Publications related to A note on a Lyapunov argument for stochastic gradient methods in the presence of noise

Understanding generalization and robustness in modern deep learning

In this thesis, we study two closely related directions: robustness and generalization in modern deep learning. Deep learning models based on empirical risk minimization are known to be often non-robust to small, worst-case perturbations known as adversari ...

EPFL2024

Residual-based attention in physics-informed neural networks

Nikolaos Stergiopoulos, Sokratis Anagnostopoulos

Driven by the need for more efficient and seamless integration of physical models and data, physics -informed neural networks (PINNs) have seen a surge of interest in recent years. However, ensuring the reliability of their convergence and accuracy remains ...

Lausanne2024

On the Generalization of Stochastic Gradient Descent with Momentum

Volkan Cevher, Kimon Antonakopoulos

While momentum-based accelerated variants of stochastic gradient descent (SGD) are widely used when training machine learning models, there is little theoretical understanding on the generalization error of such methods. In this work, we first show that th ...

Brookline2024

Deep Learning Generalization with Limited and Noisy Labels

Mahsa Forouzesh

Deep neural networks have become ubiquitous in today's technological landscape, finding their way in a vast array of applications. Deep supervised learning, which relies on large labeled datasets, has been particularly successful in areas such as image cla ...

EPFL2023

Fast Adversarial Training With Adaptive Step Size

Sabine Süsstrunk, Mathieu Salzmann, Chen Liu, Zhuoyi Huang, Yong Zhang, Jue Wang

While adversarial training and its variants have shown to be the most effective algorithms to defend against adversarial attacks, their extremely slow training process makes it hard to scale to large datasets like ImageNet. The key idea of recent works to ...

Piscataway2023

Masked Training of Neural Networks with Partial Gradients

Martin Jaggi, Sebastian Urban Stich, Amirkeivan Mohtashami

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 Extra-gradient), limiting SGD updates to a sub ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks

Florent Gérard Krzakala, Lenka Zdeborová, Ludovic Théo Stephan, Bruno Loureiro

Despite the non-convex optimization landscape, over-parametrized shallow networks are able to achieve global convergence under gradient descent. The picture can be radically different for narrow net-works, which tend to get stuck in badly-generalizing loca ...

2022

Gradient flow dynamics of shallow ReLU networks for square loss and orthogonal inputs

Nicolas Henri Bernard Flammarion, Etienne Patrice Boursier, Loucas Pillaud-Vivien

The training of neural networks by gradient descent methods is a cornerstone of the deep learning revolution. Yet, despite some recent progress, a complete theory explaining its success is still missing. This article presents, for orthogonal input vectors, ...

2022

Stochastic Second-Order Methods Improve Best-Known Sample Complexity of SGD for Gradient-Dominated Function

Patrick Thiran, Negar Kiyavash, Saber Salehkaleybar

We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of functions satisfying gradient dominance property with

1\le\alpha\le2

which holds in a wide range of applications in machine learning and signal processing. This conditio ...

NeurIPS2022

Generalization Properties of NAS under Activation and Skip Connection Search

Volkan Cevher, Grigorios Chrysos, Fanghui Liu, Zhenyu Zhu

Neural Architecture Search (NAS) has fostered the automatic discovery of stateof- the-art neural architectures. Despite the progress achieved with NAS, so far there is little attention to theoretical guarantees on NAS. In this work, we study the generaliza ...

2022

A note on a Lyapunov argument for stochastic gradient methods in the presence of noise

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Understanding generalization and robustness in modern deep learning

Residual-based attention in physics-informed neural networks

On the Generalization of Stochastic Gradient Descent with Momentum

Deep Learning Generalization with Limited and Noisy Labels

Fast Adversarial Training With Adaptive Step Size

Masked Training of Neural Networks with Partial Gradients

Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks

Gradient flow dynamics of shallow ReLU networks for square loss and orthogonal inputs

Stochastic Second-Order Methods Improve Best-Known Sample Complexity of SGD for Gradient-Dominated Function

Generalization Properties of NAS under Activation and Skip Connection Search

Understanding generalization and robustness in modern deep learning

Deep Learning Generalization with Limited and Noisy Labels

Residual-based attention in physics-informed neural networks

Masked Training of Neural Networks with Partial Gradients

Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks

On the Generalization of Stochastic Gradient Descent with Momentum

Gradient flow dynamics of shallow ReLU networks for square loss and orthogonal inputs

Stochastic Second-Order Methods Improve Best-Known Sample Complexity of SGD for Gradient-Dominated Function

Fast Adversarial Training With Adaptive Step Size

Generalization Properties of NAS under Activation and Skip Connection Search