Related papers: Realization Theory Of Recurrent Neural ODEs Using …

In this paper, we show that, under mild assumptions, input-output behavior of a continous-time recurrent neural network (RNN) can be represented by a rational or polynomial nonlinear system. The assumptions concern the activation function…

A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…

To understand the fundamental trade-offs between training stability, temporal dynamics and architectural complexity of recurrent neural networks~(RNNs), we directly analyze RNN architectures using numerical methods of ordinary differential…

Recurrent neural networks (RNNs) with continuous-time hidden states are a natural fit for modeling irregularly-sampled time series. These models, however, face difficulties when the input data possess long-term dependencies. We prove that…

Recurrent Neural Networks (RNNs) are a class of machine learning algorithms used for applications with time-series and sequential data. Recently, there has been a strong interest in executing RNNs on embedded devices. However, difficulties…

This is a tutorial paper on Recurrent Neural Network (RNN), Long Short-Term Memory Network (LSTM), and their variants. We start with a dynamical system and backpropagation through time for RNN. Then, we discuss the problems of gradient…

Long Short-Term Memory (LSTM) is a recurrent neural network (RNN) architecture that has been designed to address the vanishing and exploding gradient problems of conventional RNNs. Unlike feedforward neural networks, RNNs have cyclic…

Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE)…

Gated recurrent networks such as those composed of Long Short-Term Memory (LSTM) nodes have recently been used to improve state of the art in many sequential processing tasks such as speech recognition and machine translation. However, the…

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,…

This paper develops a model that addresses sentence embedding, a hot topic in current natural language processing research, using recurrent neural networks with Long Short-Term Memory (LSTM) cells. Due to its ability to capture long term…

In this article, we explore the effects of memory terms in continuous-layer Deep Residual Networks by studying Neural ODEs (NODEs). We investigate two types of models. On one side, we consider the case of Residual Neural Networks with…

Sequence models, and particularly Linear Recurrent Neural Networks (LRNNs) of the form $\mathbf{h}_{k+1} = \mathbf{W} \mathbf{h}_{k} + \mathbf{y}_k + \mathbf{b}$, are widely applicable in time-series analysis for dynamical systems, yet, as…

Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…

Long Short-Term Memory Recurrent Neural Networks (LSTM-RNN) are one of the most powerful dynamic classifiers publicly known. The network itself and the related learning algorithms are reasonably well documented to get an idea how it works.…

Recurrent Neural Networks (RNNs) have long been recognized for their potential to model complex time series. However, it remains to be determined what optimization techniques and recurrent architectures can be used to best realize this…

Recurrent Neural Networks (RNNs) with Long Short-Term Memory units (LSTM) are widely used because they are expressive and are easy to train. Our interest lies in empirically evaluating the expressiveness and the learnability of LSTMs in the…

This study presents a novel model for invertible sentence embeddings using a residual recurrent network trained on an unsupervised encoding task. Rather than the probabilistic outputs common to neural machine translation models, our…

Recurrent neural networks (RNNs) have drawn interest from machine learning researchers because of their effectiveness at preserving past inputs for time-varying data processing tasks. To understand the success and limitations of RNNs, it is…

Recurrent Neural Networks (RNNs) and their variants, such as Long-Short Term Memory (LSTM) networks, and Gated Recurrent Unit (GRU) networks, have achieved promising performance in sequential data modeling. The hidden layers in RNNs can be…