Graph neural networks (GNNs) are increasingly applied to physical design tasks such as congestion prediction and wirelength estimation, yet progress is hindered by inconsistent circuit representations and the absence of controlled evaluation protocols. We present R2G (RTL-to-GDSII), a multi-view circuit-graph benchmark suite that standardizes five stage-aware views with information parity (every view encodes the same attribute set, differing only in where features attach) over 30 open-source IP cores (up to 106 nodes/edges). R2G provides an end-to-end DEF-to-graph pipeline spanning synthesis, placement, and routing stages, together with loaders, unified splits, domain metrics, and reproducible baselines. By decoupling representation choice from model choice, R2G isolates a confound that prior EDA and graph-ML benchmarks leave uncontrolled. In systematic studies with GINE, GAT, and ResGatedGCN, we find: (i) view choice dominates model choice, with Test R2 varying by more than 0.3 across representations for a fixed GNN; (ii) node-centric views generalize best across both placement and routing; and (iii) decoder-head depth (3--4 layers) is the primary accuracy driver, turning divergent training into near-perfect predictions (R^2$$>0.99). Code and datasets are available at https://github.com/ShenShan123/R2G.
Figures & tables
Figure 1: Benchmark and dataset evolution across graph ML and EDA, highlighting R 2 G’s unique position at their intersection as a stage-aware, multi-view circuit-graph benchmark suite.
Designs
Category
Circuit & Graph Statistics
Function
#Gates
#Nets
#IOs
#Nodes
#Edges
ss_pcm
Audio controller
463
521
28
2.44k
2.88k
pulse code modulation
ac97_ctrl
Audio controller
10509
12531
132
58.22k
70.60k
AC97 Audio Codec Controller
vga_lcd
Video controller
97688
110587
198
531.33k
650.84k
VGA/LCD Display Controller
des3_area
Crypto core
1529
1655
190
9.78k
12.46k
3DES Enc/Dec Module
systemcdes
Crypto core
2663
2788
197
14.17k
17.02k
SystemC DES Encryption/Decryption Core
Table 1: Design corpus statistics including circuit sizes and corresponding graph scale (#Nodes and #Edges under view (b)) for representative open-source IP cores.
Figure 2: OpenROAD RTL-to-GDSII post-end flow including floorplanning, placement (global and detailed), clock-tree synthesis, routing (global and detailed), and signoff. R2G focuses on placement and routing, while earlier stages provide constraints and contextual information.
Figure 3: Original circuit schematic (a) and five complementary circuit graph views (b–f) used in R2G: (b) all-elements-as-nodes, (c) pins-as-edges, (d) nets-as-edges, (e) net–gate incidence edges, (f) net edges without pin nodes. These views support placement and routing analyses under different supervision granularities.
Unit
Name
Type
Definition
Notes
Gate
x
feat. (rout.)
Gate x (DBU)
Node (b/c/d/f); edge (e)
Gate
y
feat. (rout.)
Gate y (DBU)
Node (b/c/d/f); edge (e)
Gate
cell_type
feat.
Integer encoding of gate type
Node (b/c/d/f); edge (e)
Gate
orientation
feat.
Orientation code (0–7)
Node (b/c/d/f); edge (e)
Gate
area
feat.
Gate area (tech lib)
Node (b/c/d/f); edge (e)
Gate
place_flag
feat.
Placement status
Node (b/c/d/f); edge (e)
Table 2: Definitions of features/labels for circuit components in terms of views.
