摘要：
The talk will be divided into two parts. The first part focuses on the computation of the sparse Fourier sum of squares (FSOS) for nonnegative functions on finite abelian groups. The proposed method is based on the fast (inverse) Fourier transform, and its complexity is only quasilinear with respect to the cardinality of the group. In addition, an error analysis is provided for the sparse FSOS.
The second part is about verifying the properties of Binary Neural Networks (BNNs), focusing on robustness against adversarial attacks. Existing methods for solving this problem are typically rely on Satisfiability Modulo Theories (SMT) and Mixed-Integer Linear Programming (MILP) techniques, which are burdened with high computational complexity and often face scalability issues. We introduce an alternative approach using Semidefinite Programming relaxations derived from sparse Polynomial Optimization.

报告人介绍：
杨剑霆，现为中国科学院数学与系统科学研究院博士后，合作导师为叶科副研究员。2023年博士毕业于中国科学院数学与系统科学研究院，导师为支丽红研究员，2023-2024年在CNRS@CREATE做博士后，合作导师为Victor Magron教授和 Jean-Bernard Lasserre教授。主要研究方向为多项式优化的理论与应用。