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Applying Differentially Private Stochastic Gradient Descent (DPSGD) to training modern, large-scale neural networks such as transformer-based models is a challenging task, as the magnitude of noise added to the gradients at each iteration…

To enable learning on edge devices with fast convergence and low memory, we present a novel backpropagation-free optimization algorithm dubbed Target Projection Stochastic Gradient Descent (tpSGD). tpSGD generalizes direct random target…

In distributed training of deep neural networks, people usually run Stochastic Gradient Descent (SGD) or its variants on each machine and communicate with other machines periodically. However, SGD might converge slowly in training some deep…

Deep learning is typically performed by learning a neural network solely from data in the form of input-output pairs ignoring available domain knowledge. In this work, the Constraint Guided Gradient Descent (CGGD) framework is proposed that…

Generalization is one of the most important problems in deep learning (DL). In the overparameterized regime in neural networks, there exist many low-loss solutions that fit the training data equally well. The key question is which solution…

We study a fully decentralized federated learning algorithm, which is a novel gradient descent algorithm executed on a communication-based network. For convenience, we refer to it as a network gradient descent (NGD) method. In the NGD…

Training deep neural networks with stochastic gradient descent (SGD) can often achieve zero training loss on real-world tasks although the optimization landscape is known to be highly non-convex. To understand the success of SGD for…

The stunning empirical successes of neural networks currently lack rigorous theoretical explanation. What form would such an explanation take, in the face of existing complexity-theoretic lower bounds? A first step might be to show that…

We theoretically study the fundamental problem of learning a single neuron with a bias term ($\mathbf{x} \mapsto \sigma(<\mathbf{w},\mathbf{x}> + b)$) in the realizable setting with the ReLU activation, using gradient descent. Perhaps…

Over the past few years, an extensively studied phenomenon in training deep networks is the implicit bias of gradient descent towards parsimonious solutions. In this work, we investigate this phenomenon by narrowing our focus to deep linear…

In this paper we analyze the behaviour of the stochastic gradient descent (SGD), a widely used method in supervised learning for optimizing neural network weights via a minimization of non-convex loss functions. Since the pioneering work of…

It was conjectured that any neural network of any structure and arbitrary differentiable transfer functions at the nodes cannot learn the following problem sample efficiently when trained with gradient descent: The instances are the rows of…

This study explores the sample complexity for two-layer neural networks to learn a generalized linear target function under Stochastic Gradient Descent (SGD), focusing on the challenging regime where many flat directions are present at…

It has been shown that gradient descent can yield the zero training loss in the over-parametrized regime (the width of the neural networks is much larger than the number of data points). In this work, combining the ideas of some existing…

We show that the gradient descent algorithm provides an implicit regularization effect in the learning of over-parameterized matrix factorization models and one-hidden-layer neural networks with quadratic activations. Concretely, we show…

We demonstrate that applying an eventual decay to the learning rate (LR) in empirical risk minimization (ERM), where the mean-squared-error loss is minimized using standard gradient descent (GD) for training a two-layer neural network with…

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…

Despite the non-convex optimization landscape, over-parametrized shallow networks are able to achieve global convergence under gradient descent. The picture can be radically different for narrow networks, which tend to get stuck in…

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…

Deep learning methods operate in regimes that defy the traditional statistical mindset. Neural network architectures often contain more parameters than training samples, and are so rich that they can interpolate the observed labels, even if…