Less is More: Hop-Wise Graph Attention for Scalable and Generalizable Learning on Circuits

1 INTRODUCTION

• Circuit datasets can contain numerous large graphs, while message-passing GNNs depend on graph structure, complicating efficient distributed training.OpenABC-D provides 870k gate-level netlists, each with up to 240k logic gates.Source: §1 · p. 1
• Existing GNNs may miss varying hop depths and high-order structures in functional blocks, limiting generalization to unseen circuit designs.Prior work treats scalability and generalizability largely as separate directions; sampling may lose critical structure, while other approaches incur communication or computational overhead.Source: §1 · pp. 1–2
• HOGA precomputes hop-wise features and uses gated self-attention to form node representations without inter-node dependencies during training.The module adaptively captures important high-order structures across hops, supporting generalization across circuit designs.Source: §1 · p. 2
• 46.76% error drop and 10.0% accuracy improvement on new designs are reported for QoR prediction and functional reasoning, respectively.The introduction presents these as HOGA’s results on the two representative EDA tasks.Source: §1 · p. 2

2.1 Graph Neural Networks at Scale

• GNNs recursively aggregate neighbors across layers, requiring O(d^L) nodes for a representation and creating neighbor explosion, communication overhead, and work imbalance.Sampling methods used to improve efficiency may break circuit functionality and lead to poor accuracy; HOGA instead learns node representations independently from hop-wise features.Source: §2.1 · p. 2

2.2 Generalizable Graph Learning in EDA

• Conventional message-passing backbones may miss high-order structures such as full adders, which matter for functional reasoning and generalization to complex designs.Customized GNNs can remain task-specific or generalize poorly to complex circuit designs.Source: §2.2 · p. 2
• HOGA aims to combine scalability and generalizability through gated self-attention over hop-wise features; contrastive pretraining for generalizability adds computational cost.The paper describes scalability and generalizability as largely separate directions in prior work.Source: §2.2 · p. 2

3.1 Hop-Wise Feature Generation

• HOGA precomputes hop-wise features, then independently learns each node representation from its features, avoiding inter-node dependencies during training.The hop-wise feature generation time is generally negligible compared with overall training time.Source: §3 · p. 2, §3.1 · p. 3
• Unlike feature-augmentation approaches such as SIGN that train an MLP, HOGA learns node representations through gated aggregation of hop-wise features.The hop-wise features are stacked per node before being used to learn that node’s representation.Source: §3.1 · p. 3

3.2 Hop-Wise Gated Attention

• Gated self-attention captures second-order interactions across different hops, and stacking layers extends these to higher-order circuit structures.A simple gated layer captures same-hop interactions but misses cross-hop interactions; uniformly summing hop features also cannot focus on important hops per node.Source: §3.2 · p. 3
• An attentive readout assigns scores to hop features and adaptively aggregates the critical ones into the final node representation for downstream circuit tasks.Each score measures the importance of its corresponding hop feature to the final representation.Source: §3.2 · p. 3

3.3 Complexity analysis of HOGA

• HOGA’s total complexity is O(Kh|E|+Kh^2|V|+K^2h|V|), which the analysis simplifies to O(|E|+|V|), linear in nodes and edges.The terms cover hop-wise feature generation and gated self-attention.Source: §3.3 · p. 4

4.1 Experimental Setup

• Experiments train on OpenABC-D’s top 20 designs and test on the remaining designs; functional reasoning trains on 8-bit multipliers and evaluates bitwidths from 64 to 768.The QoR task predicts optimized AIG gate count after logic synthesis; functional reasoning identifies adder-block sum and carry-out nodes.Source: §4.1 · p. 4, Table 1 · p. 4, §4.3 · pp. 5–6

4.2 Evaluation on QoR Prediction

• HOGA-5 reduces estimation error over GCN by 46.76% on vga_lcd, while HOGA-2 improves average estimation error over GCN by 18.2%.HOGA-2 also achieves a 3.1× training speedup on a single GPU.Source: §4.2 · pp. 4–5, Table 2 · p. 5
• Training time almost linearly decreases as GPU count increases; HOGA-5 and HOGA-2 take 3.5 and 1.1 hours, respectively, on OpenABC-D.Generating hop-wise features takes 13 minutes.Source: §4.2 · p. 5, Figure 5 · p. 5

4.3 Evaluation on Functional Reasoning

• HOGA surpasses baselines on CSA and Booth multipliers, with a 10.0% accuracy improvement on the 768-bit CSA multiplier.Its accuracy rises with test multiplier bitwidth, unlike the poor baseline performance on CSA multipliers.Source: Figure 6 · p. 5, §4.3 · p. 6

4.4 Visualization on HOGA Attention Scores

• In 768-bit Booth multiplier heatmaps, HOGA emphasizes even hops 2, 4, and 6 for MAJ/XOR nodes, while PI/PO and plain AND nodes show relatively random attention scores.With one gated self-attention layer, each hop representation captures second-order interactions among hop-wise features.Source: §4.4 · p. 6, Figure 7 · p. 6

• HOGA precomputes hop-wise features and feeds them to a gated attention module to capture critical circuit structures.Source: §5 · p. 6
• HOGA scales to large-scale circuits via distributed training.Source: §5 · p. 6
• HOGA outperforms conventional GNNs when generalizing to unseen and complex circuit designs.Source: §5 · p. 6