CktHGVAE: A Symmetric Design/State Heterogeneous Graph Variational Autoencoder for Transistor-level Analog/Mixed-signal Circuit Design and Analysis
Organizations: Ritsumeikan University, 1-1-1 Noji-Higashi, Kusatsu, Shiga 525-8577, Japan
Abstract
We propose CktHGVAE, a heterogeneous graph variational autoencoder for transistor-level analog/mixedsignal CMOS circuits that takes not only design variables but also state variables as its inputs and outputs. With a single hyperparameter configuration without topology-specific tuning, comparison between model-generated and SPICE-simulated circuit operational states gives median R2 values above 0.9 for typical single-ended voltage amplifiers and the CMOS inverter, and 0.81-0.96 for differential amplifiers with larger datasets. Latent-space optimization in the PCA-reduced latent space with Bayesian optimization, evolutionary search, random search, and quasi-exhaustive search is demonstrated for a common-source voltage amplifier with NMOS input and resistive load, where the objective function is defined as a penalty for deviation from required circuit specifications. For each search strategy, 93.3 - 100% of all design candidates suggested by the model satisfy the required circuit specifications at the decoder output, and SPICE simulations verify that 90 - 100% of them indeed satisfy the requirements. The model pretrained on a batch of topologies can be transferred to unseen topologies without retraining at all, with zero-shot reconstruction median R2 values of 0.72-0.90 in three of four scenarios, including transfer from single-ended to differential topologies, although the transfer fidelity depends on the choice of pretraining topologies. Our demonstrations suggest that the proposed model can potentially serve as a basis for AMS CMOS circuit design automation.
Figures & tables
| Label | Abbreviation | Description |
|---|---|---|
| T1 | CSA-N-Res | Common-source voltage amplifier, NMOS input, resistive load |
| T2 | CSA-N-Res-SDCS | Common-source voltage amplifier, NMOS input, resistive load, source-degenerated by NMOS current-source |
| T3 | CSA-N-Res-SDRS | Common-source voltage amplifier, NMOS input, resistive load, source-degenerated by a resistor |
| T4 | CSA-N-Diode-P | Common-source voltage amplifier, NMOS input, diode-connected PMOS load |
| T5 | CSA-P-Res | Common-source voltage amplifier, PMOS input, resistive load |
| T6 | CSA-P-Res-SDCS | Common-source voltage amplifier, PMOS input, resistive load, source-degenerated by PMOS current-source |
| Variable | Domain | Mean |
|---|---|---|
| VOUT.voltage | linear | 0.9731 ( 0.0063) |
| M1.VDS | linear | 0.9250 ( 0.0133) |
| M1.VGS | linear | 0.9979 ( 0.0001) |
| M1.VDsat | linear | 0.9830 ( 0.0011) |
| M1_drain.i_pin | log10 | 0.9946 ( 0.0008) |
| M1.gds | log10 | 0.9932 ( 0.0006) |
| Topology | Abbreviation | Approximate dataset size | Median | Mean | Number of different seeds | In-domain sample rate |
|---|---|---|---|---|---|---|
| T1 | CSA-N-Res | 1,000 | 0.9858 ( 0.0031) | 0.9810 ( 0.0022) | 5 | 87.6% (2,189/2,500) |
| T2 | CSA-N-Res-SDCS | 1,000 | 0.9112 ( 0.0101) | 0.8981 ( 0.0098) | 8 | 78.9% (3,157/4,000) |
| T3 | CSA-N-Res-SDRS | 1,000 | 0.9959 ( 0.0003) | 0.9900 ( 0.0003) | 5 | 87.3% (2,182/2,500) |
| T4 | CSA-N-Diode-P | 1,000 | 0.9912 ( 0.0005) | 0.9893 ( 0.0004) | 5 | 80.0% (2,001/2,500) |
| T5 | CSA-P-Res | 1,000 | 0.9856 ( 0.0011) | 0.9722 ( 0.0056) | 5 | 93.8% (2,346/2,500) |
| T6 | CSA-P-Res-SDCS | 1,000 | 0.9527 ( 0.0032) | 0.8194 ( 0.0194) | 8 | 78.5% (3,138/4,000) |
| Quantity | Constraint | Weight |
|---|---|---|
| VOUT.voltage | >= 1.45 V | 1.0 |
| VOUT.voltage | <= 1.65 V | 1.0 |
| M1.ID | <= 2.0e-4 A | 1.0 |
| M1.gm | >= 1.0e-4 S | 2.0 |
| M1.gm/ID | >= 2.0 | 1.0 |
| Strategy | Number of candidates satisfied at decoder output | Number of candidates satisfied at SPICE simulations | Number of out-of-training-range candidates |
|---|---|---|---|
| Bayesian optimization (BO) | 30 | 28 | 0 |
| CMA-ES search (ES) | 30 | 28 | 0 |
| Random search (RND) | 30 | 30 | 3 |
| Quasi-exhaustive search (QES) | 28 | 27 | 2 |
| Scenarios | Pretrained on | Held out | Number of graphs in test split | Zero-shot reconstruction median |
|---|---|---|---|---|
| A | T1, T2, T3, T5, T7 | T6 | 293 | 0.007 ( 0.149) |
| B | T4, T8, T9 | T12 | 279 | 0.720 ( 0.100) |
| C | T1 - T9 | T10 | 292 | 0.901 ( 0.019) |
| D | T1 - T9 | T11 | 287 | 0.824 ( 0.059) |
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
| Category | Setting | Value |
|---|---|---|
| Architecture | Hidden representation width | 128 |
| Architecture | Message-passing rounds | 3 |
| Architecture | Activation function | SiLU |
| Architecture | Dropout | 0.0 |
| Architecture | Latent-vector size, device nodes | 4 |
| Architecture | Latent-vector size, terminal pin nodes | 2 |