From Mathematical to Executable Certificates for Machine Unlearning

2026-10-01

AI Summary

This study addresses the gap between theoretical guarantees and finite-precision deployment in machine unlearning by proposing ExecCert, an executable release certification framework. The method introduces a Retraining Reference Verification (RRV) mechanism alongside an incremental ridge regression head maintenance strategy under frozen representations. Notably, it presents the first incremental RRV implementation for sequential deletions, ensuring certificate validity without reconstructing evidence upon each request. Experimental results demonstrate that ExecCert maintains valid certification across four implementations, completely eliminates spurious releases, closely tracks actual errors, and significantly reduces certification overhead. Ultimately, this work successfully bridges the theoretical rigor of unlearning algorithms with their practical engineering applicability.

Abstract

Machine unlearning is needed when data must be removed because of deletion requests, outdated records, or data-quality concerns, while retraining from scratch can be costly. Certified machine unlearning methods provide mathematical guarantees, while deployed systems release concrete finite-precision artifacts produced by software. To bridge the gap between mathematical guarantees and practical deployment, we introduce Executable Release Certification (ExecCert), a release-time layer that certifies the candidate artifact considered for release. ExecCert either closes a method's native certificate for the executed candidate or applies Retraining-Reference Release Verification (RRV) to certify fidelity to current retain-set retraining. Sequential deletion makes the latter nontrivial because the exact retain-set reference and the stored numerical state evolve separately. For frozen representations with a mutable ridge head, we develop an incremental realization of RRV that maintains certified evidence across deletion requests rather than reconstructing it at each release. On four published unlearning implementations, ExecCert preserves valid certificates, changes release decisions, tightens conservative bounds, and identifies the retraining-reference fidelity supported by concrete outputs. In sequential-service experiments, RRV eliminates false releases caused by stored-equation verification while closely tracking realized error, and incremental certification remains cheaper than both fresh and maintained verified-factor alternatives once release checks become sufficiently frequent.

Problem

• Machine Unlearning
• Executable Certification
• Release Verification
• Finite-precision Artifacts
• Sequential Deletion

Innovation

• Machine Unlearning
• Executable Release Certification
• Retraining-Reference Release Verification
• Incremental Certification
• Ridge Regression