相关论文: Worker Disagreement Reveals Sharp Directions in Lo…

Recent work has highlighted a surprising alignment between gradients and the top eigenspace of the Hessian -- termed the Dominant subspace -- during neural network training. Concurrently, there has been growing interest in the distinct…

Understanding the training dynamics of deep neural networks is challenging due to their high-dimensional nature and intricate loss landscapes. Recent studies have revealed that, along the training trajectory, the gradient approximately…

Stochastic Gradient Descent (SGD) introduces anisotropic noise that is correlated with the local curvature of the loss landscape, thereby biasing optimization toward flat minima. Prior work often assumes an equivalence between the Fisher…

Stochastic Gradient Descent (SGD) based training of neural networks with a large learning rate or a small batch-size typically ends in well-generalizing, flat regions of the weight space, as indicated by small eigenvalues of the Hessian of…

Stochastic gradients for deep neural networks exhibit strong correlations along the optimization trajectory, and are often aligned with a small set of Hessian eigenvectors associated with outlier eigenvalues. Recent work shows that…

The local geometry of high dimensional neural network loss landscapes can both challenge our cherished theoretical intuitions as well as dramatically impact the practical success of neural network training. Indeed recent works have observed…

We rigorously study the relation between the training dynamics via stochastic gradient descent (SGD) and the spectra of empirical Hessian and gradient matrices. We prove that in two canonical classification tasks for multi-class…

Stochastic gradient descent (SGD) is widely used in machine learning. Although being commonly viewed as a fast but not accurate version of gradient descent (GD), it always finds better solutions than GD for modern neural networks. In order…

Stochastic Gradient Descent (SGD) has become a cornerstone of neural network optimization due to its computational efficiency and generalization capabilities. However, the gradient noise introduced by SGD is often assumed to be uncorrelated…

Stochastic gradient descent (SGD) forms the core optimization method for deep neural networks. While some theoretical progress has been made, it still remains unclear why SGD leads the learning dynamics in overparameterized networks to…

We investigate the stationary (late-time) training regime of single- and two-layer underparameterized linear neural networks within the continuum limit of stochastic gradient descent (SGD) for synthetic Gaussian data. In the case of a…

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…

Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most…

Stochastic gradient descent (SGD), a widely used algorithm in deep-learning neural networks has attracted continuing studies for the theoretical principles behind its success. A recent work reports an anomaly (inverse) relation between the…

The classical statistical learning theory implies that fitting too many parameters leads to overfitting and poor performance. That modern deep neural networks generalize well despite a large number of parameters contradicts this finding and…

While stochastic gradient descent (SGD) and variants have been surprisingly successful for training deep nets, several aspects of the optimization dynamics and generalization are still not well understood. In this paper, we present new…

Traditional analyses of gradient descent optimization show that, when the largest eigenvalue of the loss Hessian - often referred to as the sharpness - is below a critical learning-rate threshold, then training is 'stable' and training loss…

Stochastic gradient descent (SGD) and its variants enable modern artificial intelligence. However, theoretical understanding lags far behind their empirical success. It is widely believed that SGD has a curious ability to avoid sharp local…

This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of…

A large body of theory and empirical work hypothesizes a connection between the flatness of a neural network's loss landscape during training and its performance. However, there have been conceptually opposite pieces of evidence regarding…