Related papers: Training Neural Networks Using Reproducing Kernel …
In this work, we investigate the generalization properties of random feature methods. Our analysis extends prior results for Tikhonov regularization to a broad class of spectral regularization techniques and further generalizes the setting…
Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of pointwise function samples but of averages taken over intervals…
Purpose: To evaluate an iterative learning approach for enhanced performance of Robust Artificial-neural-networks for K-space Interpolation (RAKI), when only a limited amount of training data (auto-calibration signals, ACS) are available…
We develop a rigorous framework for extending neural operators to handle out-of-distribution input functions. We leverage kernel approximation techniques and provide theory for characterizing the input-output function spaces in terms of…
This paper introduces a hypothesis space for deep learning based on deep neural networks (DNNs). By treating a DNN as a function of two variables - the input variable and the parameter variable - we consider the set of DNNs where the…
A Convolutional Recurrent Neural Network (CRNN) is trained to reproduce the evolution of the spinodal decomposition process in three dimensions as described by the Cahn-Hilliard equation. A specialized, physics-inspired architecture is…
In order to better understand feature learning in neural networks, we propose a framework for understanding linear models in tangent feature space where the features are allowed to be transformed during training. We consider linear…
Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring…
This paper extends the proof of density of neural networks in the space of continuous (or even measurable) functions on Euclidean spaces to functions on compact sets of probability measures. By doing so the work parallels a more then a…
Emerged as a biology-inspired method, Spiking Neural Networks (SNNs) mimic the spiking nature of brain neurons and have received lots of research attention. SNNs deal with binary spikes as their activation and therefore derive extreme…
Multiple Kernel Learning is a conventional way to learn the kernel function in kernel-based methods. MKL algorithms enhance the performance of kernel methods. However, these methods have a lower complexity compared to deep learning models…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
Neural tangent kernel (NTK) is a powerful tool to analyze training dynamics of neural networks and their generalization bounds. The study on NTK has been devoted to typical neural network architectures, but it is incomplete for neural…
Adversarial training has emerged as a key technique to enhance model robustness against adversarial input perturbations. Many of the existing methods rely on computationally expensive min-max problems that limit their application in…
In recent years, many deep-learning based models are proposed for text classification. This kind of models well fits the training set from the statistical point of view. However, it lacks the capacity of utilizing instance-level information…
The performance of reproducing kernel Hilbert space-based methods is known to be sensitive to the choice of the reproducing kernel. Choosing an adequate reproducing kernel can be challenging and computationally demanding, especially in…
There has been a long history of works showing that neural networks have hard time extrapolating beyond the training set. A recent study by Balestriero et al. (2021) challenges this view: defining interpolation as the state of belonging to…
Consider the problem: given the data pair $(\mathbf{x}, \mathbf{y})$ drawn from a population with $f_*(x) = \mathbf{E}[\mathbf{y} | \mathbf{x} = x]$, specify a neural network model and run gradient flow on the weights over time until…
Graph neural networks (GNNs) have become a powerful tool for processing graph-structured data but still face challenges in effectively aggregating and propagating information between layers, which limits their performance. We tackle this…