(b)
(c)
(d)
(e)
(f)
Split
Model
MAE ↓
RMSE ↓
R 2 ↑
MAE ↓
RMSE ↓
R 2 ↑
MAE ↓
RMSE ↓
R 2 ↑
MAE ↓
RMSE ↓
R 2 ↑
MAE ↓
RMSE ↓
R 2 ↑
Train
GINE
0.2859
0.6117
0.9554
0.5061
0.8678
0.9017
0.3272
0.4516
0.7984
0.1649
0.2936
0.9137
0.3334
0.4563
0.7941
ResGatedGCN
0.3097
0.655
0.9489
0.4808
0.798
0.9169
0.3263
0.4477
0.8016
0.1819
0.3508
0.8767
0.3339
0.4609
0.7938
GAT
0.4762
1.1623
0.839
1.0883
1.8336
0.5611
0.4834
0.6394
0.5958
0.1812
0.3374
0.8861
0.6848
0.8683
0.2541
Validation
GINE
0.6332
1.2972
0.8219
1.095
1.6276
0.6929
0.3604
0.4516
0.748
0.4134
0.7032
0.5137
0.5431
0.6576
0.4674
ResGatedGCN
0.7485
1.4158
0.7879
0.8544
1.2884
0.8075
0.3772
0.4809
0.7142
0.3637
0.5815
0.6675
0.4462
0.5689
0.6108
Table 3: Placement results across views (b–f) and splits. Lower MAE/RMSE is better; higher R 2 is better.
(b)
(c)
(d)
(e)
(f)
Split
Model
MAE ↓
RMSE ↓
R 2 ↑
MAE ↓
RMSE ↓
R 2 ↑
MAE ↓
RMSE ↓
R 2 ↑
MAE ↓
RMSE ↓
R 2 ↑
MAE ↓
RMSE ↓
R 2 ↑
Train
GINE
0.2520
0.7796
0.9257
0.7011
1.3372
0.8716
0.4019
0.5419
0.7105
0.4188
0.5744
0.6746
0.1477
0.2130
0.9551
ResGatedGCN
0.3041
0.6848
0.9427
0.5291
0.9252
0.9385
0.3947
0.5400
0.7126
0.3805
0.5217
0.7318
0.5545
0.7204
0.4886
GAT
0.3944
1.0904
0.8547
1.4430
2.5930
0.5170
0.5659
0.7216
0.4871
0.2914
0.4246
0.8224
0.8544
1.0354
-0.0618
Validation
GINE
0.8523
1.7891
0.6529
1.7403
2.8566
0.4877
0.3892
0.5013
0.6601
0.3839
0.5155
0.6370
0.2670
0.4098
0.8143
ResGatedGCN
0.7971
1.5267
0.7472
1.0107
1.7078
0.8169
0.4222
0.5288
0.6218
0.3929
0.5237
0.6255
0.6243
0.7871
0.1746
Table 4: Routing results across views (b–f) and splits. Lower MAE/RMSE is better; higher R 2 is better.
GINE
ResGatedGCN
#layers
MAE ↓
RMSE ↓
R² ↑
#Param.
MAE ↓
RMSE ↓
R² ↑
#Param.
3
0.3489
1.0454
0.8851
0.78 M
0.3319
1.0296
0.8885
0.98 M
4
0.2594
1.0158
0.8915
0.98 M
0.3249
1.0617
0.8815
1.24 M
5
0.2991
1.0445
0.8853
1.18 M
0.2923
1.0699
0.8797
1.51 M
6
0.3312
1.2536
0.8348
1.38 M
0.3327
1.0833
0.8766
1.77 M
Table 5: Placement on view (b) vs. GNN depth (3–6). Compact stacks (3–4) yield highest accuracy; deeper (6) underperform.
GINE
ResGatedGCN
#layers
MAE ↓
RMSE ↓
R² ↑
#Param.
MAE ↓
RMSE ↓
R² ↑
#Param.
3
0.3220
1.0691
0.8759
0.78 M
0.3439
1.0682
0.8762
0.98 M
4
0.3466
1.1503
0.8664
0.98 M
0.2977
1.1141
0.8653
1.24 M
5
0.2845
1.0969
0.8694
1.18 M
0.3188
1.0768
0.8742
1.51 M
6
0.3670
1.0910
0.8708
1.38 M
0.3892
1.1495
0.8566
1.77 M
Table 6: Routing on view (b) vs. GNN depth (3–6). Performance peaks at 3 layers for both architectures; deeper stacks show diminishing returns.
