Related papers: Interprecision transfers in iterative refinement

A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function of two variables, the algorithm produces a hierarchy of triangulations and piecewise polynomial approximations…

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

Imitation learning is a way to teach robots skills that are demonstrated by humans. Transfering skills between these different kinematic structures seems to be straightforward in Cartesian space. Because of the correspondence problem,…

Transfer learning is a popular method for tuning pretrained (upstream) models for different downstream tasks using limited data and computational resources. We study how an adversary with control over an upstream model used in transfer…

A well-known problem in computing some matrix functions iteratively is the lack of a clear, commonly accepted residual notion. An important matrix function for which this is the case is the matrix exponential. Suppose the matrix exponential…

We study the performance of transformers as a function of the number of repetitions of training examples with algorithmically generated datasets. On three problems of mathematics: the greatest common divisor, modular multiplication, and…

Residual mappings have been shown to perform representation learning in the first layers and iterative feature refinement in higher layers. This interplay, combined with their stabilizing effect on the gradient norms, enables them to train…

In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…

We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the solution. A dimensional reduction of the problem is obtained…

Despite the remarkable success of deep learning systems over the last decade, a key difference still remains between neural network and human decision-making: As humans, we cannot only form a decision on the spot, but also ponder,…

We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…

We show how the notion of message passing can be used to streamline the algebra and computer coding for fast approximate inference in large Bayesian semiparametric regression models. In particular, this approach is amenable to handling…

In this work we unify a number of inference learning methods, that are proposed in the literature as alternative training algorithms to the ones based on regular error back-propagation. These inference learning methods were developed with…

In today's data driven world, storing, processing, and gleaning insights from large-scale data are major challenges. Data compression is often required in order to store large amounts of high-dimensional data, and thus, efficient inference…

Transfer learning plays a key role in modern data analysis when: (1) the target data are scarce but the source data are sufficient; (2) the distributions of the source and target data are heterogeneous. This paper develops an interpretable…

We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…

In this paper we present novel algorithmic solutions for several resource processing and data transfer multicriteria optimization problems. The results of most of the presented techniques are strategies which solve the considered problems…

Large, pre-trained models are problematic to use in resource constrained applications. Fortunately, task-aware structured pruning methods offer a solution. These approaches reduce model size by dropping structural units like layers and…

We argue for supplementing the process of training a prediction algorithm by setting up a scheme for detecting the moment when the distribution of the data changes and the algorithm needs to be retrained. Our proposed schemes are based on…

Machine learning classifiers often produce probabilistic predictions that are critical for accurate and interpretable decision-making in various domains. The quality of these predictions is generally evaluated with proper losses, such as…