相关论文: Does SGD really happen in tiny subspaces?

With the rise of big data analytics, multi-layer neural networks have surfaced as one of the most powerful machine learning methods. However, their theoretical mathematical properties are still not fully understood. Training a neural…

Low-latency deep spiking neural networks (SNNs) have become a promising alternative to conventional artificial neural networks (ANNs) because of their potential for increased energy efficiency on event-driven neuromorphic hardware. Neural…

We perform an experimental study of the dynamics of Stochastic Gradient Descent (SGD) in learning deep neural networks for several real and synthetic classification tasks. We show that in the initial epochs, almost all of the performance…

The Hessian of neural networks can be decomposed into a sum of two matrices: (i) the positive semidefinite generalized Gauss-Newton matrix G, and (ii) the matrix H containing negative eigenvalues. We observe that for wider networks,…

Classical analyses of gradient descent (GD) define a stability threshold based on the largest eigenvalue of the loss Hessian, often termed sharpness. When the learning rate lies below this threshold, training is stable and the loss…

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its…

Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is…

Adversarial training, especially projected gradient descent (PGD), has proven to be a successful approach for improving robustness against adversarial attacks. After adversarial training, gradients of models with respect to their inputs…

In the last decade, deep learning has become a major component of artificial intelligence. The workhorse of deep learning is the optimization of loss functions by stochastic gradient descent (SGD). Traditionally in deep learning, neural…

Understanding when the noise in stochastic gradient descent (SGD) affects generalization of deep neural networks remains a challenge, complicated by the fact that networks can operate in distinct training regimes. Here we study how the…

Recent studies have shown that many important aspects of neural network learning take place within the very earliest iterations or epochs of training. For example, sparse, trainable sub-networks emerge (Frankle et al., 2019), gradient…

We study the gradient descent (GD) dynamics of a depth-2 linear neural network with a single input and output. We show that GD converges at an explicit linear rate to a global minimum of the training loss, even with a large stepsize --…

Policy gradient methods hold great potential for solving complex continuous control tasks. Still, their training efficiency can be improved by exploiting structure within the optimization problem. Recent work indicates that supervised…

Deep neural networks achieve stellar generalisation on a variety of problems, despite often being large enough to easily fit all their training data. Here we study the generalisation dynamics of two-layer neural networks in a…

We present novel empirical observations regarding how stochastic gradient descent (SGD) navigates the loss landscape of over-parametrized deep neural networks (DNNs). These observations expose the qualitatively different roles of learning…

Understanding the algorithmic bias of \emph{stochastic gradient descent} (SGD) is one of the key challenges in modern machine learning and deep learning theory. Most of the existing works, however, focus on \emph{very small or even…

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

Recently, there has been growing evidence that if the width and depth of a neural network are scaled toward the so-called rich feature learning limit (\mup and its depth extension), then some hyperparameters -- such as the learning rate --…

The stochastic gradient descent (SGD) algorithm is the algorithm we use to train neural networks. However, it remains poorly understood how the SGD navigates the highly nonlinear and degenerate loss landscape of a neural network. In this…

This paper presents a theoretical analysis and practical evaluation of the main bottlenecks towards a scalable distributed solution for the training of Deep Neuronal Networks (DNNs). The presented results show, that the current state of the…