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Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…

In this paper, we show that the standard semidefinite programming (SDP) relaxation of altering current optimal power flow (AC OPF) can be equivalently reformulated as second-order cone programming (SOCP) relaxation with maximal clique- and…

The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…

Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021]…

We propose a semidefinite programming (SDP) algorithm for community detection in the stochastic block model, a popular model for networks with latent community structure. We prove that our algorithm achieves exact recovery of the latent…

Deep neural networks (DNNs) play an increasingly important role in various computer systems. In order to create these networks, engineers typically specify a desired topology, and then use an automated training algorithm to select the…

Fast and precise Lipschitz constant estimation of neural networks is an important task for deep learning. Researchers have recently found an intrinsic trade-off between the accuracy and smoothness of neural networks, so training a network…

Fine-tuning is now the primary method for adapting large neural networks, but it also introduces new integrity risks. An untrusted party can insert backdoors, change safety behavior, or overwrite large parts of a model while claiming only…

Previous studies have shown that spike-timing-dependent plasticity (STDP) can be used in spiking neural networks (SNN) to extract visual features of low or intermediate complexity in an unsupervised manner. These studies, however, used…

We introduce Sieve-SDP, a simple facial reduction algorithm to preprocess semidefinite programs (SDPs). Sieve-SDP inspects the constraints of the problem to detect lack of strict feasibility, deletes redundant rows and columns, and reduces…

Recently deep neural networks have been successfully used for various classification tasks, especially for problems with massive perfectly labeled training data. However, it is often costly to have large-scale credible labels in real-world…

Although neural networks are widely used, it remains challenging to formally verify the safety and robustness of neural networks in real-world applications. Existing methods are designed to verify the network before deployment, which are…

Formal verification of neural networks is an active topic of research, and recent advances have significantly increased the size of the networks that verification tools can handle. However, most methods are designed for verification of an…

We study Semidefinite Programming, \SDPc relaxations for Sensor Network Localization, \SNLc with anchors and with noisy distance information. The main point of the paper is to view \SNL as a (nearest) Euclidean Distance Matrix, \EDM,…

Robustness certification against bounded input noise or adversarial perturbations is increasingly important for deployment recurrent neural networks (RNNs) in safety-critical control applications. To address this challenge, we present…

There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these…

Large language models (LLMs) are increasingly integrated into real-time machine learning applications, where safeguarding user privacy is paramount. Traditional differential privacy mechanisms often struggle to balance privacy and accuracy,…

Machine Learning (ML) has exhibited substantial success in the field of Natural Language Processing (NLP). For example large language models have empirically proven to be capable of producing text of high complexity and cohesion. However,…

While semidefinite programming (SDP) problems are polynomially solvable in theory, it is often difficult to solve large SDP instances in practice. One technique to address this issue is to relax the global positive-semidefiniteness (PSD)…

HDSDP is a numerical software solving the semidefinite programming problems. The main framework of HDSDP resembles the dual-scaling interior point solver DSDP [BY2008] and several new features, including a dual method based on the…