GINE
ResGatedGCN
#layers
MAE ↓
RMSE ↓
R 2 ↑
#Param.
MAE ↓
RMSE ↓
R 2 ↑
#Param.
1
0.4708
1.1886
0.8514
0.91 M
3.1580
3.3342
-0.1689
1.18 M
2
0.3414
1.1184
0.8685
0.98 M
0.3249
1.0542
0.8832
1.24 M
3
0.0870
0.3329
0.9883
1.05 M
0.0963
0.3251
0.9889
1.31 M
4
0.0703
0.1909
0.9962
1.11 M
0.1421
0.3223
0.9891
1.38 M
Table 7: Placement on view (b) vs. head layers (1–4). Increasing head capacity stabilizes training and drives accuracy; 3–4 head layers deliver near-perfect R 2 across architectures.
GINE
ResGatedGCN
#layers
MAE ↓
RMSE ↓
R 2 ↑
#Param.
MAE ↓
RMSE ↓
R 2 ↑
#Param.
1
13.9757
54.1022
nan
0.91 M
nan
nan
nan
1.18 M
2
0.3425
1.1414
0.8586
0.98 M
0.2892
1.1276
0.8620
1.24 M
3
0.0761
0.3173
0.9891
1.05 M
0.1230
0.3823
0.9841
1.31 M
4
0.0542
0.1802
0.9965
1.11 M
0.2482
0.3824
0.9841
1.38 M
Table 8: Routing on view (b) vs. head layers (1–4). Shallow heads are unstable; accuracy improves sharply at 3 and is near-perfect at 4. Prefer 3–4 head layers for robust routing.
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
Benchmark Suite
Category
Level
Task
Statistics
Metric
#Node/G
#Edge/G
#Degree/G
OGB
ogbn-products
Product
node
C
2,449,029
61,859,140
50.5
Accuracy
ogbn-mag
Academic
node
C
1,939,743
21,111,007
21.77
Accuracy
ogbl-ppa
Bio
edge
L
576,289
30,326,273
105.2
Hits@100
ogbl-citation2
Citation
edge
L
2,927,963
30,561,187
20.9
MRR
TU
QM9
Molecules
node
R
18
19
2.07
MAE
Appendix
Table 9: Overview of existing graph datasets. Tasks include Classification (C), Regression (R), and Link prediction (L).
#nodes
#edges
avg_degree
avg_shortest path
Cat.
RTL2G
(b)
(c)
(d)
(e)
(f)
(b)
(c)
(d)
(e)
(f)
(b)
(c)
(d)
(e)
(f)
(b)
(c)
(d)
(e)
(f)
A/V ctrl.
ss_pcm
2.44k
1.01k
1.89k
1.46k
0.46k
2.88k
2.02k
2.36k
1.66k
1.01k
2.37
4.01
2.49
2.28
4.35
12.07
3.00
9.81
12.69
4.05
ac97_ctrl
58.22k
22.99k
40.86k
30.63k
10.36k
70.60k
47.20k
52.19k
36.83k
23.50k
2.43
4.11
2.55
2.40
4.54
13.41
3.00
13.76
21.20
5.65
vga_lcd
531.33k
206.01k
369.72k
275.41k
94.51k
650.84k
445.88k
455.43k
325.55k
197.12k
2.45
4.33
2.46
2.36
4.17
14.33
3.02
24.37
31.42
8.00
Average
197.33k
76.67k
137.49k
102.50k
35.11k
241.44k
165.03k
170.00k
121.35k
74.08k
2.42
4.15
2.50
2.35
4.35
13.27
3.01
15.98
21.77
5.90
Crypto Core
des3_area
9.78k
3.65k
7.94k
6.33k
1.80k
12.46k
9.29k
11.17k
9.41k
5.10k
2.55
5.09
2.81
2.97
5.66
18.16
3.28
15.43
12.42
6.13
Appendix
Table 10: Comparison of graph statistics across graph views and design categories.
