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Batch Normalization (BN) has been a standard component in designing deep neural networks (DNNs). Although the standard BN can significantly accelerate the training of DNNs and improve the generalization performance, it has several…

Batch normalization (BN) is a key facilitator and considered essential for state-of-the-art binary neural networks (BNN). However, the BN layer is costly to calculate and is typically implemented with non-binary parameters, leaving a hurdle…

Batch Normalization (BN) has been proven to be quite effective at accelerating and improving the training of deep neural networks (DNNs). However, BN brings additional computation, consumes more memory and generally slows down the training…

\emph{Batch normalization} is a successful building block of neural network architectures. Yet, it is not well understood. A neural network layer with batch normalization comprises three components that affect the representation induced by…

Empirical studies show that gradient-based methods can learn deep neural networks (DNNs) with very good generalization performance in the over-parameterization regime, where DNNs can easily fit a random labeling of the training data. Very…

Batch Normalization (BN) uses mini-batch statistics to normalize the activations during training, introducing dependence between mini-batch elements. This dependency can hurt the performance if the mini-batch size is too small, or if the…

Recent findings suggest that consecutive layers of neural networks with the ReLU activation function \emph{fold} the input space during the learning process. While many works hint at this phenomenon, an approach to quantify the folding was…

Batch Normalization (BN) is an important preprocessing step to many deep learning applications. Since it is a data-dependent process, for some homogeneous datasets it is a redundant or even a performance-degrading process. In this paper, we…

Promising resolutions of the generalization puzzle observe that the actual number of parameters in a deep network is much smaller than naive estimates suggest. The renormalization group is a compelling example of a problem which has very…

We study expected generalization bounds for the Hierarchical Federated Learning (HFL) setup using Wasserstein distance. We introduce a generalized framework in which data is sampled hierarchically, and we model it with a multi-layered tree…

Batch normalization (BN) is an important technique commonly incorporated into deep learning models to perform standardization within mini-batches. The merits of BN in improving a model's learning efficiency can be further amplified by…

Gaussian Error Linear Unit (GELU) is a widely used smooth alternative to Rectifier Linear Unit (ReLU), yet many deployment, compression, and analysis toolchains are most naturally expressed for piecewise-linear (ReLU-type) networks. We…

Batch normalization (BN) has become a critical component across diverse deep neural networks. The network with BN is invariant to positively linear re-scale transformation, which makes there exist infinite functionally equivalent networks…

Various iterative reconstruction algorithms for inverse problems can be unfolded as neural networks. Empirically, this approach has often led to improved results, but theoretical guarantees are still scarce. While some progress on…

Batch-normalization (BN) layers are thought to be an integrally important layer type in today's state-of-the-art deep convolutional neural networks for computer vision tasks such as classification and detection. However, BN layers introduce…

It is a common assumption that the activation of different layers in neural networks follow Gaussian distribution. This distribution can be transformed using normalization techniques, such as batch-normalization, increasing convergence…

A key component of most neural network architectures is the use of normalization layers, such as Batch Normalization. Despite its common use and large utility in optimizing deep architectures, it has been challenging both to generically…

Normalization is a pre-processing step that converts the data into a more usable representation. As part of the deep neural networks (DNNs), the batch normalization (BN) technique uses normalization to address the problem of internal…

Path regularization has shown to be a very effective regularization to train neural networks, leading to a better generalization property than common regularizations i.e. weight decay, etc. We propose a first near-complete (as will be made…

Inspired by BatchNorm, there has been an explosion of normalization layers in deep learning. Recent works have identified a multitude of beneficial properties in BatchNorm to explain its success. However, given the pursuit of alternative…