CktGNN: Circuit Graph Neural Network for Electronic Design Automation

• Prior representation-based methods optimize device parameters for fixed topologies, while topology optimization remains a critical and challenging task.Source: §1 · p. 2
• CktGNN uses two-level GNNs and a pre-designed subgraph basis to encode circuits and optimize topology and node features.Inner GNNs represent basis subgraphs; an outer GNN passes messages across them.Source: §1 · p. 2
• OCB provides 10K operational-amplifier circuits with extracted specifications and open-source generation and evaluation processes.The dataset supports querying circuits without circuit reconstruction and simulator runs.Source: §1 · p. 2
• CktGNN outperforms competitive GNN baselines and produces high-competitive operational amplifiers compared with human experts’ designs.Source: §1 · p. 2

2.1 GRAPH NEURAL NETWORKS

• D-VAE and DAGNN process nodes in topological order, while PACE encodes node order positionally and processes nodes simultaneously with a Transformer.Source: §2.1 · p. 3

2.2 AUTOMATED ANALOG CIRCUIT DESIGN

• Prior circuit-design methods use optimization or learning to size devices on fixed topologies; topology synthesis remains difficult and genetic approaches often produce nonfunctional topologies.Source: §2.2 · p. 3
• Circuit GNNs have supported passive-device sizing and policy-based parameter search, while this work uses a two-level GNN to optimize topology and device features together.Source: §2.2 · p. 3

3.1 TWO-LEVEL GNN FRAMEWORK WITH A SUBGRAPH BASIS

• The ordered subgraph basis restricts inner message passing to selected subgraphs, aiming to reduce topology search space while increasing expressive ability for circuit DAG encoding.For a node belonging to multiple basis subgraphs, the largest by basis order is selected; connected nodes selecting the same subgraph are merged for outer message passing.Source: §3.1 · p. 4

3.2 THE CKTGNN MODEL

• CktGNN represents circuit devices by type and features, decomposes circuits into non-overlapping basis subgraphs, and learns their representations with inner GNNs.The outer GNN processes the transformed DAG using directed message passing, gated summation, and a GRU; the output-node representation serves as the graph representation.Source: §3.2 · pp. 5–6
• The paper chooses a VAE framework because subroutine-based optimization generally needs larger training datasets, while circuit performance simulation can be time-consuming.The authors also motivate CktGNN by the complexity and size of circuit design spaces, which they say make the optimization problem highly non-convex.Source: §3.2 · p. 5

3.3 DISCUSSIONS

• For circuits with a basis containing every size-1 subgraph, an injective graph transformation exists when each basis subgraph has only one node incident to an edge crossing its boundary.The paper says the condition holds for various applications, including circuit automation, and that its operational-amplifier basis satisfies it.Source: §3.3 · p. 6
• Compared with GRU-based DAG encoders, CktGNN embeds subgraph topology through its type and uses inner GNNs to capture contextualized subgraph information.The authors identify these as reducing topology search space and addressing the limited representational ability of typically shallow GRU-based encoders.Source: §3.3 · p. 6

4 OPEN CIRCUIT BENCHMARK

• OCB uses operational amplifiers as its benchmark circuits and supports incorporating other analog circuits when corresponding circuit-graph mappings are built.The authors choose Op-Amps as difficult, commonly used evaluation circuits and describe OCB as having circuit-generation and evaluation capabilities.Source: §4 · p. 6
• Abstracting circuits into low-level functional substructures is designed to scale to analog circuits with thousands of devices while avoiding cycles during graph conversion.The paper compares this abstraction to standard synthesis of modern digital circuits.Source: §4 · p. 6
• The graph mapping uses connection points as vertices and functional substructures as edges, with polarity marking feedback versus feedforward behavior.Single-stage Op-Amps and sub-circuit modules are abstracted using behavioral models; the resulting Op-Amp graph is acyclic.Source: §4 · p. 7
• OCB converts sampled graphs into netlists for simulator evaluation and uses this loop to generate 10,000 Op-Amps with detailed specifications.The dataset can contain repeated topologies with different device parameters, and the benchmark can be augmented for other analog circuits when mappings are available.Source: §4 · p. 7

5.1 DATASET, BASELINES, AND TASKS

• The experiments use 10,000 Op-Amps, compare multiple undirected and DAG GNN baselines, and assess prediction, reconstruction, encoding time, valid and novel generation, and Bayesian-optimization FoM.Circuit properties include Gain, BW, PM, and FoM; Bayesian optimization uses batches of 50 over 10 iterations.Source: §5.1 · pp. 7–8

