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We propose kernel-gradient drifting, a one-step generative modeling framework that replaces the fixed Euclidean displacement direction in drifting models with directions induced by the kernel itself. Standard drifting is attractive because…

This paper presents a parametric family of compactly-supported positive semidefinite kernels aimed to model the covariance structure of second-order stationary isotropic random fields defined in the $d$-dimensional Euclidean space. Both the…

Quantum neural network architectures that have little-to-no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by…

Motivated by applications, we consider here new operator theoretic approaches to Conditional mean embeddings (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and…

Deep Convolutional Neural Networks (CNNs) are widely employed in modern computer vision algorithms, where the input image is convolved iteratively by many kernels to extract the knowledge behind it. However, with the depth of convolutional…

We provide a characterization for the continuous positive definite kernels on $\mathbb R^d$ that are invariant to linear isometries, i.e. invariant under the orthogonal group $O(d)$. Furthermore, we provide necessary and sufficient…

Spherical signals exist in many applications, e.g., planetary data, LiDAR scans and digitalization of 3D objects, calling for models that can process spherical data effectively. It does not perform well when simply projecting spherical data…

The advancement of deep convolutional neural networks (DCNNs) has driven significant improvement in the accuracy of recognition systems for many computer vision tasks. However, their practical applications are often restricted in…

Conformal prediction methodologies have significantly advanced the quantification of uncertainties in predictive models. Yet, the construction of confidence regions for model parameters presents a notable challenge, often necessitating…

Graph Neural Networks (GNNs) are powerful machine learning prediction models on graph-structured data. However, GNNs lack rigorous uncertainty estimates, limiting their reliable deployment in settings where the cost of errors is…

Modern cosmological research in large scale structure has witnessed an increasing number of applications of machine learning methods. Among them, Convolutional Neural Networks (CNNs) have received substantial attention due to their…

Machine learning models are increasingly used to predict material properties and accelerate atomistic simulations, but the reliability of their predictions depends on the representativeness of the training data. We present a scalable,…

Partial differential equations (PDEs) see widespread use in sciences and engineering to describe simulation of physical processes as scalar and vector fields interacting and coevolving over time. Due to the computationally expensive nature…

Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…

No existing spherical convolutional neural network (CNN) framework is both computationally scalable and rotationally equivariant. Continuous approaches capture rotational equivariance but are often prohibitively computationally demanding.…

This paper develops convolutional neural network (CNN) methods for simultaneous approximation and elliptic boundary value problems on compact Riemannian manifolds. We establish simultaneous Sobolev approximation results for single- and…

The high demand for computational and storage resources severely impede the deployment of deep convolutional neural networks (CNNs) in limited-resource devices. Recent CNN architectures have proposed reduced complexity versions (e.g.…

While Quantum Convolutional Neural Networks (QCNNs) offer a theoretical paradigm for quantum machine learning, their practical implementation is severely bottlenecked by barren plateaus -- the exponential vanishing of gradients -- and poor…

While the deployment of deep learning models on edge devices is increasing, these models often lack robustness when faced with dynamic changes in sensed data. This can be attributed to sensor drift, or variations in the data compared to…