Related papers: On Convergence and Generalization of Dropout Train…

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…

Sparsification of neural networks is one of the effective complexity reduction methods to improve efficiency and generalizability. We consider the problem of learning a one hidden layer convolutional neural network with ReLU activation…

Among many mysteries behind the success of deep networks lies the exceptional discriminative power of their learned representations as manifested by the intriguing Neural Collapse (NC) phenomenon, where simple feature structures emerge at…

Large neural networks are often overparameterised and prone to overfitting, Dropout is a widely used regularization technique to combat overfitting and improve model generalization. However, unstructured Dropout is not always effective for…

Federated Dropout is an efficient technique to overcome both communication and computation bottlenecks for deploying federated learning at the network edge. In each training round, an edge device only needs to update and transmit a…

We study neural networks with trainable low-degree rational activation functions and show that they are more expressive and parameter-efficient than modern piecewise-linear and smooth activations such as ELU, LeakyReLU, LogSigmoid, PReLU,…

Dropout, a stochastic regularisation technique for training of neural networks, has recently been reinterpreted as a specific type of approximate inference algorithm for Bayesian neural networks. The main contribution of the…

We present a simple regularization technique for Recurrent Neural Networks (RNNs) with Long Short-Term Memory (LSTM) units. Dropout, the most successful technique for regularizing neural networks, does not work well with RNNs and LSTMs. In…

When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approximation is made by neural networks, the underlying problem…

Adversarial training is a widely used strategy for making neural networks resistant to adversarial perturbations. For a neural network of width $m$, $n$ input training data in $d$ dimension, it takes $\Omega(mnd)$ time cost per training…

We derive rigorous bounds on the error resulting from the approximation of the solution of parametric hyperbolic scalar conservation laws with ReLU neural networks. We show that the approximation error can be made as small as desired with…

Each year, deep learning demonstrates new and improved empirical results with deeper and wider neural networks. Meanwhile, with existing theoretical frameworks, it is difficult to analyze networks deeper than two layers without resorting to…

An increasingly popular machine learning paradigm is to pretrain a neural network (NN) on many tasks offline, then adapt it to downstream tasks, often by re-training only the last linear layer of the network. This approach yields strong…

In this work, we study the nonlinear dynamics of a shallow neural network trained with mean-squared loss and leaky ReLU activation. Under Gaussian inputs and equal layer width k, (1) we establish, based on the equivariant gradient degree, a…

How can local-search methods such as stochastic gradient descent (SGD) avoid bad local minima in training multi-layer neural networks? Why can they fit random labels even given non-convex and non-smooth architectures? Most existing theory…

Overfitting is a major problem in training machine learning models, specifically deep neural networks. This problem may be caused by imbalanced datasets and initialization of the model parameters, which conforms the model too closely to the…

This paper follows up on a recent work of Neu et al. (2021) and presents some new information-theoretic upper bounds for the generalization error of machine learning models, such as neural networks, trained with SGD. We apply these bounds…

In order to develop complex relationships between their inputs and outputs, deep neural networks train and adjust large number of parameters. To make these networks work at high accuracy, vast amounts of data are needed. Sometimes, however,…

Successful application processing sequential data, such as text and speech, requires an improved generalization performance of recurrent neural networks (RNNs). Dropout techniques for RNNs were introduced to respond to these demands, but we…

Rectified Linear Units (ReLU) are the default choice for activation functions in deep neural networks. While they demonstrate excellent empirical performance, ReLU activations can fall victim to the dead neuron problem. In these cases, the…