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We study regularized deep neural networks (DNNs) and introduce a convex analytic framework to characterize the structure of the hidden layers. We show that a set of optimal hidden layer weights for a norm regularized DNN training problem…

Convex functions and their gradients play a critical role in mathematical imaging, from proximal optimization to Optimal Transport. The successes of deep learning has led many to use learning-based methods, where fixed functions or…

The interpretability of neural networks (NNs) is a challenging but essential topic for transparency in the decision-making process using machine learning. One of the reasons for the lack of interpretability is random weight initialization,…

The activation function is at the heart of a deep neural networks nonlinearity; the choice of the function has great impact on the success of training. Currently, many practitioners prefer the Rectified Linear Unit (ReLU) due to its…

We analyze the dynamics of training deep ReLU networks and their implications on generalization capability. Using a teacher-student setting, we discovered a novel relationship between the gradient received by hidden student nodes and the…

It is difficult to describe in mathematical terms what a neural network trained on data represents. On the other hand, there is a growing mathematical understanding of what neural networks are in principle capable of representing.…

The complexity of deep neural network algorithms for hardware implementation can be much lowered by optimizing the word-length of weights and signals. Direct quantization of floating-point weights, however, does not show good performance…

Deep neural networks (DNNs) demonstrate outstanding performance across most computer vision tasks. Some critical applications, such as autonomous driving or medical imaging, also require investigation into their behavior and the reasons…

In this work, we propose to train a deep neural network by distributed optimization over a graph. Two nonlinear functions are considered: the rectified linear unit (ReLU) and a linear unit with both lower and upper cutoffs (DCutLU). The…

The rise of deep learning has led to various successful attempts to apply deep neural networks (DNNs) for important networking tasks such as intrusion detection. Yet, running DNNs in the network control plane, as typically done in existing…

We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds…

Neural networks have shown tremendous growth in recent years to solve numerous problems. Various types of neural networks have been introduced to deal with different types of problems. However, the main goal of any neural network is to…

Amongst others, the adoption of Rectified Linear Units (ReLUs) is regarded as one of the ingredients of the success of deep learning. ReLU activation has been shown to mitigate the vanishing gradient issue, to encourage sparsity in the…

A fundamental challenge in the theory of deep learning is to understand whether gradient-based training can promote parameters belonging to certain lower-dimensional structures (e.g., sparse or low-rank sets), leading to so-called implicit…

Large neural network models have been successful in learning functions of importance in many branches of science, including physics, chemistry and biology. Recent theoretical work has shown explicit learning bounds for wide networks and…

Neural networks are universal function approximators which are known to generalize well despite being dramatically overparameterized. We study this phenomenon from the point of view of the spectral bias of neural networks. Our contributions…

We introduce a method to train Binarized Neural Networks (BNNs) - neural networks with binary weights and activations at run-time. At training-time the binary weights and activations are used for computing the parameters gradients. During…

Deep neural networks (DNNs) are state-of-the-art algorithms for multiple applications, spanning from image classification to speech recognition. While providing excellent accuracy, they often have enormous compute and memory requirements.…

In the past decade, deep learning became the prevalent methodology for predictive modeling thanks to the remarkable accuracy of deep neural networks in tasks such as computer vision and natural language processing. Meanwhile, the structure…

Recurrent Neural Networks (RNNs) are widely recognized for their proficiency in modeling temporal dependencies, making them highly prevalent in sequential data processing applications. Nevertheless, vanilla RNNs are confronted with the…