相关论文: Position: Curvature Matrices Should Be Democratize…

We show that under natural and quite general assumptions, a large part of a matrix for a bounded linear operator on a Hilbert space can be preassigned. The result is obtained in a more general setting of operator tuples leading to…

Data science workflows often integrate functionalities from a diverse set of libraries and frameworks. Tasks such as debugging require data lineage that crosses library boundaries. The problem is that the way that "lineage" is represented…

Large language models (LLMs) demonstrate impressive results in natural language processing tasks but require a significant amount of computational and memory resources. Structured matrix representations are a promising way for reducing the…

Second-order methods are emerging as promising alternatives to standard first-order optimizers such as gradient descent and ADAM for training neural networks. Though the advantages of including curvature information in computing…

This paper presents a novel approach combining convolutional layers (CLs) and large-margin metric learning for training supervised models on small datasets for texture classification. The core of such an approach is a loss function that…

During recent years, the renaissance of neural networks as the major machine learning paradigm and more specifically, the confirmation that deep learning techniques provide state-of-the-art results for most of computer vision tasks has been…

Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial differential equations (PDEs). This paper presents a rigorous…

Deep neural networks have been extremely successful at various image, speech, video recognition tasks because of their ability to model deep structures within the data. However, they are still prohibitively expensive to train and apply for…

Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…

Convolutional Neural Networks (CNNs) have become indispensable for solving machine learning tasks in speech recognition, computer vision, and other areas that involve high-dimensional data. A CNN filters the input feature using a network…

Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…

The recent impressive results of deep learning-based methods on computer vision applications brought fresh air to the research and industrial community. This success is mainly due to the process that allows those methods to learn…

Applied research in graph algorithms and combinatorial structures needs comprehensive and versatile software libraries. However, the design and the implementation of flexible libraries are challenging activities. Among the other problems…

We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neural networks to synthetic data sets constructed from…

Pruning remains an effective strategy for reducing both the costs and environmental impact associated with deploying large neural networks (NNs) while maintaining performance. Classical methods, such as OBD (LeCun et al., 1989) and OBS…

This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…

We propose meta-curvature (MC), a framework to learn curvature information for better generalization and fast model adaptation. MC expands on the model-agnostic meta-learner (MAML) by learning to transform the gradients in the inner…

Despite the successes of deep learning in computer vision, difficulties persist in recognizing objects that have undergone group-symmetric transformations rarely seen during training$\unicode{x2013}$for example objects seen in unusual…

Linear methods are ubiquitous for control and estimation problems. In this work, we present a number of tensor operator norms as a means to approximately bound the error associated with linear methods and determine the situations in which…

Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for both Newton solution of deterministic inverse problems, as…