A Graph Enhanced Symbolic Discovery Framework For Efficient Logic Optimization

Authors: Yinqi Bai, Jie Wang, Lei Chen, Zhihai Wang, Yufei Kuang, Mingxuan Yuan, Jianye HAO, Feng Wu
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: Chip Design, Logic Optimization, Symbolic Regression, Knowledge Distillation

Abstract:
The efficiency of Logic Optimization (LO) has become one of the key bottlenecks in chip design. To prompt efficient LO, previous studies propose using a key scoring function to predict and prune a large number of ineffective nodes of the LO heuristics. However, the existing scoring functions struggle to balance inference efficiency, interpretability, and generalization performance, which severely hinders their application to modern LO tools. To address this challenge, we propose a novel data-driven circuit symbolic learning framework, namely CMO, to learn lightweight, interpretable, and generalizable scoring functions. The major challenge of developing CMO is to discover symbolic functions that can well generalize to unseen circuits, i.e., the circuit symbolic generalization problem. Thus, the major technical contribution of CMO is the novel Graph Enhanced Symbolic Discovery framework, which distills dark knowledge from a well-designed Graph Neural Network (GNN) to enhance the generalization capability of the learned symbolic functions. To the best of our knowledge, CMO is *the first* graph-enhanced approach for discovering lightweight and interpretable symbolic functions that can well generalize to unseen circuits in LO. Experiments on three challenging circuit benchmarks show that the *interpretable* symbolic functions learned by CMO outperform previous state-of-the-art (SOTA) GPU-based and human-designed approaches in terms of *inference efficiency* and *generalization capability*. Moreover, we integrate CMO with the Mfs2 heuristic---one of the most time-consuming LO heuristics. The empirical results demonstrate that CMO significantly improves its efficiency while keeping comparable optimization performance when executed on a CPU-based machine, achieving up to 2.5× faster runtime.

Decision: accept (poster)
Reviewer scores: 6, 6, 8

Reviews and discussion:
<thread>
creation date:
1730031016665

thread_type:
official_review

<thread_object>
creator: reviewer_kva7

<content>
summary:
This paper proposes a method called CMO to develop lightweight and generalizable scoring functions for ranking nodes in an AIG, aiming to enhance the efficiency and performance of logic optimization. The method is clearly introduced. The paper trains a GNN and uses an MCTS-based symbolic regression method to generate symbolic scoring functions, ensuring both inference efficiency and generalization. However, some experimental details remain unclear.

strengths:
The method is clearly introduced, with comprehensive experiments demonstrating the effectiveness and performance of CMO.

weaknesses:
### Topic
The term "circuit synthesis" is not well-defined in the field of EDA, which may cause confusion. Based on the related works and experiments, this paper appears to focus on logic optimization.
### Datasets
The labels of circuit datasets should be clarified. When mentioning node-level transformation, does it mean it is effective for the current step of logic optimization or for overall performance? Effectiveness in the current step may not translate to overall performance in logic optimization.
### Experiments
The experiment part is somewhat confusing. The focus of logic optimization should be on time cost and node reduction during the online phase. The offline phase appears more like an ablation study. Experiments on generalization should be highlighted in the main part of the manuscript. Experiment 4 should showcase generalization compared to other baselines like COG, but why other SR methods? Is this an ablation study of the SR method used?
### Generalization
EPFL, IWLS, and an industrial-level dataset from Huawei HiSilicon are used to train the GNN. Are the datasets mixed to train a single GNN, or are three separate GNNs trained for each dataset?

questions:
1. Can CMO generalize to other logic optimization methods like Rewrite?
2. Can a GNN trained on one dataset generalize to another dataset?
3. How are the training dataset labels obtained?
4. The presentation of experiments is confusing. Please clarify which is the main experiment and which are ablation studies.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730147861482

thread_type:
official_review

<thread_object>
creator: reviewer_olys

<content>
summary:
This paper studies the problem of circuit synthesis (CS) via graph-based methods that can generalize to unseen circuits. The proposed method, CMO, combines symbolic function learning with Graph Neural Networks.

strengths:
1. The paper is well-written with good introduction to the domain especially for ML-audience less familiar with hardware design.
2. Choice of benchmarks and state-the-art heuristics seem to be solid with comprehensive evaluation.
3. The proposed method achieves significant speedup while maintaining optimization performance on real circuits.

weaknesses:
1. Theoretical justification and analysis are lacking – It seems combining GNN, MCTS, symbolic learning etc. leads to better results on these CS benchmarks, yet some deeper explanation and analysis can be provided to make the paper stronger.
2. Some of the writings can be improved, e.g. “However, this approach cannot capture effective information from specific circuit distribution for higher generalization performance” – Is it due to the human-designed nature and lack of adoption of machine learning from existing data?
3. Some technical errors, e.g. “Specifically, we use mean absolute error and focal loss” yet the equation (4) is an MSE loss.
4. More circuit dataset descriptions, e.g. graph sizes, and graph visualizations would provide a more solid background for ML audience.

