  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.