5.2 PREDICTIVE PERFORMANCE AND TOPOLOGY RECONSTRUCTION ACCURACY

• CktGNN achieves state-of-the-art circuit-property prediction and significantly improves topology reconstruction accuracy over the compared methods.The authors associate its contextualized message passing with improved circuit encoding and its reconstruction results with the goal of reducing topology search space.Source: §5.2 · p. 8

5.3 CIRCUIT ENCODING EFFICIENCY

• CktGNN significantly reduces training and inference time versus GRU-based D-VAE and DAGNN, with only marginal extra computation versus fully parallelized GCN.Figure 3 compares training and inference efficiency.Source: §5.3 · pp. 8–9, Figure 3 · p. 8

5.4 EFFECTIVENESS IN REAL-WORLD ELECTRONIC CIRCUIT DESIGN

• CktGNN-related decoders generate a higher proportion of valid circuits, and CktGNN-based VAE finds circuits with the highest FoM.The authors also report the best circuit-generation ability and suggest fewer simulations may make automation more cost- and time-efficient.Source: Table 2 · p. 9, §5.4 · p. 9

6 CONCLUSION AND DISCUSSIONS

• CktGNN combines a two-level GNN and pre-designed subgraph basis in a VAE-based framework for optimizing circuit topology and device parameters.The conclusion describes OCB as the first open-source benchmark for analog circuit topology generation and device-parameter optimization, and says both contributions can generalize to other analog circuits.Source: §6 · p. 9
• The authors characterize analog circuits as a critical link between the physical analog world and modern digital information, motivating further study of deep-learning design automation.They point to increasing use of deep learning for industrial digital circuits as context for anticipated attention to analog automation.Source: §6 · p. 9

A OPERATIONAL AMPLIFIERS (CIRCUITS) AND THE CORRESPONDING SUBGRAPH BASIS

• Op-Amp automation seeks a topology and device parameters that achieve specifications required by a particular application.The four selected specifications are DC gain, bandwidth, phase margin, and power consumption.Source: A OPERATIONAL AMPLIFIERS (CIRCUITS)… · p. 14
• A three-stage Op-Amp has three single-stage amplifiers on its main path, with feed-forward and feedback paths used for compensation.Its total gain is the product of the gains of the three main-path stages; the paths may include amplifiers, resistors, and capacitors.Source: A OPERATIONAL AMPLIFIERS (CIRCUITS)… · p. 14
• The design space is large because single-stage Op-Amps have varied topologies and three-stage designs can use varied compensation schemes.The paper motivates graph generation and optimization as a way to automate this time-consuming manual design process.Source: Figure 5 · p. 14, A OPERATIONAL AMPLIFIERS (CIRCUITS)… · p. 14
• The circuit graph maps a three-stage Op-Amp to five nodes, with connections represented by amplifiers, resistors, capacitors, or combinations.The stated connection types include single C or R, parallel or series C-R, and single-stage amplifiers with different polarities and directions.Source: A OPERATIONAL AMPLIFIERS (CIRCUITS)… · pp. 14–15
• The subgraph basis simplifies graph learning by representing circuits as subgraphs, while the ordering determines the transformed graph and search-space complexity.For the studied Op-Amps, reversing C and R also reverses the order of related parallel subgraphs; the authors describe the invariance as circuit-specific.Source: A OPERATIONAL AMPLIFIERS (CIRCUITS)… · pp. 15–16
• 0 of 10,000 Op-Amp circuits had different transformed graphs when the order of C and R was reversed.For the studied circuits, subgraph ordering did not affect the circuit-to-graph transformation; the authors note this need not hold for general problems.Source: A OPERATIONAL AMPLIFIERS (CIRCUITS)… · p. 16

B EXPRESSIVE ABILITY OF TWO-LEVEL GNN WITH A SUBGRAPH BSIS

• With a proper subgraph basis and order function, the two-level GNN can be strictly more powerful than message-passing GNNs and as powerful as nested GNNs on n-sized r-regular graphs.The result is stated in Corollary B.1.Source: B EXPRESSIVE ABILITY OF TWO-LEVEL GNN… · p. 17
• A basis containing all height-1 subgraphs gives a general message-passing framework, while all height-k rooted subgraphs with root-dependent ordering yield NGNN.Adding rooted subgraphs taller than 1 applies inner message passing to extract additional distance features.Source: B EXPRESSIVE ABILITY OF TWO-LEVEL GNN… · p. 17
• The basis can balance complexity and expressiveness, but this work assumes a known ordered basis for the circuit DAG optimization problem.The authors leave incorporating subgraph selection into end-to-end learning for general graph tasks to future work.Source: B EXPRESSIVE ABILITY OF TWO-LEVEL GNN… · p. 17

