Verifying Properties of Binary Neural Networks Using Sparse Polynomial Optimization

TL;DR

This paper presents a novel verification method for Binary Neural Networks using sparse polynomial optimization and semidefinite programming, improving scalability and numerical stability over traditional SAT and MILP-based approaches.

Contribution

It introduces a new verification approach leveraging semidefinite relaxations from sparse polynomial optimization, enhancing scalability and numerical stability for BNN robustness analysis.

Findings

Effective verification of BNN robustness against adversarial attacks.

Improved scalability over traditional methods.

Better numerical stability with continuous input space.

Abstract

This paper explores methods for verifying the properties of Binary Neural Networks (BNNs), focusing on robustness against adversarial attacks. Despite their lower computational and memory needs, BNNs, like their full-precision counterparts, are also sensitive to input perturbations. Established methods for solving this problem are predominantly based on Satisfiability Modulo Theories and Mixed-Integer Linear Programming techniques, which are characterized by NP complexity and often face scalability issues. We introduce an alternative approach using Semidefinite Programming relaxations derived from sparse Polynomial Optimization. Our approach, compatible with continuous input space, not only mitigates numerical issues associated with floating-point calculations but also enhances verification scalability through the strategic use of tighter first-order semidefinite relaxations. We demonstrate the effectiveness of our method in verifying robustness against both $\|.\|_\infty$ and $\|.\|_2$-based adversarial attacks.