Alignment Unlocks Complementarity: A Framework for Multiview Circuit Representation Learning

Multiview learning on Boolean circuits holds immense promise, as different graph-based representations offer complementary structural and semantic information. However, the vast structural heterogeneity between views--such as an And-Inverter Graph (AIG) versus an XOR-Majority Graph (XMG)--poses a critical barrier to effective fusion, especially for self-supervised techniques like masked modeling. Naively applying such methods fails, as the cross-view context is perceived as noise. Our key insight is that functional alignment is a necessary precondition to unlock the power of multiview self-supervision. We introduce MixGate, a framework built on a principled training curriculum that first teaches the model a shared, function-aware representation space via an Equivalence Alignment Loss. Only then do we introduce a multiview masked modeling objective, which can now leverage the aligned views as a rich, complementary signal. Extensive experiments, including a crucial ablation study, demonstrate that our alignment-first strategy transforms masked modeling from an ineffective technique into a powerful performance driver. Multiview learning on Boolean circuits holds immense promise, as different graph-based representations offer complementary structural and semantic insights. While an And-Inverter Graph (AIG) provides a detailed structural view, a format like an XOR-Majority Graph (XMG) offers a semantically richer, high-level abstraction. This multiview approach has shown remarkable empirical success, surpassing earlier models that relied on single representations Li et al. (2022); Wang et al. (2022); Wu et al. (2023); Shi et al. (2023); Deng et al. (2024); Wang et al. (2024). The key challenge, however, arises from the vast structural heterogeneity between these views.