Hyper
lr
wd
hid_dim
act
gnn_layer
dropout
head_layer
head_dim
(b)
GINE
1e-4
1e-4
256
relu
4
0.3
2
256
ResGatedGCN
1e-4
1e-4
256
relu
4
0.3
2
256
GAT
1e-4
1e-4
256
relu
4
0.3
2
256
(c)
GINE
1e-4
1e-4
256
relu
4
0.3
2
256
Appendix
Table 11: Placement Task Hyperparameters for Different Graph Views
Hyper
lr
wd
hid_dim
act
gnn_layer
dropout
head_layer
head_dim
(b)
GINE
1e-4
1e-4
256
leakyrelu
4
0.3
2
256
ResGatedGCN
1e-4
1e-4
256
leakyrelu
4
0.3
2
256
GAT
1e-4
1e-4
256
leakyrelu
4
0.3
2
256
(c)
GINE
1e-4
1e-4
256
leakyrelu
4
0.3
2
256
Appendix
Table 12: Routing Task Hyperparameters for Different Graph Views
GINE
ResGatedGCN
#layers
MAE ↓
RMSE ↓
R 2↑
#Param.
MAE ↓
RMSE ↓
R 2↑
#Param.
3
0.4552
0.6098
0.6811
0.83M
0.4521
0.6026
0.6886
1.62M
4
0.4451
0.5937
0.6975
1.03M
0.4670
0.6197
0.6704
2.08M
5
0.4837
0.6467
0.6414
1.23M
0.4700
0.6077
0.6833
2.54M
6
0.4063
0.5478
0.7427
1.42M
0.5449
0.6786
0.6051
3.00M
Appendix
Table 13: Placement on view (d) vs. GNN depth (3–6).
GINE
ResGatedGCN
#layers
MAE ↓
RMSE ↓
R 2↑
#Param.
MAE ↓
RMSE ↓
R 2↑
#Param.
3
0.5470
0.7172
0.6000
0.83M
0.5732
0.7557
0.5558
1.62M
4
0.6111
0.7920
0.5122
1.03M
0.6007
0.7826
0.5237
2.08M
5
0.5062
0.6805
0.6398
1.22M
0.5413
0.7091
0.6090
2.54M
6
0.5964
0.7571
0.5542
1.42M
0.6803
0.8942
0.3782
3.00M
Appendix
Table 14: Routing on view (d) vs. GNN depth (3–6).
GINE
ResGatedGCN
#layers
MAE ↓
RMSE ↓
R 2↑
#Param.
MAE ↓
RMSE ↓
R 2↑
#Param.
1
nan
nan
nan
0.90M
nan
nan
nan
1.95M
2
0.4451
0.5937
0.6975
1.03M
0.4670
0.6197
0.6704
2.08M
3
0.4337
0.5804
0.7109
1.10M
0.4576
0.6043
0.6866
2.15M
4
0.4359
0.5851
0.7062
1.16M
0.4418
0.5922
0.6990
2.21M
Appendix
Table 15: Placement on view (d) vs. head layers (1–4).
GINE
ResGatedGCN
#layers
MAE ↓
RMSE ↓
R 2↑
#Param.
MAE ↓
RMSE ↓
R 2↑
#Param.
1
nan
nan
nan
0.90M
nan
nan
nan
1.95M
2
0.6111
0.792
0.5122
1.03M
0.6007
0.7826
0.5237
2.08M
3
0.4637
0.6148
0.7060
1.09M
0.5678
0.7551
0.5565
2.14M
4
0.4971
0.6636
0.6581
1.16M
0.5445
0.7099
0.6089
2.21M
Appendix
Table 16: Routing on view (d) vs. head layers (1–4).
