Related papers: Convergence rates for random feature neural networ…

Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…

Recent works have derived neural networks with online correlation-based learning rules to perform \textit{kernel similarity matching}. These works applied existing linear similarity matching algorithms to nonlinear features generated with…

In this paper we study the convergence of online gradient descent algorithms in reproducing kernel Hilbert spaces (RKHSs) without regularization. We establish a sufficient condition and a necessary condition for the convergence of excess…

This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized,…

We show in this note that the Sobolev Discrepancy introduced in Mroueh et al in the context of generative adversarial networks, is actually the weighted negative Sobolev norm $||.||_{\dot{H}^{-1}(\nu_q)}$, that is known to linearize the…

We propose a novel framework for exploring weak and $L_2$ generalization errors of algorithms through the lens of differential calculus on the space of probability measures. Specifically, we consider the KL-regularized empirical risk…

We provide a simulation algorithm to simulate from a (multivariate) characteristic function, which is only accessible in a black-box format. The method is based on a generative neural network, whose loss function exploits a specific…

The celebrated universal approximation theorems for neural networks roughly state that any reasonable function can be arbitrarily well-approximated by a network whose parameters are appropriately chosen real numbers. This paper examines the…

We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…

We introduce estimatable variation neural networks (EVNNs), a class of neural networks that allow a computationally cheap estimate on the $BV$ norm motivated by the space $BMV$ of functions with bounded M-variation. We prove a universal…

We propose a new class of random feature methods for linearizing softmax and Gaussian kernels called hybrid random features (HRFs) that automatically adapt the quality of kernel estimation to provide most accurate approximation in the…

Neural networks are emerging as a powerful tool for determining the quantum states of interacting many-body fermionic systems. The standard approach trains a neural-network ansatz by minimizing the mean local energy estimated from Monte…

Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…

We present a generalization of the Cauchy/Lorentzian, Geman-McClure, Welsch/Leclerc, generalized Charbonnier, Charbonnier/pseudo-Huber/L1-L2, and L2 loss functions. By introducing robustness as a continuous parameter, our loss function…

In this work we approach attractor neural networks from a machine learning perspective: we look for optimal network parameters by applying a gradient descent over a regularized loss function. Within this framework, the optimal…

Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…

Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…

Reconstruction of a function from noisy data is often formulated as a regularized optimization problem over an infinite-dimensional reproducing kernel Hilbert space (RKHS). The solution describes the observed data and has a small RKHS norm.…

Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive…

This paper studies probabilistic rates of convergence for consensus+innovations type of algorithms in random, generic networks. For each node, we find a lower and also a family of upper bounds on the large deviations rate function, thus…