🤖 machine learning

Stable Multimodal Graph Unlearning via Feature-Dimension Aware Quantile Selection

This paper proposes FDQ, a feature-dimension aware quantile framework that adaptively applies conservative suppression thresholds to high-dimensional input projection layers in multimodal graph neural networks, thereby achieving stable and effective unlearning while preserving model utility against membership inference attacks.

Original authors: Jingjing Zhou, Yongshuai Yang, Qing Qing, Ziqi Xu, Xikun Zhang, Renqiang Luo, Ivan Lee, Feng Xia

Published 2026-05-06

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Jingjing Zhou, Yongshuai Yang, Qing Qing, Ziqi Xu, Xikun Zhang, Renqiang Luo, Ivan Lee, Feng Xia

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a massive, incredibly smart library (a multimodal graph) that organizes information using both text (like book descriptions) and images (like book covers). This library is built by a very specific architect (a Graph Neural Network) who learned to arrange everything perfectly by studying a huge collection of books.

Now, imagine a user comes along and says, "I want to forget that I ever read this specific book." They have a legal "right to be forgotten." The library needs to remove all traces of that book and its influence without having to tear down the whole building and rebuild it from scratch (which would be too slow and expensive). This process is called Graph Unlearning.

The Problem: The "Over-Correction" Mistake

The paper points out a major flaw in how current libraries handle this request.

Think of the library's architect as having two types of tools:

The Front Door (Input Layer): This is where the raw, high-definition photos and long text descriptions enter the building. Because the photos and text are so detailed (high-dimensional), this front door is huge and holds a massive amount of the architect's "knowledge" about how to understand the world.
The Inner Halls (Deeper Layers): These are the corridors where the architect connects ideas and makes final decisions.

The Old Way: When asked to forget a book, current methods act like a clumsy janitor. They grab a giant broom and sweep everywhere with the same intensity. They scrub the inner halls and the front door equally hard.

The Result: They accidentally wipe out the giant, delicate paintings on the front door (the pre-trained knowledge about images and text). The library is now "safe" regarding the forgotten book, but the whole building looks damaged, and it can't recognize new books properly anymore. The utility (performance) crashes.

The Solution: FDQ (The "Smart Filter")

The authors propose a new method called FDQ (Feature-Dimension Aware Quantile). Think of FDQ as a smart, adjustable filter that knows exactly how to handle the request.

Here is how it works, using a simple analogy:

Identify the Sensitive Zone: FDQ looks at the library and realizes, "Hey, the front door is huge and holds our most valuable, pre-painted knowledge. We can't scrub that hard."
Adjust the Broom: Instead of using the same sweeping force everywhere, FDQ uses a gentle, precise touch on the front door (the high-dimensional input layers). It only removes the absolute minimum amount of paint necessary to forget the specific book.
Be Aggressive Inside: Meanwhile, it uses a stronger, more thorough sweep in the inner halls (the deeper layers). This is where the specific connections to the forgotten book live, so it's safe to scrub these areas more aggressively to ensure the memory is truly gone.
The "Quantile" Trick: The paper uses a statistical concept called "quantiles" (like sorting a list of items from smallest to largest and picking the bottom 10%). FDQ changes the rules for the front door: it makes the "bottom 10%" list much stricter, meaning it selects fewer parameters to edit there. For the inner halls, it keeps the list standard.

Why This Matters

The paper tested this on real-world data (like fashion items with photos and titles, and books with covers and descriptions).

The Old Way: When they tried to forget a book, the library's ability to recommend other books dropped significantly. It was like forgetting one book made the librarian forget how to read entirely.
The FDQ Way: The library successfully forgot the specific book (proven by showing that hackers couldn't tell if the book was still in the system), but the librarian remained just as good at recommending other books. The "utility" stayed high.

The Bottom Line

The paper claims that by being aware of the size and importance of different parts of the network (specifically the high-dimensional input layers), FDQ prevents the "catastrophic damage" that happens when you try to forget data in complex, multimodal systems. It allows the system to forget specific data points efficiently without breaking the model's ability to understand the world.

In short: FDQ is a surgical tool that removes a specific memory without amputating the brain's ability to see and read.

Technical Summary: Stable Multimodal Graph Unlearning via Feature-Dimension Aware Quantile Selection

1. Problem Statement

Graph unlearning is essential for complying with data privacy regulations (e.g., GDPR) by removing the influence of specific data points (nodes or edges) from trained Graph Neural Networks (GNNs) without costly retraining. However, existing unlearning strategies face a critical limitation when applied to multimodal graphs.

Multimodal graphs incorporate high-dimensional features (e.g., text and images encoded by models like CLIP or ImageBind) alongside structural data. In such architectures, the input projection layers (the first layer mapping raw features to hidden spaces) contain a dominant fraction of the model's total parameters. Current unlearning methods typically apply uniform parameter selection and editing strategies across all layers. When applied to multimodal graphs, this uniformity leads to the indiscriminate modification of these sensitive, high-dimensional input layers. The paper observes that this "over-editing" destroys pre-trained cross-modal knowledge, resulting in catastrophic utility degradation (severe drops in model performance) or a weakening of the forgetting mechanism to preserve performance.

