Learning to compute, the ability to model the functional behavior of a circuit graph, is a fundamental challenge for graph representation learning. Yet, the dominant paradigm is architecturally mismatched for this task. This flawed assumption, central to mainstream message passing neural networks (MPNNs) and their conventional Transformer-based counterparts, prevents models from capturing the position-aware, hierarchical nature of computation. To resolve this, we introduce TRACE, a new paradigm built on an architecturally sound backbone and a principled learning objective. First, TRACE employs a Hierarchical Transformer that mirrors the step-by-step flow of computation, providing a faithful architectural backbone that replaces the flawed permutation-invariant aggregation. Second, we introduce function shift learning, a novel objective that decouples the learning problem. Instead of predicting the complex global function directly, our model is trained to predict only the function shift, the discrepancy between the true global function and a simple local approximation that assumes input independence. We validate this paradigm on various circuits modalities, including Register Transfer Level graphs, And-Inverter Graphs and post-mapping netlists. Across a comprehensive suite of benchmarks, TRACE substantially outperforms all prior architectures. These results demonstrate that our architecturally-aligned backbone and decoupled learning objective form a more robust paradigm for the fundamental challenge of learning the functional behavior of a circuit graph.

翻译：学习计算（即建模电路图的功能行为）是图表示学习中的一项基本挑战。然而，当前主流范式在架构上与这一任务存在根本性错配。这一有缺陷的假设——普遍存在于主流消息传递神经网络及其基于Transformer的常规变体中——阻碍了模型捕捉计算过程中位置感知与层级化本质的能力。为解决这一问题，我们提出TRACE，一种基于架构合理的骨干网络与原则性学习目标的新范式。首先，TRACE采用层级化Transformer，能够镜像计算的分步流程，提供取代有缺陷的置换不变聚合的忠实架构骨干。其次，我们提出函数移位学习，一种解耦学习问题的新颖目标。我们的模型不直接预测复杂全局函数，而是仅训练预测函数移位——即真实全局函数与假设输入独立的简单局部逼近之间的差异。我们在多种电路模态（包括寄存器传输级图、与反相器图及映射后网表）上验证了这一范式。在全面基准测试中，TRACE显著优于所有先前架构。这些结果表明，我们的架构对齐骨干与解耦学习目标为学习电路图功能行为这一根本挑战提供了更稳健的范式。