What question did this study set out to answer?

To explore formal methods for verifying the robustness of neural networks against adversarial attacks.

April 11, 2026Open Access

Formal Verication of Neural Network Robustness via Logic-Based Methods

Key Points

To explore formal methods for verifying the robustness of neural networks against adversarial attacks.
Reviewed over 130 papers on logic-based neural network verification methods.
Examined frameworks such as SMT, first-order logic, and linear temporal logic.
Analyzed practical tools like Marabou and Reluplex for verifying network properties.
Discussed a unified logical framework for compositional reasoning.
Assessed properties like local and global robustness and fairness.
Identified fundamental limitations in logic-based approaches, including expressiveness and scalability challenges.
Established soundness, completeness, and decidability of encoded problems.
Provided complexity-theoretic analysis of various robustness properties.

Abstract

The deployment of neural networks in safety-critical systems demands formalguarantees of robustness against adversarial perturbations. This survey examineslogic-based approaches to neural network robustness verication, bridging the gapbetween machine learning and formal methods. We present a comprehensive reviewof methods that encode neural network verication problems into logical formalisms,including satisability modulo theories (SMT), rst-order logic, linear temporal logic(LTL), and Hoare-style program logics. Our treatment covers the theoretical foundations of these encodingssoundness, completeness, and decidabilityas well aspractical verication tools such as Marabou, Reluplex, and VeriNet. We introducea unied logical framework that subsumes existing approaches and enables compositional reasoning about neural network properties. We survey applications to localand global robustness, fairness, monotonicity, and Lipschitz continuity, providingcomplexity-theoretic analysis for each property class. Our review covers over 130papers published between 2017 and 2025 and identies fundamental limitations oflogic-based approaches, including the expressiveness-decidability trade-o and thechallenge of scaling to modern architectures.

Formal Verication of Neural Network Robustness via Logic-Based Methods

Key Points

Abstract

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