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GraDE: A Graph Diffusion Estimator for Frequent Subgraph Discovery in Neural Architectures

Yikang Yang, Zhengxin Yang, Minghao Luo, Luzhou Peng, Hongxiao Li, Wanling Gao, Lei Wang, Jianfeng Zhan

TL;DR

GraDE addresses the challenge of discovering large, frequent subgraph motifs in neural architectures by introducing a diffusion-guided estimator that learns the distribution over subgraphs. It replaces exhaustive enumeration with a Graph Diffusion Estimator, trained on a subgraph-training set, and integrates this estimator into a beam search to prune unlikely motifs while expanding promising ones. Across NAS benchmarks and the Younger dataset, GraDE delivers substantially higher ranking accuracy and, for large subgraphs, much higher motif discovery frequency than sampling-based baselines, demonstrating scalable and effective motif discovery. The framework combines subgraph sampling, a diffusion-based frequency surrogate, and constrained search to enable practical identification of large structural motifs with strong empirical gains.

Abstract

Finding frequently occurring subgraph patterns or network motifs in neural architectures is crucial for optimizing efficiency, accelerating design, and uncovering structural insights. However, as the subgraph size increases, enumeration-based methods are perfectly accurate but computationally prohibitive, while sampling-based methods are computationally tractable but suffer from a severe decline in discovery capability. To address these challenges, this paper proposes GraDE, a diffusion-guided search framework that ensures both computational feasibility and discovery capability. The key innovation is the Graph Diffusion Estimator (GraDE), which is the first to introduce graph diffusion models to identify frequent subgraphs by scoring their typicality within the learned distribution. Comprehensive experiments demonstrate that the estimator achieves superior ranking accuracy, with up to 114\% improvement compared to sampling-based baselines. Benefiting from this, the proposed framework successfully discovers large-scale frequent patterns, achieving up to 30$\times$ higher median frequency than sampling-based methods.

GraDE: A Graph Diffusion Estimator for Frequent Subgraph Discovery in Neural Architectures

TL;DR

GraDE addresses the challenge of discovering large, frequent subgraph motifs in neural architectures by introducing a diffusion-guided estimator that learns the distribution over subgraphs. It replaces exhaustive enumeration with a Graph Diffusion Estimator, trained on a subgraph-training set, and integrates this estimator into a beam search to prune unlikely motifs while expanding promising ones. Across NAS benchmarks and the Younger dataset, GraDE delivers substantially higher ranking accuracy and, for large subgraphs, much higher motif discovery frequency than sampling-based baselines, demonstrating scalable and effective motif discovery. The framework combines subgraph sampling, a diffusion-based frequency surrogate, and constrained search to enable practical identification of large structural motifs with strong empirical gains.

Abstract

Finding frequently occurring subgraph patterns or network motifs in neural architectures is crucial for optimizing efficiency, accelerating design, and uncovering structural insights. However, as the subgraph size increases, enumeration-based methods are perfectly accurate but computationally prohibitive, while sampling-based methods are computationally tractable but suffer from a severe decline in discovery capability. To address these challenges, this paper proposes GraDE, a diffusion-guided search framework that ensures both computational feasibility and discovery capability. The key innovation is the Graph Diffusion Estimator (GraDE), which is the first to introduce graph diffusion models to identify frequent subgraphs by scoring their typicality within the learned distribution. Comprehensive experiments demonstrate that the estimator achieves superior ranking accuracy, with up to 114\% improvement compared to sampling-based baselines. Benefiting from this, the proposed framework successfully discovers large-scale frequent patterns, achieving up to 30 higher median frequency than sampling-based methods.
Paper Structure (50 sections, 2 theorems, 83 equations, 11 figures, 11 tables, 7 algorithms)

This paper contains 50 sections, 2 theorems, 83 equations, 11 figures, 11 tables, 7 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Network Motif Discovery
  4. Graph Generative Models
  5. Preliminaries
  6. Research Objective: Frequent Subgraph Discovery
  7. Theoretical Foundation: Graph Diffusion Models
  8. Method
  9. Subgraph Sampling
  10. Graph Diffusion Estimator
  11. Factorized Realization and Parameterization
  12. Beam Search
  13. Experiments
  14. Experimental Setup
  15. The Performance of Graph Diffusion Estimator
  16. ...and 35 more sections

Key Result

Theorem 4.2

For any $0 \leq s < t \leq T$, the forward transition probability from $G_s$ to $G_t$ is given by: where the transition probability for the $i$-th node from state $x_s^i$ to $x_t^i$ is given by: The transition probability $p_{t|s}(e_t^{ij}|e_s^{ij})$ for the edge between nodes $i$ and $j$ is given analogously.

Figures (11)

  • Figure 1: Overview of the GraDE framework. The proposed pipeline operates in three stages: (1) Subgraph Sampling, where a representative training set is collected from target architectures; (2) Estimator Construction, where a graph diffusion model is trained to fit the subgraph frequency distribution, enabling the GraDE estimator to serve as a frequency surrogate by scoring the structural typicality of any query candidate instance; (3) Beam Search, where motifs are discovered by iteratively expanding candidates and leveraging GraDE scores to retain only the top-$N$ promising subgraphs at each size $k$ to prune the search space.
  • Figure 2: Spearman's $\rho$ across different estimation rounds. All estimators (DisCo-E, DeFoG-E, and DiGress-E) are paired with the Rand-ESU sampling method at a fixed sampling density of 0.1. The parameter $k$ in the legend denotes the subgraph size.
  • Figure 3: Spearman's $\rho$ across different sampling densities. All estimators (DisCo-E, DeFoG-E, and DiGress-E) are paired with Rand-ESU. The subgraph size is fixed to 5. The estimation rounds are fixed to 20 for DisCo-E and DiGress-E, and 60 for DeFoG-E.
  • Figure 4: Spearman's $\rho$ across different sampling methods. DisCo-E, DiGress-E, and DeFoG-E are estimators. The subgraph size is fixed to 5. The sampling density is fixed to 0.1. Estimation rounds are fixed to 20 for DisCo-E and DiGress-E, and 60 for DeFoG-E.
  • Figure 5: Median frequencies of top-50 discovered subgraphs. GraDE(Rand-ESU), GraDE(Rand-FaSE), and GraDE(NRS) denote the GraDE framework with corresponding sampling methods.
  • ...and 6 more figures

Theorems & Definitions (4)

  • Definition 3.1: Subgraph Counting Problem
  • Definition 3.2: Frequent Subgraph Discovery
  • Theorem 4.2: Forward Transition Probability
  • Theorem 4.3: Reverse Transition Probability