Smoothing the Black-Box: Signed-Distance Supervision for Black-Box Model Copying

• URL: http://arxiv.org/abs/2601.20773v1
• Date: Wed, 28 Jan 2026 17:00:04 GMT
• Title: Smoothing the Black-Box: Signed-Distance Supervision for Black-Box Model Copying
• Authors: Rubén Jiménez, Oriol Pujol,
• Abstract summary: Black-box copying provides a practical mechanism to upgrade legacy models.<n>When restricted to hard-label outputs, copying turns into a discontinuous surface reconstruction problem.<n>We propose a distance-based copying framework that replaces hard-label supervision with signed distances to the teacher's decision boundary.
• Score: 0.6015898117103069
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Deployed machine learning systems must continuously evolve as data, architectures, and regulations change, often without access to original training data or model internals. In such settings, black-box copying provides a practical refactoring mechanism, i.e. upgrading legacy models by learning replicas from input-output queries alone. When restricted to hard-label outputs, copying turns into a discontinuous surface reconstruction problem from pointwise queries, severely limiting the ability to recover boundary geometry efficiently. We propose a distance-based copying (distillation) framework that replaces hard-label supervision with signed distances to the teacher's decision boundary, converting copying into a smooth regression problem that exploits local geometry. We develop an $α$-governed smoothing and regularization scheme with Hölder/Lipschitz control over the induced target surface, and introduce two model-agnostic algorithms to estimate signed distances under label-only access. Experiments on synthetic problems and UCI benchmarks show consistent improvements in fidelity and generalization accuracy over hard-label baselines, while enabling distance outputs as uncertainty-related signals for black-box replicas.

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