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Nuclear-norm regularization plays a vital role in many learning tasks, such as low-rank matrix recovery (MR), and low-rank representation (LRR). Solving this problem directly can be computationally expensive due to the unknown rank of…

Multiple kernel learning is a type of multiview learning that combines different data modalities by capturing view-specific patterns using kernels. Although supervised multiple kernel learning has been extensively studied, until recently,…

Retrieval-Augmented Generation (RAG) significantly enhances Large Language Models (LLMs), but simultaneously exposes a critical vulnerability to knowledge poisoning attacks. Existing attack methods like PoisonedRAG remain detectable due to…

We present BadGD, a unified theoretical framework that exposes the vulnerabilities of gradient descent algorithms through strategic backdoor attacks. Backdoor attacks involve embedding malicious triggers into a training dataset to disrupt…

Recently, low-rank matrix recovery theory has been emerging as a significant progress for various image processing problems. Meanwhile, the group sparse coding (GSC) theory has led to great successes in image restoration (IR) problem with…

Compared to classical deep neural networks its binarized versions can be useful for applications on resource-limited devices due to their reduction in memory consumption and computational demands. In this work we study deep neural networks…

Massive multiple-input-multiple-output (M-MIMO) features a capability for spatial multiplexing of large number of users. This number becomes even more extreme in extra-large (XL-MIMO), a variant of M-MIMO where the antenna array is of very…

Rank aggregation with pairwise comparisons has shown promising results in elections, sports competitions, recommendations, and information retrieval. However, little attention has been paid to the security issue of such algorithms, in…

The Branch-and-bound (B&B) algorithm is the main solver for Mixed Integer Linear Programs (MILPs), where the selection of branching variable is essential to computational efficiency. However, traditional heuristics for branching often fail…

DNN is presenting human-level performance for many complex intelligent tasks in real-world applications. However, it also introduces ever-increasing security concerns. For example, the emerging adversarial attacks indicate that even very…

With the advent of DeepSeek-R1, a new wave of reinforcement learning (RL) methods has emerged that seem to unlock stronger mathematical reasoning. However, a closer look at the open-source ecosystem reveals a critical limitation: with…

Deep Neural Network (DNN) classifiers are vulnerable to adversarial attack, where an imperceptible perturbation could result in misclassification. However, the vulnerability of DNN-based image ranking systems remains under-explored. In this…

This paper provides a unified and detailed presentation of root-node style algebraic multigrid (AMG). Algebraic multigrid is a popular and effective iterative method for solving large, sparse linear systems that arise from discretizing…

Bayesian neural networks (BNNs) demonstrate promising success in improving the robustness and uncertainty quantification of modern deep learning. However, they generally struggle with underfitting at scale and parameter efficiency. On the…

Augmented Lagrangian Method (ALM) combined with Burer-Monteiro (BM) factorization, dubbed ALM-BM, offers a powerful approach for solving large-scale low-rank semidefinite programs (SDPs). Despite its empirical success, the theoretical…

Deployment of neural networks on resource-constrained devices demands models that are both compact and robust to adversarial inputs. However, compression and adversarial robustness often conflict. In this work, we introduce a dynamical…

This paper introduces RDA, a pioneering approach designed to address two primary deficiencies prevalent in previous endeavors aiming at stealing pre-trained encoders: (1) suboptimal performances attributed to biased optimization objectives,…

Despite the enormous success of machine learning models in various applications, most of these models lack resilience to (even small) perturbations in their input data. Hence, new methods to robustify machine learning models seem very…

Weighted low rank approximation is a fundamental problem in numerical linear algebra, and it has many applications in machine learning. Given a matrix $M \in \mathbb{R}^{n \times n}$, a non-negative weight matrix $W \in \mathbb{R}_{\geq…

Retrieval-Augmented Generation (RAG) increases the reliability and trustworthiness of the LLM response and reduces hallucination by eliminating the need for model retraining. It does so by adding external data into the LLM's context. We…