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Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine…
Deep neural networks are powerful tools to model observations over time with non-linear patterns. Despite the widespread use of neural networks in such settings, most theoretical developments of deep neural networks are under the assumption…
Recurrent neural networks have shown remarkable success in modeling sequences. However low resource situations still adversely affect the generalizability of these models. We introduce a new family of models, called Lattice Recurrent Units…
In a previous paper, we have shown that a recurrent neural network (RNN) can be used to detect cellular network radio signal degradations accurately. We unexpectedly found, though, that accuracy gains diminished as we added layers to the…
Recurrent Neural Networks (RNNs) are powerful tools for solving sequence-based problems, but their efficacy and execution time are dependent on the size of the network. Following recent work in simplifying these networks with model pruning…
Recurrent Neural Networks (RNN) are known as powerful models for handling sequential data, and especially widely utilized in various natural language processing tasks. In this paper, we propose Contextual Recurrent Units (CRU) for enhancing…
Recurrent neural networks (RNNs) are known to be difficult to train due to the gradient vanishing and exploding problems and thus difficult to learn long-term patterns and construct deep networks. To address these problems, this paper…
There are time series that are amenable to recurrent neural network (RNN) solutions when treated as sequences, but some series, e.g. asynchronous time series, provide a richer variation of feature types than current RNN cells take into…
Deep neural networks (DNNs) have emerged as key enablers of machine learning. Applying larger DNNs to more diverse applications is an important challenge. The computations performed during DNN training and inference are dominated by…
Recurrent neural networks (RNNs) such as Long Short Term Memory (LSTM) networks have become popular in a variety of applications such as image processing, data classification, speech recognition, and as controllers in autonomous systems. In…
Recurrent neural networks (RNNs) have represented for years the state of the art in neural machine translation. Recently, new architectures have been proposed, which can leverage parallel computation on GPUs better than classical RNNs.…
In this review paper, we give a comprehensive overview of the large variety of approximation results for neural networks. Approximation rates for classical function spaces as well as benefits of deep neural networks over shallow ones for…
Recurrent Neural Network (RNN) has been widely applied for sequence modeling. In RNN, the hidden states at current step are full connected to those at previous step, thus the influence from less related features at previous step may…
We explore the architecture of recurrent neural networks (RNNs) by studying the complexity of string sequences it is able to memorize. Symbolic sequences of different complexity are generated to simulate RNN training and study parameter…
Several variants of recurrent neural networks (RNNs) with orthogonal or unitary recurrent matrices have recently been developed to mitigate the vanishing/exploding gradient problem and to model long-term dependencies of sequences. However,…
One fundamental problem in deep learning is understanding the outstanding performance of deep Neural Networks (NNs) in practice. One explanation for the superiority of NNs is that they can realize a large class of complicated functions,…
Recurrent Neural Networks (RNN) are widely used to solve a variety of problems and as the quantity of data and the amount of available compute have increased, so have model sizes. The number of parameters in recent state-of-the-art networks…
We study ReLU deep neural networks (DNNs) by investigating their connections with the hierarchical basis method in finite element methods. First, we show that the approximation schemes of ReLU DNNs for $x^2$ and $xy$ are composition…
Classical neural network approximation results take the form: for every function $f$ and every error tolerance $\epsilon > 0$, one constructs a neural network whose architecture and weights depend on $\epsilon$. This paper introduces a…
Expansion property of a graph refers to its strong connectivity as well as sparseness. It has been reported that deep neural networks can be pruned to a high degree of sparsity while maintaining their performance. Such pruning is essential…