FuncFormer: Circuit Representation Learning via the Flow of Functional Propagation

Learning expressive representations for Boolean logic circuits is a fundamental challenge at the intersection of graph learning and Electronic $\mbox{Design}$ Automation (EDA). Existing Graph Neural $\mbox{Networks}$ (GNNs) primarily rely on topological message passing, which often fails to capture the strict causal dependencies and discrete functional semantics of logic gates. In this paper, we $\mbox{propose} \textbf{FuncFormer}$, a Graph Transformer that incorporates $\textbf{functional simulation}$ not as a proxy task, but as a fundamental inductive bias directly into the representation learning process. Unlike standard GNNs which typically rely on isotropic aggregation, FuncFormer $\textbf{encodes the intrinsic flow of functional propagation}$ by analyzing randomized simulation traces as they evolve through the network. This approach effectively aligns the continuous embedding manifold with the discrete Boolean function space, effectively mitigating structural aliasing. By integrating these deterministic signal trajectories with a scalable dual-path attention mechanism, our model preserves functional consistency across long-range dependencies in both combinational and sequential circuits. Empirical results demonstrate that FuncFormer significantly outperforms state-of-the-art models (e.g., DeepGate4) in Quality-of-Results (QoR) prediction and formal verification tasks, exhibiting robust generalization to unseen circuit scales.