Related papers: Optimization of Fast Algorithms for Global Quadrat…
Optimization tasks over relational data, such as clustering, often suffer from the prohibitive cost of join operations, which are necessary to access the full dataset. While geometric data structures like BBD trees yield fast approximation…
The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…
Mixture-of-Experts Large Language Models (MoE-LLMs) achieve strong performance but incur substantial memory overhead due to massive expert parameters. Mixed-precision quantization mitigates this cost by allocating expert-wise bit-widths…
Quantitative MRI (qMRI) offers tissue-specific biomarkers that can be tracked over time or compared across populations; however, its adoption in clinical research is hindered by significant computational demands of parameter estimation.…
Recent studies suggest that gradient-based methods applied to relaxed box-constrained Quadratic Unconstrained Binary Optimization (QUBO) formulations can outperform classical heuristics in some large-scale regimes, often relying on heavy…
We propose a patchwise local Fourier extension method for approximating smooth functions on general two dimensional domains with curved boundaries. The domain is embedded into a Cartesian background grid and decomposed into rectangular…
Low-bit floating-point (FP) formats, such as FP8, provide significant acceleration and memory savings in model training thanks to native hardware support on modern GPUs and NPUs. However, we analyze that FP8 quantization offers speedup…
Gradient boosting decision trees (GBDTs) have seen widespread adoption in academia, industry and competitive data science due to their state-of-the-art performance in many machine learning tasks. One relative downside to these models is the…
Many problems in real life can be converted to combinatorial optimization problems (COPs) on graphs, that is to find a best node state configuration or a network structure such that the designed objective function is optimized under some…
Existing methods for merging experts during model training and fine-tuning predominantly rely on Euclidean geometry, which assumes a flat parameter space. This assumption can limit the model's generalization ability, especially during the…
We consider strongly convex distributed consensus optimization over connected networks. EFIX, the proposed method, is derived using quadratic penalty approach. In more detail, we use the standard reformulation { transforming the original…
The Internet of Things has experienced significant growth and has become an integral part of various industries. This expansion has given rise to the Industrial IoT initiative where industries are utilizing IoT technology to enhance…
We design accelerated algorithms with improved rates for several fundamental classes of optimization problems. Our algorithms all build upon techniques related to the analysis of primal-dual extragradient methods via relative Lipschitzness…
The combinatorial problem Max-Cut has become a benchmark in the evaluation of local search heuristics for both quantum and classical optimisers. In contrast to local search, which only provides average-case performance guarantees, the…
We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…
We study the expressibility and learnability of convex optimization solution functions and their multi-layer architectural extension. The main results are: \emph{(1)} the class of solution functions of linear programming (LP) and quadratic…
This paper introduces a novel, robust, and computationally efficient framework for high-quality quadrilateral mesh generation on general two-dimensional domains. The core of the proposed approach is a novel method for computing cross fields…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
Explicit representations of densities for linear parabolic partial differential equations are useful in order to design computation schemes of high accuracy for a considerable class of diffusion models. Approximations of lower order based…