Related papers: Fourier-domain Variational Formulation and Its Wel…

The dynamics of power grids are governed by a large number of nonlinear differential and algebraic equations (DAEs). To safely operate the system, operators need to check that the states described by these DAEs stay within prescribed limits…

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (1) not naturally amenable to gradient-based optimization, and (2) incompatible…

Machine learning is at the heart of managing the real-world problems associated with massive data. With the success of neural networks on such large-scale problems, more research in machine learning is being conducted now than ever before.…

VQC can be understood through the lens of Fourier analysis. It is already well-known that the function space represented by any circuit architecture can be described through a truncated Fourier sum. We show that the spectrum available to…

Deep belief networks are used extensively for unsupervised stochastic learning on large datasets. Compared to other deep learning approaches their layer-by-layer learning makes them highly scalable. Unfortunately, the principles by which…

Deep neural networks exhibit a simplicity bias, a well-documented tendency to favor simple functions over complex ones. In this work, we cast new light on this phenomenon through the lens of the Minimum Description Length principle,…

Unsupervised domain adaptation (UDA) plays a crucial role in addressing distribution shifts in machine learning. In this work, we improve the theoretical foundations of UDA proposed in Acuna et al. (2021) by refining their…

The ability to predict future outcomes conditioned on observed video frames is crucial for intelligent decision-making in autonomous systems. Recently, deep recurrent architectures have been applied to the task of video prediction. However,…

Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach…

Distributed learning is the problem of inferring a function in the case where training data is distributed among multiple geographically separated sources. Particularly, the focus is on designing learning strategies with low computational…

Standard supervised machine learning assumes that the distribution of the source samples used to train an algorithm is the same as the one of the target samples on which it is supposed to make predictions. However, as any data scientist…

Convolutional neural network (CNN) has achieved impressive success in computer vision during the past few decades. The image convolution operation helps CNNs to get good performance on image-related tasks. However, the image convolution has…

An important characteristic of neural networks is their ability to learn representations of the input data with effective features for prediction, which is believed to be a key factor to their superior empirical performance. To better…

The traditional statistical inference is static, in the sense that the estimate of the quantity of interest does not affect the future evolution of the quantity. In some sequential estimation problems however, the future values of the…

Domain generalization (DG), aiming at models able to work on multiple unseen domains, is a must-have characteristic of general artificial intelligence. DG based on single source domain training data is more challenging due to the lack of…

Federated learning, a distributed learning paradigm, utilizes multiple clients to build a robust global model. In real-world applications, local clients often operate within their limited domains, leading to a `domain shift' across clients.…

The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the…

Supervised models of NLP rely on large collections of text which closely resemble the intended testing setting. Unfortunately matching text is often not available in sufficient quantity, and moreover, within any domain of text, data is…

Representation learning is the dominant technique for unsupervised domain adaptation, but existing approaches often require the specification of "pivot features" that generalize across domains, which are selected by task-specific…

Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…