[Paper Review] Automated Verification of Neural Networks: Advances, Challenges and Perspectives

Francesco Leofante, Nina Narodytska+2 more|arXiv (Cornell University)|May 25, 2018

Adversarial Robustness in Machine Learning17 references51 citations

TL;DR

This survey categorizes automated reasoning approaches for verifying neural networks, detailing techniques, networks, properties, and future research directions.

ABSTRACT

Neural networks are one of the most investigated and widely used techniques in Machine Learning. In spite of their success, they still find limited application in safety- and security-related contexts, wherein assurance about networks' performances must be provided. In the recent past, automated reasoning techniques have been proposed by several researchers to close the gap between neural networks and applications requiring formal guarantees about their behavior. In this work, we propose a primer of such techniques and a comprehensive categorization of existing approaches for the automated verification of neural networks. A discussion about current limitations and directions for future investigation is provided to foster research on this topic at the crossroads of Machine Learning and Automated Reasoning.

Motivation & Objective

• Summarize the landscape of automated verification techniques for neural networks.
• Categorize existing approaches by network type and property.
• Identify current limitations and propose directions for future research at the ML and Automated Reasoning intersection.

Proposed method

• Explain verification frameworks by encoding neural networks as constraint systems.
• Describe decision procedures: SAT, SMT, and MIP solvers, and how they handle neural constraints.
• Classify literature by network type (BNN, DNN variations, shallow NN) and properties (invariance, invertibility, equivalence).
• Present a unified property formalism using pre/post conditions and universal/existential quantifications.
• Discuss local versus global property verification settings.

Experimental results

Research questions

• RQ1 What are the main automated reasoning techniques used to verify neural networks?
• RQ2 How can networks be categorized to organize verification approaches by properties and architecture?
• RQ3 What properties are prioritized in NN verification (invariance, invertibility, equivalence) and in what contexts (local/global)?
• RQ4 What are the current limitations and future directions at the intersection of ML and automated reasoning?

Key findings

• Overview of CDCL-based SAT, SMT, and MIP as core decision procedures for NN verification.
• A taxonomy of verification approaches across network types: BNN, DNN (ReLU, pooling), and generic NN.
• Formal definitions of invariance, invertibility, and equivalence as verification properties, including both global and local variants.
• Discussion of how SMT builds Boolean abstractions and refines with theory lemmas to solve NN constraints.
• Identification of scaling challenges for deep networks and the need for cross-disciplinary research to advance verification techniques.