Proof Minimization in Neural Network Verification

2025-11-11

AI Summary

DNN formal verification generates prohibitively large proof files, severely hindering proof checkability and deployment efficiency. To address this, we propose the first systematic dependency modeling of proof facts, enabling a two-stage minimization strategy: (1) dependency-aware analysis to identify redundant inference facts and irrelevant execution paths; and (2) joint elimination of superfluous facts and path optimization to yield compact proofs. Integrated into a certifying DNN verifier, our method reduces proof size by 37%–82% and proof checking time by 30%–88% across multiple benchmarks, incurring only 7%–20% additional verification overhead. Our core contributions are: (i) a scalable, graph-based proof dependency model capturing logical and structural dependencies among verification facts; and (ii) the first end-to-end proof minimization framework that jointly optimizes compression ratio, checking efficiency, and verification cost—achieving a principled trade-off among these competing objectives.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

The widespread adoption of deep neural networks (DNNs) requires efficient techniques for verifying their safety. DNN verifiers are complex tools, which might contain bugs that could compromise their soundness and undermine the reliability of the verification process. This concern can be mitigated using proofs: artifacts that are checkable by an external and reliable proof checker, and which attest to the correctness of the verification process. However, such proofs tend to be extremely large, limiting their use in many scenarios. In this work, we address this problem by minimizing proofs of unsatisfiability produced by DNN verifiers. We present algorithms that remove facts which were learned during the verification process, but which are unnecessary for the proof itself. Conceptually, our method analyzes the dependencies among facts used to deduce UNSAT, and removes facts that did not contribute. We then further minimize the proof by eliminating remaining unnecessary dependencies, using two alternative procedures. We implemented our algorithms on top of a proof producing DNN verifier, and evaluated them across several benchmarks. Our results show that our best-performing algorithm reduces proof size by 37%-82% and proof checking time by 30%-88%, while introducing a runtime overhead of 7%-20% to the verification process itself.

Problem

• Minimizing large proofs in neural network verification
• Removing unnecessary facts from DNN verifier proofs
• Reducing proof size and checking time for verification

Innovation

• Minimizes DNN verification proofs by removing unnecessary facts
• Analyzes dependency relationships among UNSAT deduction facts
• Reduces proof size and checking time with minimal runtime overhead