2. Methodology: The FDQ Framework

The authors propose FDQ (Feature-Dimension Aware Quantile), a framework designed to enable stable unlearning in high-dimensional multimodal graphs. FDQ integrates with diagonal Fisher Information Matrix (FIM) based importance estimation but introduces a novel, adaptive quantile selection mechanism.

Core Mechanism: Feature-Dimension Aware Quantile

Instead of applying a global quantile threshold $k$ to select parameters for suppression across the entire network, FDQ adapts the selection strength based on the layer's role and the input feature dimension $d$ :

Layer Partitioning: The model parameters are divided into input-projection layers ( $\theta_{in}$ ), which process high-dimensional raw features, and deeper layers ( $\theta_{deep}$ ).
Adaptive Thresholding: FDQ defines a layer-specific scaling factor $\alpha^{(\ell)}$ $α^{(ℓ)}$ . For input layers where the feature dimension $d$ $d$ exceeds a threshold $\tau$ $τ$ , the effective quantile $k^{(\ell)}_{eff}$ $k_{e f f}^{(ℓ)}$ is tightened (reduced) by a factor $\rho$ $ρ$ (where $\rho < 1$ $ρ < 1$ ).
- Formula: $k^{(\ell)}_{eff} = \alpha^{(\ell)} \cdot k$ .
- Effect: This results in a more conservative selection (fewer parameters modified) for the sensitive input layers, while allowing deeper layers to remain editable under standard thresholds.
Suppression Set Construction:
- Node Unlearning: The framework computes FIM-based importance scores for the training set, the forget set, and the neighbor set (to capture message-passing effects). Two suppression scores ( $b_1$ and $b_2$ ) are derived to identify parameters specialized to the forget set.
- Edge Unlearning: An influenced-set approximation is used to estimate the impact of edge removal.
- Selection & Scaling: Parameters are selected if their suppression scores fall below the FDQ-adjusted quantile thresholds. Selected parameters are then dampened by a ratio of their score to the threshold, capped by a maximum scaling factor $\gamma$ .

Pipeline

The FDQ pipeline operates in three steps:

Compute diagonal FIMs for relevant data sets (retain, forget, and neighbor/influenced sets).
Construct per-parameter suppression scores based on Fisher ratios.
Apply FDQ-guided, layer-wise quantile thresholds to select and scale parameters, avoiding the reconstruction of raw data.

3. Key Contributions

The paper outlines three primary contributions:

Identification of a Critical Limitation: The authors demonstrate that existing graph unlearning methods suffer from severe utility degradation on multimodal graphs due to the structural imbalance of parameters, specifically the over-editing of high-dimensional input projection layers.
Proposal of FDQ: A novel framework that adapts parameter selection thresholds based on feature dimensions. It enables stable unlearning by protecting essential multimodal knowledge in input layers while maintaining effective forgetting in deeper layers. It supports both node and edge unlearning without raw data reconstruction.
Empirical Validation: Extensive experiments on real-world multimodal datasets (Ele-Fashion and Goodreads-NC) demonstrate that FDQ consistently outperforms state-of-the-art methods in preserving utility while maintaining effective privacy protection against membership inference attacks.

4. Experimental Results

The authors evaluated FDQ on two multimodal node classification datasets using various encoder combinations (e.g., CLIP, ImageBind, T5+ViT).

Utility Preservation: FDQ consistently achieved the highest Unlearning F1 scores across both datasets and all encoder combinations. On the large-scale Goodreads-NC dataset, FDQ showed significant advantages over baselines like GNNDelete (which suffered Out-Of-Memory errors with ImageBind) and other methods that exhibited notable utility drops.
Privacy Protection: Under Membership Inference Attacks (MIA), FDQ reduced the AUC-ROC scores to near 50% (random guessing), indicating strong forgetting effectiveness. In contrast, baselines like GNNDelete showed higher AUC values, suggesting residual membership signals.
Robustness to Poisoning: In edge unlearning scenarios involving poisoned edges, FDQ maintained high performance after removing the poisoned influence, whereas other methods showed substantial performance drops.
Efficiency: FDQ demonstrated high computational efficiency, completing unlearning in sub-second to few-second ranges, significantly faster than retraining-heavy or complex influence-estimation baselines.
Ablation Studies: Removing the feature-dimension awareness (using uniform quantiles) or the quantile-tail selection mechanism resulted in lower F1 scores, confirming that both components are necessary for optimal performance, particularly on larger, more complex graphs.

5. Significance and Claims

The paper claims that FDQ offers a principled and robust solution for privacy-aware unlearning in high-dimensional multimodal graph systems. Its significance lies in addressing the specific structural vulnerability of multimodal GNNs where input layers dominate the parameter space. By introducing a feature-dimension-aware mechanism, FDQ resolves the trade-off between effective forgetting and model utility that plagues existing uniform editing strategies.

The authors position FDQ as a practical tool for the lifecycle management of multimodal graph models, ensuring compliance with data privacy regulations without compromising the rich representations learned from text and visual modalities. They acknowledge a limitation regarding the sensitivity to hyperparameters controlling edit strength, noting that these may require tuning in practice.