Related papers: Gradient Clipping Beyond Vector Norms: A Spectral …

Gradient clipping is a fundamental tool in Deep Learning, improving the high-probability convergence of stochastic first-order methods like SGD, AdaGrad, and Adam under heavy-tailed noise, which is common in training large language models.…

By ensuring differential privacy in the learning algorithms, one can rigorously mitigate the risk of large models memorizing sensitive training data. In this paper, we study two algorithms for this purpose, i.e., DP-SGD and DP-NSGD, which…

Optimization under heavy-tailed noise has become popular recently, since it better fits many modern machine learning tasks, as captured by empirical observations. Concretely, instead of a finite second moment on gradient noise, a bounded…

Motivated by understanding and analysis of large-scale machine learning under heavy-tailed gradient noise, we study decentralized optimization with gradient clipping, i.e., in which certain clipping operators are applied to the gradients or…

State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extragradient), limiting SGD…

Methods with adaptive stepsizes, such as AdaGrad and Adam, are essential for training modern Deep Learning models, especially Large Language Models. Typically, the noise in the stochastic gradients is heavy-tailed for the later ones.…

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…

We develop a worst-case complexity theory for stochastically preconditioned stochastic gradient descent (SPSGD) and its accelerated variants under heavy-tailed noise, a setting that encompasses widely used adaptive methods such as Adam,…

Regularization is essential for avoiding over-fitting to training data in network optimization, leading to better generalization of the trained networks. The label noise provides a strong implicit regularization by replacing the target…

Gradient clipping is widely used to stabilize deep network training, but its formulation as a hard, fixed threshold limits flexibility and ignores gradient distribution dynamics. We propose SPAMP (Statistical Per-layer Adaptive Modulation…

We present and analyze a novel regularized form of the gradient clipping algorithm, proving that it converges to global minima of the loss surface of deep neural networks under the squared loss, provided that the layers are of sufficient…

In this paper, we propose a new accelerated stochastic first-order method called clipped-SSTM for smooth convex stochastic optimization with heavy-tailed distributed noise in stochastic gradients and derive the first high-probability…

Clipping the gradient is a known approach to improving gradient descent, but requires hand selection of a clipping threshold hyperparameter. We present AutoClip, a simple method for automatically and adaptively choosing a gradient clipping…

An algorithm is said to be adaptive to a certain parameter (of the problem) if it does not need a priori knowledge of such a parameter but performs competitively to those that know it. This dissertation presents our work on adaptive…

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,…

Previous research has shown that constraining the gradient of loss function with respect to model-predicted probabilities can enhance the model robustness against noisy labels. These methods typically specify a fixed optimal threshold for…

A growing lesson from neural network optimization is that optimizer design should respect how the model is parametrized. Scale-invariant methods become important because their normalized layerwise updates can not only support hyperparameter…

Recently, the study of heavy-tailed noises in first-order nonconvex stochastic optimization has gotten a lot of attention since it was recognized as a more realistic condition as suggested by many empirical observations. Specifically, the…

Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world…

Stochastic gradient algorithms are often unstable when applied to functions that do not have Lipschitz-continuous and/or bounded gradients. Gradient clipping is a simple and effective technique to stabilize the training process for problems…