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QGraphLIME - Explaining Quantum Graph Neural Networks

Haribandhu Jena, Jyotirmaya Shivottam, Subhankar Mishra

TL;DR

QGraphLIME addresses the explainability challenge of Quantum Graph Neural Networks by treating explanations as distributions over local, structure-preserving surrogate models trained on perturbed graphs to account for quantum measurement noise. The method introduces nonlinear HSIC-based surrogates, ensemble-uncertainty metrics (Top-$k$ Inclusion Probability, IQR, flip probabilities), and a distribution-free DK-W bound to guarantee surrogate coverage with a finite sample budget. Empirically on synthetic graphs with ground-truth targets, QGraphLIME delivers accurate, stable explanations and reveals trade-offs between perturbation design, surrogate nonlinearity, and measurement regime, especially in multi-target scenarios. The framework provides rigorous uncertainty quantification and practical guidance for scaling explainability to broader QGNNs and real-world datasets as quantum resources mature.

Abstract

Quantum graph neural networks offer a powerful paradigm for learning on graph-structured data, yet their explainability is complicated by measurement-induced stochasticity and the combinatorial nature of graph structure. In this paper, we introduce QuantumGraphLIME (QGraphLIME), a model-agnostic, post-hoc framework that treats model explanations as distributions over local surrogates fit on structure-preserving perturbations of a graph. By aggregating surrogate attributions together with their dispersion, QGraphLIME yields uncertainty-aware node and edge importance rankings for quantum graph models. The framework further provides a distribution-free, finite-sample guarantee on the size of the surrogate ensemble: a Dvoretzky-Kiefer-Wolfowitz bound ensures uniform approximation of the induced distribution of a binary class probability at target accuracy and confidence under standard independence assumptions. Empirical studies on controlled synthetic graphs with known ground truth demonstrate accurate and stable explanations, with ablations showing clear benefits of nonlinear surrogate modeling and highlighting sensitivity to perturbation design. Collectively, these results establish a principled, uncertainty-aware, and structure-sensitive approach to explaining quantum graph neural networks, and lay the groundwork for scaling to broader architectures and real-world datasets, as quantum resources mature. Code is available at https://github.com/smlab-niser/qglime.

QGraphLIME - Explaining Quantum Graph Neural Networks

TL;DR

QGraphLIME addresses the explainability challenge of Quantum Graph Neural Networks by treating explanations as distributions over local, structure-preserving surrogate models trained on perturbed graphs to account for quantum measurement noise. The method introduces nonlinear HSIC-based surrogates, ensemble-uncertainty metrics (Top- Inclusion Probability, IQR, flip probabilities), and a distribution-free DK-W bound to guarantee surrogate coverage with a finite sample budget. Empirically on synthetic graphs with ground-truth targets, QGraphLIME delivers accurate, stable explanations and reveals trade-offs between perturbation design, surrogate nonlinearity, and measurement regime, especially in multi-target scenarios. The framework provides rigorous uncertainty quantification and practical guidance for scaling explainability to broader QGNNs and real-world datasets as quantum resources mature.

Abstract

Quantum graph neural networks offer a powerful paradigm for learning on graph-structured data, yet their explainability is complicated by measurement-induced stochasticity and the combinatorial nature of graph structure. In this paper, we introduce QuantumGraphLIME (QGraphLIME), a model-agnostic, post-hoc framework that treats model explanations as distributions over local surrogates fit on structure-preserving perturbations of a graph. By aggregating surrogate attributions together with their dispersion, QGraphLIME yields uncertainty-aware node and edge importance rankings for quantum graph models. The framework further provides a distribution-free, finite-sample guarantee on the size of the surrogate ensemble: a Dvoretzky-Kiefer-Wolfowitz bound ensures uniform approximation of the induced distribution of a binary class probability at target accuracy and confidence under standard independence assumptions. Empirical studies on controlled synthetic graphs with known ground truth demonstrate accurate and stable explanations, with ablations showing clear benefits of nonlinear surrogate modeling and highlighting sensitivity to perturbation design. Collectively, these results establish a principled, uncertainty-aware, and structure-sensitive approach to explaining quantum graph neural networks, and lay the groundwork for scaling to broader architectures and real-world datasets, as quantum resources mature. Code is available at https://github.com/smlab-niser/qglime.

Paper Structure

This paper contains 40 sections, 2 theorems, 22 equations, 11 figures, 11 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Related Work
  4. Background
  5. Graph Neural Networks (GNNs)
  6. Structural GraphLIME (StGraphLIME)
  7. Hilbert-Schmidt Independence Criterion (HSIC)
  8. HSIC Lasso (HSIC-L1) for individual node/edge selection.
  9. Group-Regularized HSIC Lasso (HSIC-G).
  10. Equivariant Quantum Graph Circuits (EQGCs)
  11. Quantum LIME (Q-LIME)
  12. Quantum GraphLIME
  13. Top-$k$ Inclusion Probability (TIP)
  14. Interquartile Range (IQR)
  15. Flip Probabilities under Element Removal
  16. ...and 25 more sections

Key Result

Theorem 1

Let $\EuScript{P}$ denote the true CDF of the scalar statistic $\mathcal{T}(S)$ induced by the ensemble-generation randomness, and let $\hat{\EuScript{P}}_m$ be the empirical CDF from $m$ i.i.d. surrogates $S_1, \dots, S_m$. For any $\epsilon > 0$ and $\delta\in(0, 1)$, if then, with probability at least $1 - \delta$, so, the surrogate ensemble captures the distribution of $\mathcal{T}(S)$ withi

Figures (11)

  • Figure 1: QGraphLIME Workflow: Our method generates locally perturbed graph datasets ($\{D_i\}_{i=1}^m$) from an input graph and evaluates them with a trained QGNN ($f_\theta$) to capture quantum stochasticity. An ensemble of surrogate models $\Xi = \{S_i\}_{i=1}^m$ is fit on $(D_i, f_\theta(D_i))$, with boundary dispersion used to quantify explanation uncertainty. Aggregated surrogate attributions rank influential nodes or edges, yielding stable, uncertainty-aware explanations; see Algorithm \ref{['alg:qgraphlime']}.
  • Figure 2: Case 1 - Single-Target: Explanation Score variation across surrogates per node due to quantum stochasticity. Left - Input Graph; Center - QGLIME-HSIC L1; Right - HSIC-G.
  • Figure 3: Case 2 - Dual-Target: Explanation Score variation across surrogates per node due to quantum stochasticity. Left - Input Graph; Center - QGLIME-HSIC L1; Right - HSIC-G.
  • Figure 4: Effect of Different Perturbation Strategies: Explanation Score variation across surrogates per node due to quantum stochasticity for Case 1 (top) and Case 2 (bottom) under Random Walk perturbation. Left - HSIC-L1 surrogate; Right - HSIC-Group surrogate.
  • Figure 5: Effect of Different Perturbation Strategies: Explanation Score variation across surrogates per node due to quantum stochasticity for Case 1 (top) and Case 2 (bottom) under Random Node perturbation. Left - HSIC-L1 surrogate; Right - HSIC-Group surrogate.
  • ...and 6 more figures

Theorems & Definitions (3)

  • Theorem 1: Minimum surrogate count
  • proof
  • Corollary 2: Simultaneous guarantee across graphs/statistics