questions:
N/A
</content>
</thread_object>

</thread>
<thread>
creation date:
1730752134077

thread_type:
official_review

<thread_object>
creator: reviewer_s1pc

<content>
summary:
This authors propose a novel data-driven circuit symbolic learning framework, CMO. It learns a symbolic scoring function balancing inference efficiency, interpretability, and generalization performance. While existing approaches often struggle with these trade-offs in modern circuit synthesis (CS) tools, CMO demonstrates superior capability in discovering lightweight and interpretable symbolic functions from a decomposed symbolic space. The major technical contribution of CMO is the Graph Enhanced Symbolic Discovery (GESD) framework, which employs a specially designed Graph Neural Network (GNN) to guide the generation of symbolic trees. CMO is the first graph-enhanced approach for discovering lightweight and interpretable symbolic functions that effectively generalize to unseen circuits in CS.

strengths:
1. Overall, the proposed work is well-structured with a profound related work.
2. This paper proposes a novel circuit symbolic learning framework to learn efficient, interpretable, and generalizable symbolic functions that are reliable and simple to deploy in modern CS tools.
3. CMO is the first graph-enhanced approach for discovering lightweight and interpretable symbolic functions that can well generalize to unseen circuits in CS.  
4. Extensive experimental results show the effectiveness of the proposed CMO over existing works.

weaknesses:
The link between the two methods in sections 4.1 and 4.2 needs to be further elucidated, and it is not currently possible to visualize in the text the specific interrelationships between the two methods. For example, what is the role of si in section 4.1 in section 4.2 and what is the flow of the calculations for si.

questions:
Please check weakness
</content>
</thread_object>

</thread>
<thread>
creation date:
1733282752028

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
Summary of our responses

comment:
Dear Area Chair,

We are writing as the authors of the paper "A Graph Enhanced Symbolic Discovery Framework for Efficient Logic Synthesis" (ID: 7225). We would like to express our sincere gratitude for your dedication and support throughout the review process. 

The reviewers rated our work as **8** Accept (Reviewer kVA7), **6 (raised to 7)** Weak Accept (Reviewer oLys), and **6** Weak accept (Reviewer s1pC), respectively.

For your convenience, we **have prepared a summary of our responses** and outlined how we have addressed the reviewers' concerns as follows. We sincerely hope that this summary will facilitate your review and lighten your workload. Thank you once again for your time and support. 

### Summary of our responses
Our paper has received encouraging positive feedbacks from the reviewers, such as **"the paper is well-structured"** (Reviewer s1pC), **"a profound related work"** (Reviewer s1pC), **"well-written"** (Reviewer oLyS), **"Choice of benchmarks and heuristics are solid"** (Reviewer oLyS), **"achieves significant speedup"** (Reviewer oLyS), **"clearly introduced"** (Reviewer kVA7) and **"comprehensive experiments"** (Reviewer kVA7 and s1pC).

**Reviewer kVA7** has replied that "My main concerns previously were the misused terms, vague details, and the lack of baselines. **Most of them have been addressed** in the rebuttal or revised in the manuscript by the authors. Thus, I decided to **raise my score to 7/8**. I hope the authors can retain these revisions in the manuscript and make them clear.". 

**Reviewer oLys** has replied that "I appreciate authors' response and would like to raise my **overall rating to 7**." While we regret that ICLR does not include a score of 7 in its rating scale, we humbly believe this indicates **the reviewer's propensity to accept the paper**.

**Reviewer s1pC** has **provided many positive comments** on our work, such as "well-structured", "profound related work" and "comprehensive expreiments". While we regret not receiving a response to our follow-up, we humbly believe that we have effectively addressed the reviewer’s primary concerns. Below, we summarize how we have addressed the reviewer's feedback.

- **Clarification for the interrelationships between the two Sections in method.** We have clarified that the two methods are presented **in a progressive relationship**. Section 4.2 provides a detailed explanation of the method introduced in Section 4.1. In the revised version, we’ve added both textual explanations and diagrams to clearly illustrate this progression.

- **Explanation for the role and calculations flow of the score $s_i $.** We have explained that the score $s_i $ is calculated to **predict and prune ineffective nodes** in an unseen circuit, thereby **accelerating the CS heuristics**. In the revised version, we’ve added three detailed algorithms that outline the step-by-step calculation process of $s_i $.

Once again, thank you very much for your time and efforts throughout the review period.

Best,

Authors
</content>
</thread_object>

</thread>


Metareview:
metareview:
This paper studies the problem of Logic Optimization, where the goal is to optimize circuits. The paper proposes a new data-driven symbolic learning framework (CMO). The proposed  method trains a GNN and uses an MCTS-based symbolic regression method to generate symbolic scoring functions, ensuring both inference efficiency and generalization. Overall the reviewers found the paper to be well-written and the experiments are convincing. There were some concerns (such as misuse of terms) but most of them were addressed in the response period.