C PROOF OF THEOREM 3.2

• The graphlizer selects a transformed DAG with the fewest nodes, where each node represents a subgraph from the basis.The proof first establishes that the input DAG can be converted into transformed DAGs, then imposes the minimum-node rule.Source: C PROOF OF THEOREM 3.2 · p. 17
• When transformed graphs use the same number of basis subgraphs, their subgraph tuples are sorted by the order function to choose an output.The proof uses lexicographical sorting for the ordering operation.Source: C PROOF OF THEOREM 3.2 · p. 17
• These rules make subgraph selection injective, and fixed within-subgraph connections make the transformed DAG's encoding of the input order uniform.Connections between subgraphs are uniquely dependent on the input DAG.Source: C PROOF OF THEOREM 3.2 · p. 17

D EXPERIMENT DETAILS AND ADDITIONAL RESULTS

• GCN and GIN use three graph-convolution layers with mean pooling; NGNN uses rooted-subgraph height 3 and a three-layer GIN base.Graphormer and PACE use five Transformer encoder layers and six attention heads; DAGNN uses two-layer directed graph convolutions.Source: D EXPERIMENT DETAILS AND ADDITIONAL… · p. 17
• The experiments ran on Tesla P100 and GeForce GTX 1080 Ti GPUs, with five independent trials when reporting means and standard deviations.Source: D EXPERIMENT DETAILS AND ADDITIONAL… · p. 18
• CktGNN's latent-space Bayesian optimization yields a circuit with the largest FoM score among the competitive DAG encoders and undirected-graph GNNs.Figure 8 presents exemplary optimal circuits detected by Bayesian optimization.Source: D EXPERIMENT DETAILS AND ADDITIONAL… · p. 18, Figure 8 · p. 18

E MORE DETAILS ABOUT TRAINING AND EVALUATION

• CktGNN can be trained with supervised learning or as a DAG encoder in a VAE, whose decoder generates transformed DAGs from the latent space.Two fully connected layers predict the approximate posterior mean and variance; the VAE loss combines reconstruction loss with α times KL divergence, with α set to 0.005.Source: E MORE DETAILS ABOUT TRAINING AND… · p. 18
• The VAE training uses mini-batches of 64 for 200 epochs, with an initial learning rate of 1E-4 reduced by a factor of 0.1 after 20 epochs without loss improvement.The loss is reconstruction loss plus α KL divergence, with α set to 0.005.Source: E MORE DETAILS ABOUT TRAINING AND… · p. 18
• Validity and novelty are measured by sampling 1,000 points from a prior standard-normal latent space, decoding each 10 times, then computing proportions of valid circuits and circuits not seen in training.A valid circuit has one input and one output node, is a DAG, and has no R or C node in its main path.Source: E MORE DETAILS ABOUT TRAINING AND… · p. 18

F MORE DETAILS ABOUT DECODER

• The decoder builds circuits subgraph by subgraph from basis B, predicting subgraph types, node features, and connections until it generates an output type.It maps a latent vector to an initial hidden state and updates representations as each subgraph is added.Source: F MORE DETAILS ABOUT DECODER · p. 19

G RECENT UPDATE OF OCB DATABASE

• The updated OCB release stores 10,000 successfully simulated circuits in Ckt-Bench101 after fixing missing circuit specifications that had indicated failed simulations.Previously, missing specifications such as bandwidth and gain were assigned a value of -inf.Source: G RECENT UPDATE OF OCB DATABASE · p. 19
• CktGNN achieves state-of-the-art performance in predictive tests on Ckt-Bench101 and real-world electronic circuit design, as reported in Table G and Table 4.Table 3 reports predictive performance on Ckt-Bench101; Table 4 concerns effectiveness in real-world circuit design.Source: G RECENT UPDATE OF OCB DATABASE · p. 19, Table 3 · p. 19, Table 4 · p. 19
• Ckt-Bench301 provides a search space for testing Bayesian optimization algorithms, and Table 5 reports results on that benchmark.The stated purpose is to support machine-learning researchers without requiring circuit-generator or simulator expertise.Source: G RECENT UPDATE OF OCB DATABASE · pp. 19–20, Table 5 · p. 19