EDA problems are graph-structured, but not all graph-structured problems call for the same GNN computation. We argue that successful GNN-for-EDA methods are those whose propagation, aggregation, and supervision align with the native algebra of the target task. Concretely: static timing analysis is a max-plus/min-plus recurrence on a topologically ordered DAG, structurally aligned with asynchronous DAG-GNNs; placement is governed by hypergraph wirelength and density penalties and is exploited by differentiable placers rather than by message-passing GNNs alone; routing congestion is a sparse demand-supply field over a layout grid; switching-activity propagation is a probabilistic recurrence on a directed netlist; IR drop is a linear system on the power-delivery network; and analog symmetry extraction is a discrete constraint-prediction problem on schematic graphs. Through these task-by-task alignments we (i) review the GNN architectural toolkit relevant to circuits, (ii) formalize how circuit graphs differ from generic graphs (directed, heterogeneous, multi-scale, with sequential and clock structure), (iii) characterize where current methods succeed and where the algebra-architecture mismatch limits them, and (iv) identify failure modes--stage leakage, proxy-to-signoff gap, calibration, and design-distribution shift--that we believe are likely to dominate the next phase of work. We position the paper as a GNN-for-EDA, task-aligned analysis rather than a comprehensive AI-for-chip-design survey. Continuous SE(3)-equivariant geometric GNNs are usually mismatched to Manhattan digital layout, and LLM-for-RTL, HLS, and RL/diffusion-based topology generation are outside our scope.
Routability prediction enables rapid evaluation of placement quality without routing, providing effective feedback for routability-driven placement optimization. Recent machine learning methods have achieved efficient routability prediction through data-driven approach. However, their prediction performance highly depends on the capability of input representations to capture essential circuit information. To address the limitations of existing circuit representations in simultaneously preserving logical topology, physical layout and routing resource information, this paper proposes HGRP, a heterogeneous graph neural network for routability prediction. HGRP models the cells, nets, and routing grids as distinct types of nodes and explicitly represents topological connectivity, spatial mapping, and grid adjacency, thereby constructing a heterogeneous graph representation that preserves multi-level circuit semantics. Based on the representation, a heterogeneous message passing mechanism is developed to enable information interaction and feature fusion among distinct types of nodes, effectively learning the complex correlations between circuit structures and routing behaviors. Experimental results on the CircuitNet dataset show that HGRP improves F1-score by 18.69% relative improvements compared with the state-of-the-art in the congestion prediction task. The source code is publicly available at https://github.com/ShenShan123/HGPR.
Yule Sheng, Yue Yuan, Shan Shen +1
Nanjing University of Science and Technology, Nanjing, China
Graph Neural Networks (GNNs) show strong promise for circuit analysis, but scaling to modern large-scale circuit graphs is limited by GPU memory and training cost, especially for deep models. We revisit deep GNNs for circuit graphs and show that, when trainable, they significantly outperform shallow architectures, motivating an efficient, domain-specific training framework. We propose Grouped-Sparse-Reversible GNN (GSR-GNN), which enables training GNNs with up to hundreds of layers while reducing both compute and memory overhead. GSR-GNN integrates reversible residual modules with a group-wise sparse nonlinear operator that compresses node embeddings without sacrificing task-relevant information, and employs an optimized execution pipeline to eliminate fragmented activation storage and reduce data movement. On sampled circuit graphs, GSR-GNN achieves up to 87.2% peak memory reduction and over 30× training speedup with negligible degradation in correlation-based quality metrics, making deep GNNs practical for large-scale EDA workloads.
Yuebo Luo, Shiyang Li, Yifei Feng +3
University of Minnesota, Twin Cities Minneapolis, Minnesota, USA · New York University Brooklyn, New York, USA · Stevens Institute of Technology Hoboken, New Jersy, USA