Related papers: Universal Approximation of Functions on Sets

As deep learning models grow in complexity and the volume of training data increases, reducing storage and computational costs becomes increasingly important. Dataset distillation addresses this challenge by synthesizing a compact set of…

A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves…

Deep Learning has recently emerged as a perfect prognosis downscaling technique to compute high-resolution fields from large-scale coarse atmospheric data. Despite their promising results to reproduce the observed local variability, they…

We propose semi-random features for nonlinear function approximation. The flexibility of semi-random feature lies between the fully adjustable units in deep learning and the random features used in kernel methods. For one hidden layer…

Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward:…

Probably the most important problem in machine learning is the preliminary biasing of a learner's hypothesis space so that it is small enough to ensure good generalisation from reasonable training sets, yet large enough that it contains a…

In high dimensional settings, density estimation algorithms rely crucially on their inductive bias. Despite recent empirical success, the inductive bias of deep generative models is not well understood. In this paper we propose a framework…

Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional…

We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…

We introduce a unified framework, formulated as general latent space models, to study complex higher-order network interactions among multiple entities. Our framework covers several popular models in recent network analysis literature,…

Fine-grained and instance-level recognition methods are commonly trained and evaluated on specific domains, in a model per domain scenario. Such an approach, however, is impractical in real large-scale applications. In this work, we address…

Currently, deep neural networks are the state of the art on problems such as speech recognition and computer vision. In this extended abstract, we show that shallow feed-forward networks can learn the complex functions previously learned by…

Deep learning methods are known to generalize well from training to future data, even in an overparametrized regime, where they could easily overfit. One explanation for this phenomenon is that even when their *ambient dimensionality*,…

The accuracy of density-functional theory (DFT) is determined by the quality of the approximate functionals, such as exchange-correlation in electronic DFT and the excess functional in the classical DFT formalism of fluids. The exact…

Bayesian deep learning all too often underfits so that the Bayesian prediction is less accurate than a simple point estimate. Uncertainty quantification then comes at the cost of accuracy. For linearized models, the null space of the…

Data-driven approaches such as deep learning can result in predictive models for material properties with exceptional accuracy and efficiency. However, in many applications, data is sparse, severely limiting their accuracy and…

Deep metric learning (DML) involves training a network to learn a semantically meaningful representation space. Many current approaches mine n-tuples of examples and model interactions within each tuplets. We present a novel, compositional…

Tabular foundation models aim to learn universal representations of tabular data that transfer across tasks and domains, enabling applications such as table retrieval, semantic search and table-based prediction. Despite the growing number…

As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…