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

arXiv: https://arxiv.org/abs/2601.20773 · HTML: https://mlsanity.com/paper/2601.20773/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Builds on (most cited first, 16 of 16)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Stealing Machine Learning Models via Prediction APIs](https://mlsanity.com/paper/1609.02943/) (2016)
- [Decision-Based Adversarial Attacks: Reliable Attacks Against Black-Box Machine Learning Models](https://mlsanity.com/paper/1712.04248/) (2017)
- [Self-Distillation Amplifies Regularization in Hilbert Space](https://mlsanity.com/paper/2002.05715/) (2020)
- [Knowledge Distillation with Adversarial Samples Supporting Decision Boundary](https://mlsanity.com/paper/1805.05532/) (2018)
- [Zero-Shot Knowledge Distillation from a Decision-Based Black-Box Model](https://mlsanity.com/paper/2106.03310/) (2021)
- [Data Minimization for GDPR Compliance in Machine Learning Models](https://mlsanity.com/paper/2008.04113/) (2020)
- [Understanding the Gains from Repeated Self-Distillation](https://mlsanity.com/paper/2407.04600/) (2024)
- [Explainability in AI Policies: A Critical Review of Communications, Reports, Regulations, and Standards in the EU, US, and UK](https://mlsanity.com/paper/2304.11218/) (2023)
- [Even your Teacher Needs Guidance: Ground-Truth Targets Dampen Regularization Imposed by Self-Distillation](https://mlsanity.com/paper/2102.13088/) (2021)
- [Copying Machine Learning Classifiers](https://mlsanity.com/paper/1903.01879/) (2019)
- [Bridging the Gap between Decision and Logits in Decision-based Knowledge Distillation for Pre-trained Language Models](https://mlsanity.com/paper/2306.08909/) (2023)
- [Sampling Unknown Decision Functions to Build Classifier Copies](https://mlsanity.com/paper/1910.00237/) (2019)
- [Towards a Privacy and Security-Aware Framework for Ethical AI: Guiding the Development and Assessment of AI Systems](https://mlsanity.com/paper/2403.08624/) (2024)
- [Exploring Query Efficient Data Generation towards Data-free Model Stealing in Hard Label Setting](https://mlsanity.com/paper/2412.15276/) (2024)
- [A Scalable and Efficient Iterative Method for Copying Machine Learning Classifiers](https://mlsanity.com/paper/2302.02667/) (2023)

## Abstract (arXiv)

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 H"older/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.