulate the structural properties of AIGs, they usually fail to fully capture the functionality of Boolean logic. Moreover, most GNNs designed for AIGs (also called AIGNNs) either rely on a large amount of training data or require complex supervisory tasks, making it difficult to maintain high training efficiency and prediction accuracy. In this work, for the first time, we focus on breaking the bottleneck of AIGNNs by augmenting their capability of functional representation, providing an efficient solution called PolarGate, which naturally aligns the message passing process with the logical functionality of AIGs. Specifically, we map the behavior of the logic gate into an ambipolar state space, customize differentiable logical operators, and design a functionality-aware message passing strategy. Experimental results on two logically related tasks (i.e., signal probability prediction and truth-table distance prediction) show that PolarGate outperforms the state-of-the-art GNN-based methods for Boolean representation, with an improvement of 62.1 % (40.6%) in learning capability and $79.5 \%(85.6 \%)$ in efficiency on two tasks. The code is avaliable at https://github.com/BUPT-GAMMA/PolarGate.