We introduce a novel method based on semidefinite program (SDP) for the tight and efficient verification of neural networks. The proposed SDP relaxation advances present state art in SDP-based network by adding set linear constraints eigenvectors. extend this combining it with branch-and-bound that can provably close gap up to zero. show formally approach leads tighter solution than art. report...

Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space structure can be instrumental in improving accuracy and enhancing robustness with respect to noise. We demonstrate a three-pronged procedure for robust called PES: (1) Projection data space. (2) Estimation pole locations....

In recent years we witness the proliferation of semidefinite programming bounds in combinatorial optimization [1,5,8], quantum computing [9,2,3,6,4] and even in complexity theory [7]. Examples to such bounds include the semidefinite relaxation for the maximal cut problem [5], and the quantum value of multi-prover interactive games [3,4]. The first semidefinite programming bound, which gained fa...

With the work of Khot and Vishnoi [18] as a starting point, we obtain integrality gaps for certain strong SDP relaxations of U G. Specifically, we exhibit a U G gap instance for the basic semidefinite program strengthened by all valid linear inequalities on the inner products of up to exp(Ω(log log n)1/4) vectors. For a stronger relaxation obtained from the basic semidefinite ...

We study the exactness of semidefinite programming (SDP) relaxation quadratically constrained quadratic programs (QCQPs). With aggregate sparsity matrix from data matrices a QCQP with n variables, rank and positive semidefiniteness are examined. prove that if is not less than \(n-1\) remains after replacing some off-diagonal nonzero elements zeros, then standard SDP provides an exact optimal so...