# DeepGate: Learning Neural Representations of Logic Gates

arXiv: https://arxiv.org/abs/2111.14616 · HTML: https://mlsanity.com/paper/2111.14616/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 26 Nov 2021.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2001.05566/) (2020)
- [Pre-Trained Models: Past, Present and Future](https://mlsanity.com/paper/2106.07139/) (2021)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [D-VAE: A Variational Autoencoder for Directed Acyclic Graphs](https://mlsanity.com/paper/1904.11088/) (2019)
- [Machine Learning for Electronic Design Automation: A Survey](https://mlsanity.com/paper/2102.03357/) (2021)
- [Directed Acyclic Graph Neural Networks](https://mlsanity.com/paper/2101.07965/) (2021)
- [SocialGCN: An Efficient Graph Convolutional Network based Model for Social Recommendation](https://mlsanity.com/paper/1811.02815/) (2018)
- [Net2: A Graph Attention Network Method Customized for Pre-Placement Net Length Estimation](https://mlsanity.com/paper/2011.13522/) (2020)

## Built on by (most cited first, 30 of 37)

- [LLM4EDA: Emerging Progress in Large Language Models for Electronic Design Automation](https://mlsanity.com/paper/2401.12224/) (2023)
- [DeepGate2: Functionality-Aware Circuit Representation Learning](https://mlsanity.com/paper/2305.16373/) (2023)
- [DeepGate3: Towards Scalable Circuit Representation Learning](https://mlsanity.com/paper/2407.11095/) (2024)
- [DeepCircuitX: A Comprehensive Repository-Level Dataset for RTL Code Understanding, Generation, and PPA Analysis](https://mlsanity.com/paper/2502.18297/) (2025)
- [DeepGate4: Efficient and Effective Representation Learning for Circuit Design at Scale](https://mlsanity.com/paper/2502.01681/) (2025)
- [DeepSAT: An EDA-Driven Learning Framework for SAT](https://mlsanity.com/paper/2205.13745/) (2022)
- [Retrieval-Guided Reinforcement Learning for Boolean Circuit Minimization](https://mlsanity.com/paper/2401.12205/) (2024)
- [TAG: Learning Circuit Spatial Embedding From Layouts](https://mlsanity.com/paper/2209.03465/) (2022)
- [NetTAG: A Multimodal RTL-and-Layout-Aligned Netlist Foundation Model via Text-Attributed Graph](https://mlsanity.com/paper/2504.09260/) (2025)
- [Revolution or Hype? Seeking the Limits of Large Models in Hardware Design](https://mlsanity.com/paper/2509.04905/) (2025)
- [DeepSeq: Deep Sequential Circuit Learning](https://mlsanity.com/paper/2302.13608/) (2023)
- [MMCircuitEval: A Comprehensive Multimodal Circuit-Focused Benchmark for Evaluating LLMs](https://mlsanity.com/paper/2507.19525/) (2025)
- [Verilog-to-PyG -- A Framework for Graph Learning and Augmentation on RTL Designs](https://mlsanity.com/paper/2311.05722/) (2023)
- [PreRoutGNN for Timing Prediction with Order Preserving Partition: Global Circuit Pre-training, Local Delay Learning and Attentional Cell Modeling](https://mlsanity.com/paper/2403.00012/) (2024)
- [Circuit Transformer: A Transformer That Preserves Logical Equivalence](https://mlsanity.com/paper/2403.13838/) (2024)
- [DeepSeq2: Enhanced Sequential Circuit Learning with Disentangled Representations](https://mlsanity.com/paper/2411.00530/) (2024)
- [OpenLS-DGF: An Adaptive Open-Source Dataset Generation Framework for Machine Learning Tasks in Logic Synthesis](https://mlsanity.com/paper/2411.09422/) (2024)
- [DeepCell: Self-Supervised Multiview Fusion for Circuit Representation Learning](https://mlsanity.com/paper/2502.06816/) (2025)
- [DICE: Device-level Integrated Circuits Encoder with Graph Contrastive Pretraining](https://mlsanity.com/paper/2502.08949/) (2025)
- [SeaDAG: Semi-autoregressive Diffusion for Conditional Directed Acyclic Graph Generation](https://mlsanity.com/paper/2410.16119/) (2024)
- [GenEDA: Towards Generative Netlist Functional Reasoning via Cross-Modal Circuit Encoder-Decoder Alignment](https://mlsanity.com/paper/2504.09485/) (2025)
- [FuncGNN: Learning Functional Semantics of Logic Circuits with Graph Neural Networks](https://mlsanity.com/paper/2506.06787/) (2025)
- [Alignment Unlocks Complementarity: A Framework for Multiview Circuit Representation Learning](https://mlsanity.com/paper/2509.20968/) (2025)
- [BDD2Seq: Enabling Scalable Reversible-Circuit Synthesis via Graph-to-Sequence Learning](https://mlsanity.com/paper/2511.08315/) (2025)
- [STELLAR: Structure-guided LLM Assertion Retrieval and Generation for Formal Verification](https://mlsanity.com/paper/2601.19903/) (2025)
- [SiHGNN: Leveraging Properties of Semantic Graphs for Efficient HGNN Acceleration](https://mlsanity.com/paper/2408.15089/) (2024)
- [Learning Library Cell Representations in Vector Space](https://mlsanity.com/paper/2503.22900/) (2025)
- [Modeling Relational Logic Circuits for And-Inverter Graph Convolutional Network](https://mlsanity.com/paper/2508.11991/) (2025)
- [TRACE: Learning to Compute on Circuit Graphs](https://mlsanity.com/paper/2509.21886/) (2025)
- [BoolSkeleton: Boolean Network Skeletonization via Homogeneous Pattern Reduction](https://mlsanity.com/paper/2511.02196/) (2025)

## Abstract (arXiv)

Applying deep learning (DL) techniques in the electronic design automation (EDA) field has become a trending topic. Most solutions apply well-developed DL models to solve specific EDA problems. While demonstrating promising results, they require careful model tuning for every problem. The fundamental question on "How to obtain a general and effective neural representation of circuits?" has not been answered yet. In this work, we take the first step towards solving this problem. We propose DeepGate, a novel representation learning solution that effectively embeds both logic function and structural information of a circuit as vectors on each gate. Specifically, we propose transforming circuits into unified and-inverter graph format for learning and using signal probabilities as the supervision task in DeepGate. We then introduce a novel graph neural network that uses strong inductive biases in practical circuits as learning priors for signal probability prediction. Our experimental results show the efficacy and generalization capability of DeepGate.