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Neural networks often operate in the overparameterized regime, in which there are far more parameters than training samples, allowing the training data to be fit perfectly. That is, training the network effectively learns an interpolating…

The training process of neural networks usually optimize weights and bias parameters of linear transformations, while nonlinear activation functions are pre-specified and fixed. This work develops a systematic approach to constructing…

In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU). We give an algorithm to train a ReLU DNN with one hidden layer to *global optimality* with runtime…

Deep learning training training algorithms are a huge success in recent years in many fields including speech, text,image video etc. Deeper and deeper layers are proposed with huge success with resnet structures having around 152 layers.…

Computational models of vision have traditionally been developed in a bottom-up fashion, by hierarchically composing a series of straightforward operations - i.e. convolution and pooling - with the aim of emulating simple and complex cells…

Recent studies have shown that the choice of activation function can significantly affect the performance of deep learning networks. However, the benefits of novel activation functions have been inconsistent and task dependent, and…

We scrutinize the structural and operational aspects of deep learning models, particularly focusing on the nuances of learnable parameters (weight) statistics, distribution, node interaction, and visualization. By establishing correlations…

A wide variety of activation functions have been proposed for neural networks. The Rectified Linear Unit (ReLU) is especially popular today. There are many practical reasons that motivate the use of the ReLU. This paper provides new…

Gated recurrent neural networks have achieved remarkable results in the analysis of sequential data. Inside these networks, gates are used to control the flow of information, allowing to model even very long-term dependencies in the data.…

The purported "black box" nature of neural networks is a barrier to adoption in applications where interpretability is essential. Here we present DeepLIFT (Deep Learning Important FeaTures), a method for decomposing the output prediction of…

Despite the empirical success of DNN, their internal training dynamics remain difficult to characterize. In ReLU-based models, the activation pattern induced by a given input determines the piecewise-linear region in which the network…

An activation function has crucial role in a deep neural network. A simple rectified linear unit (ReLU) are widely used for the activation function. In this paper, a weighted sigmoid gate unit (WiG) is proposed as the activation function.…

Activation function is a key component in deep learning that performs non-linear mappings between the inputs and outputs. Rectified Linear Unit (ReLU) has been the most popular activation function across the deep learning community.…

"Deep Learning"/"Deep Neural Nets" is a technological marvel that is now increasingly deployed at the cutting-edge of artificial intelligence tasks. This dramatic success of deep learning in the last few years has been hinged on an enormous…

Mean field theory has been successfully used to analyze deep neural networks (DNN) in the infinite size limit. Given the finite size of realistic DNN, we utilize the large deviation theory and path integral analysis to study the deviation…

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…

We provide a theoretical explanation of the role of the number of nodes at each layer in deep neural networks. We prove that the largest variation of a deep neural network with ReLU activation function arises when the layer with the fewest…

This study introduces PINN4PF, an end-to-end deep learning architecture for power flow (PF) analysis that effectively captures the nonlinear dynamics of large-scale modern power systems. The proposed neural network (NN) architecture…

This paper introduces two recurrent neural network structures called Simple Gated Unit (SGU) and Deep Simple Gated Unit (DSGU), which are general structures for learning long term dependencies. Compared to traditional Long Short-Term Memory…

Activation functions influence behavior and performance of DNNs. Nonlinear activation functions, like Rectified Linear Units (ReLU), Exponential Linear Units (ELU) and Scaled Exponential Linear Units (SELU), outperform the linear…