Related papers: When Do Neural Networks Outperform Kernel Methods?
The largely successful method of training neural networks is to learn their weights using some variant of stochastic gradient descent (SGD). Here, we show that the solutions found by SGD can be further improved by ensembling a subset of the…
Node classification in structural networks has been proven to be useful in many real world applications. With the development of network embedding, the performance of node classification has been greatly improved. However, nearly all the…
Spiking Neural Networks (SNNs), providing more realistic neuronal dynamics, have been shown to achieve performance comparable to Artificial Neural Networks (ANNs) in several machine learning tasks. Information is processed as spikes within…
Contemporary wisdom based on empirical studies suggests that standard recurrent neural networks (RNNs) do not perform well on tasks requiring long-term memory. However, precise reasoning for this behavior is still unknown. This paper…
The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…
The Neural Tangent Kernel (NTK) characterizes the behavior of infinitely-wide neural networks trained under least squares loss by gradient descent. Recent works also report that NTK regression can outperform finitely-wide neural networks…
Artificial neural networks (ANNs) have become a very powerful tool in the approximation of high-dimensional functions. Especially, deep ANNs, consisting of a large number of hidden layers, have been very successfully used in a series of…
This paper addresses the scalability problem of Bayesian deep neural networks. The performance of deep neural networks is undermined by the fact that these algorithms have poorly calibrated measures of uncertainty. This restricts their…
While the depth of modern Convolutional Neural Networks (CNNs) surpasses that of the pioneering networks with a significant margin, the traditional way of appending supervision only over the final classifier and progressively propagating…
Gradient descent typically converges to a single minimum of the training loss without mechanisms to explore alternative minima that may generalize better. Searching for diverse minima directly in high-dimensional parameter space is…
Spiking neural networks (SNNs) have closer dynamics to the brain than current deep neural networks. Their low power consumption and sample efficiency make these networks interesting. Recently, several deep convolutional spiking neural…
This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The…
We perform an experimental study of the dynamics of Stochastic Gradient Descent (SGD) in learning deep neural networks for several real and synthetic classification tasks. We show that in the initial epochs, almost all of the performance…
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…
We study nonparametric regression by an over-parameterized two-layer neural network trained by gradient descent (GD) in this paper. We show that, if the neural network is trained by GD with early stopping, then the trained network renders a…
Developing strong AI signifies the arrival of technological singularity, contributing greatly to advancing human civilization and resolving social issues. Neural networks (NNs) and deep learning, which utilize NNs, are expected to lead to…
Wide neural networks are biased towards learning certain functions, influencing both the rate of convergence of gradient descent (GD) and the functions that are reachable with GD in finite training time. As such, there is a great need for…
Understanding the properties of neural networks trained via stochastic gradient descent (SGD) is at the heart of the theory of deep learning. In this work, we take a mean-field view, and consider a two-layer ReLU network trained via SGD for…
Kolmogorov--Arnold Networks (KANs), a recently proposed neural network architecture, have gained significant attention in the deep learning community, due to their potential as a viable alternative to multi-layer perceptrons (MLPs) and…
Convolutional Neural Networks (CNNs) are the predominant model used for a variety of medical image analysis tasks. At inference time, these models are computationally intensive, especially with volumetric data. In principle, it is possible…