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FROG: Fair Removal on Graphs

Ziheng Chen, Jiali Cheng, Hadi Amiri, Kaushiki Nag, Lu Lin, Sijia Liu, Xiangguo Sun, Gabriele Tolomei

TL;DR

FROG tackles the problem that graph unlearning can inadvertently worsen fairness by altering topology. It introduces a bi-level framework that first augments the graph with fairness-aware edge additions and then sparsifies the structure to achieve unlearning, optimizing both the unlearning loss and a fairness loss. The approach leverages differentiable edge augmentation via Gumbel-softmax and a contrastive fairness objective, followed by a sparsity-driven pruning that respects a limited modification budget. Worst-case evaluation demonstrates FROG’s robustness against adversarial forget requests, with experiments showing improved unlearning efficacy and reduced disparate impact across multiple graph benchmarks, making it practical for privacy-preserving, fair graph learning.

Abstract

With growing emphasis on privacy regulations, machine unlearning has become increasingly critical in real-world applications such as social networks and recommender systems, many of which are naturally represented as graphs. However, existing graph unlearning methods often modify nodes or edges indiscriminately, overlooking their impact on fairness. For instance, forgetting links between users of different genders may inadvertently exacerbate group disparities. To address this issue, we propose a novel framework that jointly optimizes both the graph structure and the model to achieve fair unlearning. Our method rewires the graph by removing redundant edges that hinder forgetting while preserving fairness through targeted edge augmentation. We further introduce a worst-case evaluation mechanism to assess robustness under challenging scenarios. Experiments on real-world datasets show that our approach achieves more effective and fair unlearning than existing baselines.

FROG: Fair Removal on Graphs

TL;DR

FROG tackles the problem that graph unlearning can inadvertently worsen fairness by altering topology. It introduces a bi-level framework that first augments the graph with fairness-aware edge additions and then sparsifies the structure to achieve unlearning, optimizing both the unlearning loss and a fairness loss. The approach leverages differentiable edge augmentation via Gumbel-softmax and a contrastive fairness objective, followed by a sparsity-driven pruning that respects a limited modification budget. Worst-case evaluation demonstrates FROG’s robustness against adversarial forget requests, with experiments showing improved unlearning efficacy and reduced disparate impact across multiple graph benchmarks, making it practical for privacy-preserving, fair graph learning.

Abstract

With growing emphasis on privacy regulations, machine unlearning has become increasingly critical in real-world applications such as social networks and recommender systems, many of which are naturally represented as graphs. However, existing graph unlearning methods often modify nodes or edges indiscriminately, overlooking their impact on fairness. For instance, forgetting links between users of different genders may inadvertently exacerbate group disparities. To address this issue, we propose a novel framework that jointly optimizes both the graph structure and the model to achieve fair unlearning. Our method rewires the graph by removing redundant edges that hinder forgetting while preserving fairness through targeted edge augmentation. We further introduce a worst-case evaluation mechanism to assess robustness under challenging scenarios. Experiments on real-world datasets show that our approach achieves more effective and fair unlearning than existing baselines.

Paper Structure

This paper contains 17 sections, 2 theorems, 28 equations, 7 figures, 2 tables.

Key Result

theorem 1

Given a 1-layer $g_{\boldsymbol{\omega}}$ with row-normalized adjacency $\tilde{\mathbf{A}}=\mathbf{D}^{-1}\mathbf{A}$ ($\mathbf{D}$ is the degree matrix) for feature smoothing and weight matrix $\mathbf{W}$. Suppose $\exists K>0, \forall v\in \mathcal{V}, ||\mathbf{X}_v||_2\leq K$, then the dyadic

Figures (7)

  • Figure 1: The impact of removing edges on the fairness of graph unlearning algorithms is shown. The $x$-axis represents the homophily ratio, defined as the proportion of a node’s neighbors with identical sensitive features. And the $y$-axis indicates $\Delta_{DP}$, a measure of dyadic fairness.
  • Figure 2: Schematics of FROG: $\bm{(i)}$ Request for edges removal; $\bm{(ii)}$ Adding edges to mitigate bias caused by edge removal; and $\bm{(iii)}$ Removing redundant edges that obstruct the unlearning process.
  • Figure 3: Effectiveness and fairness performance of edge unlearning on Cora, CiteSeer, OGB-Collab, Facebook, and Pubmed.
  • Figure 4: Effectiveness and fairness performance of node unlearning.
  • Figure 5: Worst-case unlearning (left) and worst-case fairness (right) performance on CiteSeer and Cora.
  • ...and 2 more figures

Theorems & Definitions (2)

  • theorem 1
  • theorem 2