Bounding the Black Box: A Statistical Certification Framework for AI Risk Regulation

2026-04-23

AI Summary

Current AI regulation lacks a quantifiable definition of “acceptable risk” and corresponding verification mechanisms, hindering compliance certification for high-risk systems. This work proposes the first two-stage statistical certification framework for black-box AI: regulatory authorities first define an acceptable failure probability and input domain; then, leveraging RoMA/gRoMA methods, the framework computes an auditable upper bound on the failure rate for AI systems of arbitrary architecture without requiring access to internal model details. By adapting aviation safety certification paradigms to AI governance, the approach employs statistical hypothesis testing and scalable black-box verification to generate legally defensible safety certificates. It directly aligns with regulatory requirements such as the EU AI Act and shifts accountability upstream to developers.

Technology Category

• Philosophy and Ethics of AI: Safety, Robustness & Trustworthiness
• Machine Learning: Calibration & Uncertainty Quantification
• Natural Language Processing: Safety and Robustness

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Security and privacy of machine learning and AI applications

Abstract

Artificial intelligence now decides who receives a loan, who is flagged for criminal investigation, and whether an autonomous vehicle brakes in time. Governments have responded: the EU AI Act, the NIST Risk Management Framework, and the Council of Europe Convention all demand that high-risk systems demonstrate safety before deployment. Yet beneath this regulatory consensus lies a critical vacuum: none specifies what ``acceptable risk'' means in quantitative terms, and none provides a technical method for verifying that a deployed system actually meets such a threshold. The regulatory architecture is in place; the verification instrument is not. This gap is not theoretical. As the EU AI Act moves into full enforcement, developers face mandatory conformity assessments without established methodologies for producing quantitative safety evidence - and the systems most in need of oversight are opaque statistical inference engines that resist white-box scrutiny. This paper provides the missing instrument. Drawing on the aviation certification paradigm, we propose a two-stage framework that transforms AI risk regulation into engineering practice. In Stage One, a competent authority formally fixes an acceptable failure probability $δ$ and an operational input domain $\varepsilon$ - a normative act with direct civil liability implications. In Stage Two, the RoMA and gRoMA statistical verification tools compute a definitive, auditable upper bound on the system's true failure rate, requiring no access to model internals and scaling to arbitrary architectures. We demonstrate how this certificate satisfies existing regulatory obligations, shifts accountability upstream to developers, and integrates with the legal frameworks that exist today.

Problem

• AI risk regulation
• statistical certification
• black-box AI
• acceptable risk
• verification

Innovation

• statistical certification
• black-box verification
• AI risk regulation
• failure probability bound
• regulatory compliance