Advancing Neural Network Verification through Hierarchical Safety Abstract Interpretation

TL;DR

This paper introduces a hierarchical safety verification framework for deep neural networks using abstract interpretation, enabling nuanced safety assessments with potentially less computational effort than traditional binary methods.

Contribution

It proposes a new Abstract DNN-Verification problem that assesses multiple safety levels, enhancing the granularity of neural network safety analysis.

Findings

Allows ranking adversarial inputs by safety violation levels

Achieves comparable or reduced computational effort compared to binary verification

Demonstrates effectiveness on reinforcement learning and benchmark tasks

Abstract

Traditional methods for formal verification (FV) of deep neural networks (DNNs) are constrained by a binary encoding of safety properties, where a model is classified as either safe or unsafe (robust or not robust). This binary encoding fails to capture the nuanced safety levels within a model, often resulting in either overly restrictive or too permissive requirements. In this paper, we introduce a novel problem formulation called Abstract DNN-Verification, which verifies a hierarchical structure of unsafe outputs, providing a more granular analysis of the safety aspect for a given DNN. Crucially, by leveraging abstract interpretation and reasoning about output reachable sets, our approach enables assessing multiple safety levels during the FV process, requiring the same (in the worst case) or even potentially less computational effort than the traditional binary verification approach. Specifically, we demonstrate how this formulation allows rank adversarial inputs according to their abstract safety level violation, offering a more detailed evaluation of the model's safety and robustness. Our contributions include a theoretical exploration of the relationship between our novel abstract safety formulation and existing approaches that employ abstract interpretation for robustness verification, complexity analysis of the novel problem introduced, and an empirical evaluation considering both a complex deep reinforcement learning task (based on Habitat 3.0) and standard DNN-Verification benchmarks.