Generalised Eigenvalue Geometry of Semantic Adversarial Attacks

• URL: http://arxiv.org/abs/2606.19212v1
• Date: Wed, 17 Jun 2026 15:47:57 GMT
• Title: Generalised Eigenvalue Geometry of Semantic Adversarial Attacks
• Abstract summary: We develop a continuous local model of semantic paraphrase perturbations.<n>Worst-case local displacement of the target representation is governed by the largest generalised eigenvalue of a matrix pencil.<n>For uniform control over classes of affine readouts, we derive a distribution-free VC bound for binary attackability indicators.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent empirical work shows that semantically equivalent paraphrases can fool financial sentiment classifiers: although a paraphrase remains close to the original under a strong reference embedding, it may shift the target model's representation enough to change the predicted class. Existing robustness theory either assumes a single-model threat model or focuses mainly on empirical attack algorithms. We develop a continuous local model of semantic paraphrase perturbations that captures this two-model structure. We show that the worst-case local displacement of the target representation, subject to a proxy-model budget, is governed by the largest generalised eigenvalue of a matrix pencil $(A,B)$ constructed from the Jacobians of the two embedding maps. The resulting attackability index $λ^*(x)$ is intrinsic to the local paraphrase geometry and the chosen embedders, yields a closed-form prediction-flip condition for affine readouts, and supports conservative population and finite-sample attackability certificates. For uniform control over classes of affine readouts, we derive a distribution-free VC bound for binary attackability indicators and a scale-sensitive margin bound based on an attackability-adjusted margin that subtracts a local geometric penalty from the standard classifier margin. We also connect the continuous theory to discrete paraphrase search, identify an asymmetry between successful and unsuccessful finite searches, and give a covering condition under which the discrete and continuous settings agree. Finally, we propose an empirical verification framework using soft-token relaxations and generated paraphrase sets to assess the local eigenvalue geometry, prediction-flip condition, and finite-search approximation on a deployed financial-text classifier.

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