Related papers: Understanding Gradient Descent on Edge of Stabilit…
The phenomenon that stochastic gradient descent (SGD) favors flat minima has played a critical role in understanding the implicit regularization of SGD. In this paper, we provide an explanation of this striking phenomenon by relating the…
Understanding the dynamics of optimization in deep learning is increasingly important as models scale. While stochastic gradient descent (SGD) and its variants reliably find solutions that generalize well, the mechanisms driving this…
Stochastic Gradient Descent (SGD) and its momentum variants form the backbone of deep learning optimization, yet the underlying dynamics of their gradient behavior remain insufficiently understood. In this work, we reinterpret gradient…
Uniform stability is a notion of algorithmic stability that bounds the worst case change in the model output by the algorithm when a single data point in the dataset is replaced. An influential work of Hardt et al. (2016) provides strong…
The largest eigenvalue of the Hessian, or sharpness, of neural networks is a key quantity to understand their optimization dynamics. In this paper, we study the sharpness of deep linear networks for univariate regression. Minimizers can…
Stochastic Gradient Descent (SGD) is a central tool in machine learning. We prove that SGD converges to zero loss, even with a fixed (non-vanishing) learning rate - in the special case of homogeneous linear classifiers with smooth monotone…
In this paper we study the stability and its trade-off with optimization error for stochastic gradient descent (SGD) algorithms in the pairwise learning setting. Pairwise learning refers to a learning task which involves a loss function…
Recent empirical and theoretical work has shown that the dynamics of the large eigenvalues of the training loss Hessian have some remarkably robust features across models and datasets in the full batch regime. There is often an early period…
Gradient descent, or negative gradient flow, is a standard technique in optimization to find minima of functions. Many implementations of gradient descent rely on discretized versions, i.e., moving in the gradient direction for a set step…
The generalization mystery of overparametrized deep nets has motivated efforts to understand how gradient descent (GD) converges to low-loss solutions that generalize well. Real-life neural networks are initialized from small random values…
We establish the asymptotic implicit bias of gradient descent (GD) for generic non-homogeneous deep networks under exponential loss. Specifically, we characterize three key properties of GD iterates starting from a sufficiently small…
The gradient descent (GD) method -- is a fundamental and likely the most popular optimization algorithm in machine learning (ML), with a history traced back to a paper in 1847 (Cauchy, 1847). It was studied under various assumptions,…
This article examines the implicit regularization effect of Stochastic Gradient Descent (SGD). We consider the case of SGD without replacement, the variant typically used to optimize large-scale neural networks. We analyze this algorithm in…
The simplicity of gradient descent (GD) made it the default method for training ever-deeper and complex neural networks. Both loss functions and architectures are often explicitly tuned to be amenable to this basic local optimization. In…
Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate. This lies in stark contrast to practical wisdom and empirical studies, such as the work of J. Cohen et al.…
The Sharpness Aware Minimization (SAM) optimization algorithm has been shown to control large eigenvalues of the loss Hessian and provide generalization benefits in a variety of settings. The original motivation for SAM was a modified loss…
We consider distributed optimization under communication constraints for training deep learning models. We propose a new algorithm, whose parameter updates rely on two forces: a regular gradient step, and a corrective direction dictated by…
During neural network training, the sharpness of the Hessian matrix of the training loss rises until training is on the edge of stability. As a result, even nonstochastic gradient descent does not accurately model the underlying dynamical…
Private machine learning involves addition of noise while training, resulting in lower accuracy. Intuitively, greater stability can imply greater privacy and improve this privacy-utility tradeoff. We study this role of stability in private…
Deep neural networks have been shown to achieve state-of-the-art performance in several machine learning tasks. Stochastic Gradient Descent (SGD) is the preferred optimization algorithm for training these networks and asynchronous SGD…