Related papers: Two-Dimensional Adaptive Fourier Decomposition
One of the most appealing aspects of machine learning for material design is its high throughput exploration of chemical spaces, but to reach the ceiling of ML-aided exploration, more than current model architectures and processing…
Aspect-orientation is a relatively new paradigm that introduces abstractions to modularize the implementation of system-wide policies. It is based on a composition operation, called aspect weaving, that implicitly modifies a base system by…
In this paper, we develop a unified convergence analysis framework for the Accelerated Smoothed GAp ReDuction algorithm (ASGARD) introduced in [20, Tran-Dinh et al, 2015] Unlike[20], the new analysis covers three settings in a single…
A $k$-submodular function naturally generalizes submodular functions by taking as input $k$ disjoint subsets, rather than a single subset. Unlike standard submodular maximization, which only requires selecting elements for the solution,…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
Over-the-air (OTA) federated learning (FL) has been well recognized as a scalable paradigm that exploits the waveform superposition of the wireless multiple-access channel to aggregate model updates in a single use. Existing OTA-FL designs…
Multimodal camera-LiDAR fusion technology has found extensive application in 3D object detection, demonstrating encouraging performance. However, existing methods exhibit significant performance degradation in challenging scenarios…
Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can…
In this work we propose a new deep learning tool called deep dictionary learning. Multi-level dictionaries are learnt in a greedy fashion, one layer at a time. This requires solving a simple (shallow) dictionary learning problem, the…
This research introduces an FPGA-based hardware accelerator to optimize the Singular Value Decomposition (SVD) and Fast Fourier transform (FFT) operations in AI models. The proposed design aims to improve processing speed and reduce…
Efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes. Here, we argue for the…
It has been shown that dimension reduction methods such as PCA may be inherently prone to unfairness and treat data from different sensitive groups such as race, color, sex, etc., unfairly. In pursuit of fairness-enhancing dimensionality…
We examine sparse grid quadrature on weighted tensor products (WTP) of reproducing kernel Hilbert spaces on products of the unit sphere, in the case of worst case quadrature error for rules with arbitrary quadrature weights. We describe a…
Retrieval-augmented generation (RAG) has emerged as a paradigm for grounding large language models in external knowledge, yet most existing RAG systems assume centralized knowledge access and ample computation. These assumptions break down…
We give an new arithmetic algorithm to compute the generalized Discrete Fourier Transform (DFT) over finite groups $G$. The new algorithm uses $O(|G|^{\omega/2 + o(1)})$ operations to compute the generalized DFT over finite groups of Lie…
We propose a federated version of adaptive gradient methods, particularly AdaGrad and Adam, within the framework of over-the-air model training. This approach capitalizes on the inherent superposition property of wireless channels,…
We propose a new algorithm for Adaptive Finite Element Methods (AFEMs) based on smoothing iterations (S-AFEM), for linear, second-order, elliptic partial differential equations (PDEs). The algorithm is inspired by the ascending phase of the…
We present an adaptive algorithm for effectively solving rough differential equations (RDEs) using the log-ODE method. The algorithm is based on an error representation formula that accurately describes the contribution of local errors to…
This paper presents a novel paradigm in simulation-based engineering sciences by introducing a new framework called Generative Parametric Design (GPD). The GPD framework enables the generation of new designs along with their corresponding…
Submodular maximization has been widely studied over the past decades, mostly because of its numerous applications in real-world problems. It is well known that the standard greedy algorithm guarantees a worst-case approximation factor of…