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In this article, we recover singularly-perturbed linear differential systems from their turning points and reduce the rank of the singularity in the parameter to its minimal integer value. Our treatment is Moser-based; that is to say it is…
Monotonicity constraints are powerful regularizers in statistical modelling. They can support fairness in computer-aided decision making and increase plausibility in data-driven scientific models. The seminal min-max (MM) neural network…
Submodularity is an important property of set functions and has been extensively studied in the literature. It models set functions that exhibit a diminishing returns property, where the marginal value of adding an element to a set…
Large language models (LLMs) have shown impressive capabilities across various tasks, but their performance on domain-specific tasks remains limited. While methods like retrieval augmented generation and fine-tuning can help to address…
Applying a sparse constraint on the beam pattern has been suggested to suppress the sidelobe of the minimum variance distortionless response (MVDR) beamformer recently. To further improve the performance, we add a mixed norm constraint on…
Federated fine-tuning offers a promising approach for tuning Large Language Models (LLMs) on edge devices while preserving data privacy. However, fine-tuning these models on edge devices remains challenging due to high memory,…
Block majorization-minimization (BMM) is a simple iterative algorithm for nonconvex optimization that sequentially minimizes a majorizing surrogate of the objective function in each block coordinate while the other block coordinates are…
We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \in [0,1]^{m \times n}$, a vector $b \in [1,\infty)^m$, and a monotone…
In this paper, a multi-objective optimization problem (MOOP) is proposed for maximizing the achievable finite blocklength (FBL) rate while minimizing the utilized channel blocklengths (CBLs) in a reconfigurable intelligent surface…
In downlink multiuser multiple-input multiple-output (MIMO) systems, block diagonalization (BD) is a practical linear precoding scheme which achieves the same degrees of freedom (DoF) as the optimal linear/nonlinear precoding schemes.…
Integrated sensing and communication (ISAC) is a key enabling technique for future wireless networks owing to its efficient hardware and spectrum utilization. In this paper, we focus on dual-functional waveform design for a multi-input…
In this paper, we investigate the challenges of complementary-label learning (CLL), a specialized form of weakly-supervised learning (WSL) where models are trained with labels indicating classes to which instances do not belong, rather than…
In this paper, we study a fundamental problem in submodular optimization, which is called sequential submodular maximization. Specifically, we aim to select and rank a group of $k$ items from a ground set $V$ such that the weighted…
In this paper, we propose a majorization-minimization (MM) algorithm for high-dimensional fused lasso regression (FLR) suitable for parallelization using graphics processing units (GPUs). The MM algorithm is stable and flexible as it can…
In this paper we consider parallelization for applications whose objective can be expressed as maximizing a non-monotone submodular function under a cardinality constraint. Our main result is an algorithm whose approximation is arbitrarily…
In-Context Learning (ICL) enables large language models (LLMs) to achieve rapid task adaptation by learning from demonstrations. With the increase in available context length of LLMs, recent experiments have shown that the performance of…
We consider the problem of minimising functions represented as a difference of lattice submodular functions. We propose analogues to the SupSub, SubSup and ModMod routines for lattice submodular functions. We show that our…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Design Structure Matrix (DSM) modularization, the task of partitioning system elements into cohesive modules, is a fundamental combinatorial challenge in engineering design. Traditional methods treat modularization as a pure graph…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…