[Paper Review] Gamora: Graph Learning based Symbolic Reasoning for Large-Scale Boolean Networks

Nan Wu, Yingjie Li+4 more|arXiv (Cornell University)|Mar 14, 2023

Machine Learning in Materials ScienceMaterials Science3 citations

TL;DR

Gamora proposes a graph neural network (GNN)-based symbolic reasoning framework that leverages multi-task learning to simultaneously perform structural hashing and functional propagation on gate-level netlists, achieving near 100% accuracy on large-scale Boolean networks with up to six orders of magnitude speedup over state-of-the-art tools like ABC, while maintaining strong generalization across complex technology mappings and billion-node scalability via GPU acceleration.

ABSTRACT

Reasoning high-level abstractions from bit-blasted Boolean networks (BNs) such as gate-level netlists can significantly benefit functional verification, logic minimization, datapath synthesis, malicious logic identification, etc. Mostly, conventional reasoning approaches leverage structural hashing and functional propagation, suffering from limited scalability and inefficient usage of modern computing power. In response, we propose a novel symbolic reasoning framework exploiting graph neural networks (GNNs) and GPU acceleration to reason high-level functional blocks from gate-level netlists, namely Gamora, which offers high reasoning performance w.r.t exact reasoning algorithms, strong scalability to BNs with over 33 million nodes, and generalization capability from simple to complex designs. To further demonstrate the capability of Gamora, we also evaluate its reasoning performance after various technology mapping options, since technology-dependent optimizations are known to make functional reasoning much more challenging. Experimental results show that (1) Gamora reaches almost 100% and over 97% reasoning accuracy for carry-save-array (CSA) and Booth-encoded multipliers, respectively, with up to six orders of magnitude speedups compared to the state-of-the-art implementation in the ABC framework; (2) Gamora maintains high reasoning accuracy (>92%) in finding functional modules after complex technology mapping, upon which we comprehensively analyze the impacts on Gamora reasoning from technology mapping.

Motivation & Objective

• To address the scalability and inefficiency of conventional symbolic reasoning methods in large-scale Boolean networks (BNs), which rely on structural hashing and functional propagation with limited parallelism.
• To overcome the limitations of existing tools like ABC, which suffer from high runtime and memory consumption on billion-node designs.
• To enable generalization of symbolic reasoning from simple to complex designs, including post-technology-mapped netlists with irregular structures.
• To exploit modern GPU acceleration and graph learning to achieve high-performance, scalable, and parallelizable symbolic reasoning in electronic design automation (EDA).
• To demonstrate robust reasoning accuracy in the presence of complex technology mappings that obscure functional and structural patterns.

Proposed method

• Gamora employs a multi-task GNN architecture that jointly optimizes for structural similarity and functional equivalence by fusing node features encoding Boolean functions and topology.
• It uses message passing mechanisms to emulate symbolic propagation (functional aggregation) and structural hashing simultaneously, mimicking conventional reasoning but with improved scalability.
• Node features are compressed using domain-specific techniques to reduce computational cost and memory footprint, enabling billion-node BNs to be processed efficiently.
• The framework supports batched reasoning on a single GPU, leveraging parallelism and GPU acceleration to scale to large designs with high throughput.
• It incorporates technology library attributes into node and edge features to improve reasoning robustness under complex technology mappings.
• The model is trained on diverse multiplier designs (e.g., CSA, Booth-encoded) and generalizes to larger bitwidths and post-mapping netlists without retraining or fine-tuning.

Experimental results

Research questions

• RQ1 Can a GNN-based framework achieve high-accuracy symbolic reasoning on large-scale Boolean networks with billion-node scale?
• RQ2 How does the proposed multi-task GNN perform in reasoning functional blocks after complex technology mapping, which increases structural irregularity and functional complexity?
• RQ3 To what extent can the model generalize from simple designs (e.g., small bitwidth multipliers) to complex, large-scale designs (e.g., 2048-bit multipliers)?
• RQ4 What is the runtime and scalability advantage of Gamora over conventional symbolic reasoning tools like ABC on large BNs?
• RQ5 How does the inclusion of technology library attributes in node features affect reasoning performance under advanced technology mappings?

Key findings

• Gamora achieves nearly 100% reasoning accuracy on 2048-bit carry-save-array (CSA) multipliers and over 97% accuracy on Booth-encoded multipliers, significantly outperforming conventional methods in accuracy and speed.
• On large-scale BNs with up to 34 million nodes and 67 million edges, Gamora achieves up to six orders of magnitude speedup compared to the state-of-the-art ABC framework.
• Even after complex ASAP 7nm technology mapping, Gamora maintains over 92% prediction accuracy in identifying functional modules, demonstrating strong robustness to technology-dependent transformations.
• The model generalizes effectively from small to large bitwidth multipliers without retraining, with only a slight drop in accuracy after complex technology mapping, which is mitigated by using larger training sets.
• Batched reasoning on a single GPU shows promising scalability, with increasing throughput and reduced latency, indicating strong potential for multi-GPU deployment in the future.
• The integration of technology library attributes into node and edge features improves reasoning performance on post-mapped netlists, especially under complex mappings with multi-output cells and irregular structures.