相关论文: An Approximation Algorithm for training One-Node R…

Deep neural network with rectified linear units (ReLU) is getting more and more popular recently. However, the derivatives of the function represented by a ReLU network are not continuous, which limit the usage of ReLU network to situations…

The high computational complexity associated with training deep neural networks limits online and real-time training on edge devices. This paper proposed an end-to-end training and inference scheme that eliminates multiplications by…

We explore the phase diagram of approximation rates for deep neural networks and prove several new theoretical results. In particular, we generalize the existing result on the existence of deep discontinuous phase in ReLU networks to…

We study the problem of PAC learning one-hidden-layer ReLU networks with $k$ hidden units on $\mathbb{R}^d$ under Gaussian marginals in the presence of additive label noise. For the case of positive coefficients, we give the first…

We consider the natural problem of learning a ReLU network from queries, which was recently remotivated by model extraction attacks. In this work, we present a polynomial-time algorithm that can learn a depth-two ReLU network from queries…

A recent line of research on deep learning focuses on the extremely over-parameterized setting, and shows that when the network width is larger than a high degree polynomial of the training sample size $n$ and the inverse of the target…

While it is well-known that neural networks enjoy excellent approximation capabilities, it remains a big challenge to compute such approximations from point samples. Based on tools from Information-based complexity, recent work by Grohs and…

The success of deep architectures is at least in part attributed to the layer-by-layer unsupervised pre-training that initializes the network. Various papers have reported extensive empirical analysis focusing on the design and…

In recent years, stochastic gradient descent (SGD) based techniques has become the standard tools for training neural networks. However, formal theoretical understanding of why SGD can train neural networks in practice is largely missing.…

We consider the problem of univariate nonlinear function approximation using shallow neural networks (NN) with a rectified linear unit (ReLU) activation function. We show that the $L_2$ based approximation problem is ill-conditioned and the…

We study the problem of PAC learning a linear combination of $k$ ReLU activations under the standard Gaussian distribution on $\mathbb{R}^d$ with respect to the square loss. Our main result is an efficient algorithm for this learning task…

We study the problem of learning a single neuron with respect to the $L_2^2$-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal…

It has been shown that neural network classifiers are not robust. This raises concerns about their usage in safety-critical systems. We propose in this paper a regularization scheme for ReLU networks which provably improves the robustness…

We study the generalization of two-layer ReLU neural networks in a univariate nonparametric regression problem with noisy labels. This is a problem where kernels (\emph{e.g.} NTK) are provably sub-optimal and benign overfitting does not…

Activation functions play a critical role in deep neural networks by shaping gradient flow, optimization stability, and generalization. While ReLU remains widely used due to its simplicity, it suffers from gradient sparsity and dead-neuron…

This paper considers the problem of learning a single ReLU neuron with squared loss (a.k.a., ReLU regression) in the overparameterized regime, where the input dimension can exceed the number of samples. We analyze a Perceptron-type…

Understanding the fundamental mechanism behind the success of deep neural networks is one of the key challenges in the modern machine learning literature. Despite numerous attempts, a solid theoretical analysis is yet to be developed. In…

We investigate online nonlinear regression with continually running recurrent neural network networks (RNNs), i.e., RNN-based online learning. For RNN-based online learning, we introduce an efficient first-order training algorithm that…

We improve the effectiveness of propagation- and linear-optimization-based neural network verification algorithms with a new tightened convex relaxation for ReLU neurons. Unlike previous single-neuron relaxations which focus only on the…

Solving mixed-integer optimization problems with embedded neural networks with ReLU activation functions is challenging. Big-M coefficients that arise in relaxing binary decisions related to these functions grow exponentially with the…