相关论文: On the rates of convergence for learning with conv…

Convolutional neural networks (CNNs) have been shown to achieve optimal approximation and estimation error rates (in minimax sense) in several function classes. However, previous analyzed optimal CNNs are unrealistically wide and difficult…

Convolutional neural networks (CNNs) have been employed along with Variational Monte Carlo methods for finding the ground state of quantum many-body spin systems with great success. In order to do so, however, a CNN with only linearly many…

Multi-layer feedforward networks have been used to approximate a wide range of nonlinear functions. An important and fundamental problem is to understand the learnability of a network model through its statistical risk, or the expected…

We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters. We propose a novel algorithm called approximate gradient descent for training CNNs, and show that, with high…

This paper studies the approximation capacity of ReLU neural networks with norm constraint on the weights. We prove upper and lower bounds on the approximation error of these networks for smooth function classes. The lower bound is derived…

Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical…

We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a…

We study the approximation capacity of some variation spaces corresponding to shallow ReLU$^k$ neural networks. It is shown that sufficiently smooth functions are contained in these spaces with finite variation norms. For functions with…

Convolutional neural networks (CNNs) have succeeded in many practical applications. However, their high computation and storage requirements often make them difficult to deploy on resource-constrained devices. In order to tackle this issue,…

The state-of-the-art performance for several real-world problems is currently reached by convolutional neural networks (CNN). Such learning models exploit recent results in the field of deep learning, typically leading to highly performing,…

Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…

It is widely believed that the practical success of Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) owes to the fact that CNNs and RNNs use a more compact parametric representation than their Fully-Connected Neural…

The recent success of neural networks in pattern recognition and classification problems suggests that neural networks possess qualities distinct from other more classical classifiers such as SVMs or boosting classifiers. This paper studies…

We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…

Although convolutional neural networks (CNNs) are now widely used in various computer vision applications, its huge resource demanding on parameter storage and computation makes the deployment on mobile and embedded devices difficult.…

The convolutional neural network (CNN) learns the same object in different positions in images, which can improve the recognition accuracy of the model. An implication of this is that CNN may know where the object is. The usefulness of the…

We introduce a novel scheme to train binary convolutional neural networks (CNNs) -- CNNs with weights and activations constrained to {-1,+1} at run-time. It has been known that using binary weights and activations drastically reduce memory…

Convolutional neural networks (CNNs) are one of the most successful computer vision systems to solve object recognition. Furthermore, CNNs have major applications in understanding the nature of visual representations in the human brain. Yet…

Convolutional neural network (CNN) is widely used in computer vision applications. In the networks that deal with images, CNNs are the most time-consuming layer of the networks. Usually, the solution to address the computation cost is to…

It is shown that over-parameterized neural networks can achieve minimax optimal rates of convergence (up to logarithmic factors) for learning functions from certain smooth function classes, if the weights are suitably constrained or…