Related papers: Implicit Regularization and Generalization in Over…
Pruning neural network parameters is often viewed as a means to compress models, but pruning has also been motivated by the desire to prevent overfitting. This motivation is particularly relevant given the perhaps surprising observation…
Overparameterization is central to the success of deep learning, yet the mechanisms by which it improves optimization remain incompletely understood. We analyze weight-space symmetries in neural networks and show that overparameterization…
We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…
Neural network optimization remains one of the most consequential yet poorly understood challenges in modern AI research, where improvements in training algorithms can lead to enhanced feature learning in foundation models,…
This paper studies how neural network architecture affects the speed of training. We introduce a simple concept called gradient confusion to help formally analyze this. When gradient confusion is high, stochastic gradients produced by…
We study regularization in the context of small sample-size learning with over-parameterized neural networks. Specifically, we shift focus from architectural properties, such as norms on the network weights, to properties of the internal…
Stochastic gradient descent (SGD) is a pillar of modern machine learning, serving as the go-to optimization algorithm for a diverse array of problems. While the empirical success of SGD is often attributed to its computational efficiency…
A recent line of research has shown that gradient-based algorithms with random initialization can converge to the global minima of the training loss for over-parameterized (i.e., sufficiently wide) deep neural networks. However, the…
Over-parameterization and adaptive methods have played a crucial role in the success of deep learning in the last decade. The widespread use of over-parameterization has forced us to rethink generalization by bringing forth new phenomena,…
In this paper, we derive a novel bound on the generalization error of Magnitude-Based pruning of overparameterized neural networks. Our work builds on the bounds in Arora et al. [2018] where the error depends on one, the approximation…
Multi-epoch, small-batch, Stochastic Gradient Descent (SGD) has been the method of choice for learning with large over-parameterized models. A popular theory for explaining why SGD works well in practice is that the algorithm has an…
Random Matrix Theory (RMT) is applied to analyze weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as LeNet5…
It is widely believed that the implicit regularization of SGD is fundamental to the impressive generalization behavior we observe in neural networks. In this work, we demonstrate that non-stochastic full-batch training can achieve…
Neural networks with a large number of parameters often do not overfit, owing to implicit regularization that favors \lq good\rq{} networks. Other related and puzzling phenomena include properties of flat minima, saddle-to-saddle dynamics,…
Deep neural networks (DNNs) have demonstrated dominating performance in many fields; since AlexNet, networks used in practice are going wider and deeper. On the theoretical side, a long line of works has been focusing on training neural…
The mechanisms by which certain training interventions, such as increasing learning rates and applying batch normalization, improve the generalization of deep networks remains a mystery. Prior works have speculated that "flatter" solutions…
An important question in deep learning is how higher-order optimization methods affect generalization. In this work, we analyze a stochastic Gauss-Newton (SGN) method with Levenberg-Marquardt damping and mini-batch sampling for training…
Recently there has been significant theoretical progress on understanding the convergence and generalization of gradient-based methods on nonconvex losses with overparameterized models. Nevertheless, many aspects of optimization and…
Recent works have cast some light on the mystery of why deep nets fit any data and generalize despite being very overparametrized. This paper analyzes training and generalization for a simple 2-layer ReLU net with random initialization, and…
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…