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Batch normalization (BN) is central to modern deep networks, but its effect on the realized function during training remains less understood than its optimization benefits. We study training-time BN in continuous piecewise-affine (CPA)…

Batch normalization (BN) is a ubiquitous operation in deep neural networks, primarily used to improve stability and regularization during training. BN centers and scales feature maps using sample means and variances, which are naturally…

Modern deep neural network training is typically based on mini-batch stochastic gradient optimization. While the use of large mini-batches increases the available computational parallelism, small batch training has been shown to provide…

Though remarkable progress has been achieved in various vision tasks, deep neural networks still suffer obvious performance degradation when tested in out-of-distribution scenarios. We argue that the feature statistics (mean and standard…

Covariate shift has been shown to sharply degrade both predictive accuracy and the calibration of uncertainty estimates for deep learning models. This is worrying, because covariate shift is prevalent in a wide range of real world…

Fine-tuning pre-trained neural network models has become a widely adopted approach across various domains. However, it can lead to the distortion of pre-trained feature extractors that already possess strong generalization capabilities.…

Bayesian neural networks (BNN) and deep ensembles are principled approaches to estimate the predictive uncertainty of a deep learning model. However their practicality in real-time, industrial-scale applications are limited due to their…

Overfitting negatively impacts the generalization ability of deep neural networks (DNNs) in both natural and adversarial training. Existing methods struggle to consistently address different types of overfitting, typically designing…

We study overparameterization in generative adversarial networks (GANs) that can interpolate the training data. We show that overparameterization can improve generalization performance and accelerate the training process. We study the…

Trained with a sufficiently large training and testing dataset, Deep Neural Networks (DNNs) are expected to generalize. However, inputs may deviate from the training dataset distribution in real deployments. This is a fundamental issue with…

Advancements in parallel processing have lead to a surge in multilayer perceptrons' (MLP) applications and deep learning in the past decades. Recurrent Neural Networks (RNNs) give additional representational power to feedforward MLPs by…

Batch Normalization (BN) techniques have been proposed to reduce the so-called Internal Covariate Shift (ICS) by attempting to keep the distributions of layer outputs unchanged. Experiments have shown their effectiveness on training deep…

We examine the role of memorization in deep learning, drawing connections to capacity, generalization, and adversarial robustness. While deep networks are capable of memorizing noise data, our results suggest that they tend to prioritize…

Despite its empirical success and recent theoretical progress, there generally lacks a quantitative analysis of the effect of batch normalization (BN) on the convergence and stability of gradient descent. In this paper, we provide such an…

We conduct mathematical analysis on the effect of batch normalization (BN) on gradient backpropogation in residual network training, which is believed to play a critical role in addressing the gradient vanishing/explosion problem, in this…

Modern neural network architectures have achieved remarkable accuracies but remain highly dependent on their training data, often lacking interpretability in their learned mappings. While effective on large datasets, they tend to overfit on…

Normalization operations are essential for state-of-the-art neural networks and enable us to train a network from scratch with a large learning rate (LR). We attempt to explain the real effect of Batch Normalization (BN) from the…

Batch Normalization (BatchNorm) is a technique that improves the training of deep neural networks, especially Convolutional Neural Networks (CNN). It has been empirically demonstrated that BatchNorm increases performance, stability, and…

Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior…

Despite huge successes on a wide range of tasks, neural networks are known to sometimes struggle to generalise to unseen data. Many approaches have been proposed over the years to promote the generalisation ability of neural networks,…