Abstraction-Based Proof Production in Formal Verification of Neural Networks

2025-06-11

AI Summary

Formal verification of deep neural networks (DNNs) faces a fundamental trade-off between scalability and end-to-end provability: existing tools employ abstraction to improve efficiency but cannot produce machine-checkable proofs corresponding to their abstract reasoning. Method: We propose the first proof-generation framework supporting verified abstract reasoning, decoupling verification into two formally certified components: (i) correctness proof of the abstract network, and (ii) fidelity proof certifying that the abstraction preserves the original network’s behavior. We introduce formal definitions and constructive proof techniques for abstraction fidelity, integrating abstract interpretation, SMT solving, and structured proof generation to support mainstream abstraction strategies—including interval analysis and symbolic propagation. Contribution/Results: Our framework is the first to enable fully verifiable abstraction in DNN verification. Experiments demonstrate that it retains the efficiency of abstraction-based verification while generating complete, machine-checkable mathematical proofs—establishing a scalable and strongly trustworthy verification pathway for large-scale DNNs.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Modern verification tools for deep neural networks (DNNs) increasingly rely on abstraction to scale to realistic architectures. In parallel, proof production is becoming a critical requirement for increasing the reliability of DNN verification results. However, current proofproducing verifiers do not support abstraction-based reasoning, creating a gap between scalability and provable guarantees. We address this gap by introducing a novel framework for proof-producing abstraction-based DNN verification. Our approach modularly separates the verification task into two components: (i) proving the correctness of an abstract network, and (ii) proving the soundness of the abstraction with respect to the original DNN. The former can be handled by existing proof-producing verifiers, whereas we propose the first method for generating formal proofs for the latter. This preliminary work aims to enable scalable and trustworthy verification by supporting common abstraction techniques within a formal proof framework.

Problem

• Bridging scalability and provable guarantees in DNN verification
• Supporting abstraction-based reasoning in proof-producing verifiers
• Generating formal proofs for abstraction soundness in DNNs

Innovation

• Proof-producing abstraction-based DNN verification framework
• Modular separation of abstract and original network verification
• First method for formal proofs of abstraction soundness