Related papers: Optimized numerical inverse Laplace transformation

We propose a generalization of Laplace transformations to the case of linear partial differential operators (LPDOs) of arbitrary order in R^n. Practically all previously proposed differential transformations of LPDOs are particular cases of…

A framework for robust optimization under uncertainty based on the use of the generalized inverse distribution function (GIDF), also called quantile function, is here proposed. Compared to more classical approaches that rely on the usage of…

The Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method is a cutting-edge distributed optimization algorithm known for its superior numerical performance. It relies on each agent transmitting information to a central…

We reexamine Smale's alpha theory as a way to certify a numerical solution to an analytic system. For a given point and a system, Smale's alpha theory determines whether Newton's method applied to this point shows the quadratic convergence…

While Supervised Fine-Tuning (SFT) and Rejection Sampling Fine-Tuning (RFT) are standard for LLM alignment, they either rely on costly expert data or discard valuable negative samples, leading to data inefficiency. To address this, we…

In this paper, we present Neural Adaptive Tomography (NeAT), the first adaptive, hierarchical neural rendering pipeline for multi-view inverse rendering. Through a combination of neural features with an adaptive explicit representation, we…

With the rise of Transformer models in NLP and CV domain, Multi-Head Attention has been proven to be a game-changer. However, its expensive computation poses challenges to the model throughput and efficiency, especially for the long…

The Transformer architecture revolutionized the field of natural language processing (NLP). Transformers-based models (e.g., BERT) power many important Web services, such as search, translation, question-answering, etc. While enormous…

This study explores the quantisation-aware training (QAT) on time series Transformer models. We propose a novel adaptive quantisation scheme that dynamically selects between symmetric and asymmetric schemes during the QAT phase. Our…

The nonlinear Fourier transform (NLFT) extends the classical Fourier transform by replacing addition with matrix multiplication. While the NLFT on $\mathrm{SU}(1,1)$ has been widely studied, its $\mathrm{SU}(2)$ variant has only recently…

The problem of minimizing a sum of local convex objective functions over a networked system captures many important applications and has received much attention in the distributed optimization field. Most of existing work focuses on…

The Vision Transformer (ViT) excels in accuracy when handling high-resolution images, yet it confronts the challenge of significant spatial redundancy, leading to increased computational and memory requirements. To address this, we present…

High-order numerical methods enhance Transformer performance in tasks like NLP and CV, but introduce a performance-efficiency trade-off due to increased computational overhead. Our analysis reveals that conventional efficiency techniques,…

We introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are considered as linear…

Recent years have seen a phenomenal rise in performance and applications of transformer neural networks. The family of transformer networks, including Bidirectional Encoder Representations from Transformer (BERT), Generative Pretrained…

Finite Element codes used for solving the mechanical equilibrium equations in transient problems associated to (time-dependent) viscoelastic media generally relies on time-discretized versions of the selected constitutive law. Recent…

We study sampling from posterior distributions in Bayesian linear inverse problems where $A$, the parameters to observables operator, is computationally expensive. In many applications, $A$ can be factored in a manner that facilitates the…

We present a same-level comparison of the most prominent inversion methods for the reconstruction of the matter density field in the quasi-linear regime from the Ly$\alpha$ forest flux. Moreover, we present a pathway for refining the…

We design a family of image classification architectures that optimize the trade-off between accuracy and efficiency in a high-speed regime. Our work exploits recent findings in attention-based architectures, which are competitive on highly…

We study a Newton-like method for the minimization of an objective function that is the sum of a smooth convex function and an l-1 regularization term. This method, which is sometimes referred to in the literature as a proximal Newton…