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Domain generalization aims at training machine learning models to perform robustly across different and unseen domains. Several recent methods use multiple datasets to train models to extract domain-invariant features, hoping to generalize…

The aim of this paper is to provide a mathematical analysis of transformer architectures using a self-attention mechanism with layer normalization. In particular, observed patterns in such architectures resembling either clusters or uniform…

As an indispensable component, Batch Normalization (BN) has successfully improved the training of deep neural networks (DNNs) with mini-batches, by normalizing the distribution of the internal representation for each hidden layer. However,…

Utilizing recently introduced concepts from statistics and quantitative risk management, we present a general variant of Batch Normalization (BN) that offers accelerated convergence of Neural Network training compared to conventional BN. In…

Normalization techniques have only recently begun to be exploited in supervised learning tasks. Batch normalization exploits mini-batch statistics to normalize the activations. This was shown to speed up training and result in better…

We propose a novel learning framework based on neural mean-field dynamics for inference and estimation problems of diffusion on networks. Our new framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node…

We study the role of $L_2$ regularization in deep learning, and uncover simple relations between the performance of the model, the $L_2$ coefficient, the learning rate, and the number of training steps. These empirical relations hold when…

Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averaging over large batches. Long plateaus in which one observes…

Normalization methods are a central building block in the deep learning toolbox. They accelerate and stabilize training, while decreasing the dependence on manually tuned learning rate schedules. When learning from multi-modal…

We study the role of depth in training randomly initialized overparameterized neural networks. We give a general result showing that depth improves trainability of neural networks by improving the conditioning of certain kernel matrices of…

In real-world scenarios, the number of training samples across classes usually subjects to a long-tailed distribution. The conventionally trained network may achieve unexpected inferior performance on the rare class compared to the frequent…

Strong, correlated noise in recurrent neural circuits often passes through nonlinear transfer functions, complicating dynamical mean-field analyses of complex phenomena such as transients and bifurcations. We introduce a method that…

In machine learning, there is a long history of trying to build neural networks that can learn from fewer example data by baking in strong geometric priors. However, it is not always clear a priori what geometric constraints are appropriate…

Batch Normalization (BN) is a core and prevalent technique in accelerating the training of deep neural networks and improving the generalization on Computer Vision (CV) tasks. However, it fails to defend its position in Natural Language…

Batch normalization (BN) is widely used in modern deep neural networks, which has been shown to represent the domain-related knowledge, and thus is ineffective for cross-domain tasks like unsupervised domain adaptation (UDA). Existing BN…

Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…

A significant advance in accelerating neural network training has been the development of normalization methods, permitting the training of deep models both faster and with better accuracy. These advances come with practical challenges: for…

Training deep neural networks is a very demanding task, especially challenging is how to adapt architectures to improve the performance of trained models. We can find that sometimes, shallow networks generalize better than deep networks,…

Batch Normalization (BN) is widely used in {centralized} deep learning to improve convergence and generalization. However, in {federated} learning (FL) with decentralized data, prior work has observed that training with BN could hinder…

An obstacle to artificial general intelligence is set by continual learning of multiple tasks of different nature. Recently, various heuristic tricks, both from machine learning and from neuroscience angles, were proposed, but they lack a…