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arXiv · 2609.38991

Anchoring Adversarial Trajectories to Data Manifolds: A Bilevel Transfer Optimization Framework

Yaohua Liu·Yifan Guo·Jiaxin Gao
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Abstract

A key bottleneck in adversarial transfer is a trajectory-level geometric disconnect: ambient gradients often drift away from the intrinsic data manifold, causing surrogate-specific overfitting. To rectify this, we propose Manifold Anchored Bilevel Transfer (MABT), a unified framework that anchors adversarial trajectories to the shared semantic subspace. MABT introduces a relaxed manifold-anchoring operator as a semantic rectifier to suppress off-manifold noise. With this constraint, we cast transfer attack generation as a distributional bilevel optimization problem that learns a geometry-aligned initialization by minimizing expected transfer risk under a surrogate uncertainty distribution. We further develop a Hessian-free solver with linear-time complexity to handle the resulting hierarchy. Experiments demonstrate improved transferability for 10 baseline attackers across 28 attack configurations, diverse victim architectures, and defense mechanisms.

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Yaohua Liu, Yifan Guo, Jiaxin Gao. 2026-09-30. Anchoring Adversarial Trajectories to Data Manifolds: A Bilevel Transfer Optimization Framework. https://arxiv.org/abs/2609.38991

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