Related papers: Differentiation via Logarithmic Expansions

The FLAME methodology for deriving linear algebra algorithms from specification, first introduced around 2000, has been successfully applied to a broad cross section of operations. An open question has been whether it can yield algorithms…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

We study two practically important cases of model based clustering using Gaussian Mixture Models: (1) when there is misspecification and (2) on high dimensional data, in the light of recent advances in Gradient Descent (GD) based…

We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor…

Label distribution learning (LDL) is an effective method to predict the label description degree (a.k.a. label distribution) of a sample. However, annotating label distribution (LD) for training samples is extremely costly. So recent…

We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…

Semantic segmentation and instance level segmentation made substantial progress in recent years due to the emergence of deep neural networks (DNNs). A number of deep architectures with Convolution Neural Networks (CNNs) were proposed that…

Building on the successes of local kernel methods for approximating the solutions to partial differential equations (PDE) and the evaluation of definite integrals (quadrature/cubature), a local estimate of the error in such approximations…

In this paper, we propose two linearized finite difference schemes for solving the logarithmic Schr\"odinger equation (LogSE) without the need for regularization of the logarithmic term. These two schemes employ the first-order and the…

We present the numerical analysis of a finite element method (FEM) for one-dimensional Dirichlet problems involving the logarithmic Laplacian (the pseudo-differential operator that appears as a first-order expansion of the fractional…

The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…

We introduce Dynamic Nested Depth (DND), a novel method that improves performance for off-the-shelf LLMs by selecting critical tokens to reprocess in a nested depth manner. Specifically, at the end of the given transformer layer, DND…

Label distribution learning (LDL) is an effective method to predict the relative label description degree (a.k.a. label distribution) of a sample. However, the label distribution is not a complete representation of an instance because it…

Approximate probabilistic inference algorithms are central to many fields. Examples include sequential Monte Carlo inference in robotics, variational inference in machine learning, and Markov chain Monte Carlo inference in statistics. A key…

We describe a systematic expansion for full QCD. The leading term in the expansion gives the valence approximation. The expansion reproduces full QCD if an infinite number of higher terms are included.

The growing gap between the increasing complexity of large language models (LLMs) and the limited computational budgets of edge devices poses a key challenge for efficient on-device inference, despite gradual improvements in hardware…

We consider in this paper the formulation of approximate inference in Bayesian networks as a problem of exact inference on an approximate network that results from deleting edges (to reduce treewidth). We have shown in earlier work that…

A branch and bound algorithm is developed for global optimization. Branching in the algorithm is accomplished by subdividing the feasible set using ellipses. Lower bounds are obtained by replacing the concave part of the objective function…

We outline a new algorithm to solve coupled systems of differential equations in one continuous variable $x$ (resp. coupled difference equations in one discrete variable $N$) depending on a small parameter $\epsilon$: given such a system…

We study the variational inference problem of minimizing a regularized R\'enyi divergence over an exponential family. We propose to solve this problem with a Bregman proximal gradient algorithm. We propose a sampling-based algorithm to…