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Deep neural networks (DNNs), the agents of deep learning (DL), require a massive number of parallel/sequential operations, which makes it difficult to comprehend them and impedes proper diagnosis. Without better knowledge of DNNs' internal…
Generalization error defines the discriminability and the representation power of a deep model. In this work, we claim that feature space design using deep compositional function plays a significant role in generalization along with…
Deep learning relies on a very specific kind of neural networks: those superposing several neural layers. In the last few years, deep learning achieved major breakthroughs in many tasks such as image analysis, speech recognition, natural…
Deep Neural Networks (DNNs) are everywhere, frequently performing a fairly complex task that used to be unimaginable for machines to carry out. In doing so, they do a lot of decision making which, depending on the application, may be…
This paper proposes a sparse Bayesian treatment of deep neural networks (DNNs) for system identification. Although DNNs show impressive approximation ability in various fields, several challenges still exist for system identification…
Deep learning techniques have demonstrated significant capacity in modeling some of the most challenging real world problems of high complexity. Despite the popularity of deep models, we still strive to better understand the underlying…
Deep neural networks (DNNs) have proven to be quite effective in a vast array of machine learning tasks, with recent examples in cyber security and autonomous vehicles. Despite the superior performance of DNNs in these applications, it has…
It has been recognized that heavily overparameterized deep neural networks (DNNs) exhibit surprisingly good generalization performance in various machine-learning tasks. Although benefits of depth have been investigated from different…
Standard deep neural networks (DNNs) are commonly trained in an end-to-end fashion for specific tasks such as object recognition, face identification, or character recognition, among many examples. This specificity often leads to…
In this work, we introduce a novel probabilistic representation of deep learning, which provides an explicit explanation for the Deep Neural Networks (DNNs) in three aspects: (i) neurons define the energy of a Gibbs distribution; (ii) the…
We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…
Children possess the ability to learn multiple cognitive tasks sequentially, which is a major challenge toward the long-term goal of artificial general intelligence. Existing continual learning frameworks are usually applicable to Deep…
Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…
Deep convolutional neural networks (DCNNs) have shown remarkable performance in image classification tasks in recent years. Generally, deep neural network architectures are stacks consisting of a large number of convolutional layers, and…
The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…
We develop a minimax rate analysis to describe the reason that deep neural networks (DNNs) perform better than other standard methods. For nonparametric regression problems, it is well known that many standard methods attain the minimax…
Overparameterised deep neural networks (DNNs) are highly expressive and so can, in principle, generate almost any function that fits a training dataset with zero error. The vast majority of these functions will perform poorly on unseen…
Deep neural networks (DNNs) have proven to be highly effective in a variety of tasks, making them the go-to method for problems requiring high-level predictive power. Despite this success, the inner workings of DNNs are often not…
Deep neural networks (DNNs) have achieved remarkable success in various tasks (e.g., image classification, speech recognition, and natural language processing (NLP)). However, researchers have demonstrated that DNN-based models are…
Advanced deep neural networks (DNNs), designed by either human or AutoML algorithms, are growing increasingly complex. Diverse operations are connected by complicated connectivity patterns, e.g., various types of skip connections. Those…