相关论文: Semialgebraic Representation of Monotone Deep Equi…

Semilinear parabolic partial differential equations (PDEs) are fundamental to modeling complex dynamical systems across scientific domains. The Deep Backward Stochastic Differential Equation (BSDE) method is a promising approach for…

We propose and analyse a new Milstein type scheme for simulating stochastic differential equations (SDEs) with highly nonlinear coefficients. Our work is motivated by the need to justify multi-level Monte Carlo simulations for…

A globally robust deep neural network resists perturbations on all meaningful inputs. Current robustness certification methods emphasize local robustness, struggling to scale and generalize. This paper presents a systematic and efficient…

A set is called semidefinite representable or semidefinite programming (SDP) representable if it can be represented as the projection of a higher dimensional set which is represented by some Linear Matrix Inequality (LMI). This paper…

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…

Consistency regularization and pseudo-labeling have significantly advanced semi-supervised learning (SSL). Prior works have effectively employed Mixup for consistency regularization in SSL. However, our findings indicate that applying Mixup…

Recent years have witnessed a resurgence in using ReLU neural networks (NNs) to represent model predictive control (MPC) policies. However, determining the required network complexity to ensure closed-loop performance remains a fundamental…

The amount of manually labeled data is limited in medical applications, so semi-supervised learning and automatic labeling strategies can be an asset for training deep neural networks. However, the quality of the automatically generated…

As large language models (LLMs) become increasingly capable and widely adopted, benchmarks play a central role in assessing their practical utility. For example, SWE-Bench Verified has emerged as a critical benchmark for evaluating LLMs'…

Deep-learning based speech separation models confront poor generalization problem that even the state-of-the-art models could abruptly fail when evaluating them in mismatch conditions. To address this problem, we propose an…

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz constant in neural…

In model predictive control (MPC) for hybrid systems, solving optimization problems efficiently and with guarantees on worst-case computational complexity is critical to satisfy the real-time constraints in these applications. These…

The core issue in semi-supervised learning (SSL) lies in how to effectively leverage unlabeled data, whereas most existing methods tend to put a great emphasis on the utilization of high-confidence samples yet seldom fully explore the usage…

In this paper, we consider the problem of minimizing a general homogeneous quadratic function, subject to three real or four complex homogeneous quadratic inequality or equality constraints. For this problem, we present a sufficient and…

This paper introduces MixDiff, a new self-supervised learning (SSL) pre-training framework that combines real and synthetic images. Unlike traditional SSL methods that predominantly use real images, MixDiff uses a variant of Stable…

This paper develops new semidefinite programming (SDP) relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation performance. The first class of problem…

The accuracy and complexity of machine learning algorithms based on kernel optimization are determined by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…

Supervised deep learning methods have shown promise for large-scale channel estimation (LCE), but their reliance on ground-truth channel labels greatly limits their practicality in real-world systems. In this paper, we propose an…

In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence of stabilized quadratic…

This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…