Recurrent Neural Networks (RNNs), and specifically a variant with Long Short-Term Memory (LSTM), are enjoying renewed interest as a result of successful applications in a wide range of machine learning problems that involve sequential data. However, while LSTMs provide exceptional results in practice, the source of their performance and their limitations remain rather poorly understood. Using character-level language models as an interpretable testbed, we aim to bridge this gap by providing an analysis of their representations, predictions and error types. In particular, our experiments reveal the existence of interpretable cells that keep track of long-range dependencies such as line lengths, quotes and brackets. Moreover, our comparative analysis with finite horizon n-gram models traces the source of the LSTM improvements to long-range structural dependencies. Finally, we provide analysis of the remaining errors and suggests areas for further study.
@cite_22: Despite the recent achievements in machine learning, we are still very far from achieving real artificial intelligence. In this paper, we discuss the limitations of standard deep learning approaches and show that some of these limitations can be overcome by learning how to grow the complexity of a model in a structured way. Specifically, we study the simplest sequence prediction problems that are beyond the scope of what is learnable with standard recurrent networks, algorithmically generated sequences which can only be learned by models which have the capacity to count and to memorize sequences. We show that some basic algorithms can be learned from sequential data using a recurrent network associated with a trainable memory.
@cite_28: 
@cite_29: This chapter contains sections titled: The Problem, The Generalized Delta Rule, Simulation Results, Some Further Generalizations, Conclusion
@cite_9: Recurrent neural networks can be used to map input sequences to output sequences, such as for recognition, production or prediction problems. However, practical difficulties have been reported in training recurrent neural networks to perform tasks in which the temporal contingencies present in the input output sequences span long intervals. We show why gradient based learning algorithms face an increasingly difficult problem as the duration of the dependencies to be captured increases. These results expose a trade-off between efficient learning by gradient descent and latching on information for long periods. Based on an understanding of this problem, alternatives to standard gradient descent are considered. >
@cite_3: There are two widely known issues with properly training recurrent neural networks, the vanishing and the exploding gradient problems detailed in (1994). In this paper we attempt to improve the understanding of the underlying issues by exploring these problems from an analytical, a geometric and a dynamical systems perspective. Our analysis is used to justify a simple yet effective solution. We propose a gradient norm clipping strategy to deal with exploding gradients and a soft constraint for the vanishing gradients problem. We validate empirically our hypothesis and proposed solutions in the experimental section.
@cite_6: We extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a Turing Machine or Von Neumann architecture but is differentiable end-to-end, allowing it to be efficiently trained with gradient descent. Preliminary results demonstrate that Neural Turing Machines can infer simple algorithms such as copying, sorting, and associative recall from input and output examples.
@cite_0: Neural machine translation is a recently proposed approach to machine translation. Unlike the traditional statistical machine translation, the neural machine translation aims at building a single neural network that can be jointly tuned to maximize the translation performance. The models proposed recently for neural machine translation often belong to a family of encoder-decoders and consists of an encoder that encodes a source sentence into a fixed-length vector from which a decoder generates a translation. In this paper, we conjecture that the use of a fixed-length vector is a bottleneck in improving the performance of this basic encoder-decoder architecture, and propose to extend this by allowing a model to automatically (soft-)search for parts of a source sentence that are relevant to predicting a target word, without having to form these parts as a hard segment explicitly. With this new approach, we achieve a translation performance comparable to the existing state-of-the-art phrase-based system on the task of English-to-French translation. Furthermore, qualitative analysis reveals that the (soft-)alignments found by the model agree well with our intuition.
@cite_19: Abstract Backpropagation is often viewed as a method for adapting artificial neural networks to classify patterns. Based on parts of the book by Rumelhart and colleagues, many authors equate backpropagation with the generalized delta rule applied to fully-connected feedforward networks. This paper will summarize a more general formulation of backpropagation, developed in 1974, which does more justice to the roots of the method in numerical analysis and statistics, and also does more justice to creative approaches expressed by neural modelers in the past year or two. It will discuss applications of backpropagation to forecasting over time (where errors have been halved by using methods other than least squares), to optimization, to sensitivity analysis, and to brain research. This paper will go on to derive a generalization of backpropagation to recurrent systems (which input their own output), such as hybrids of perceptron-style networks and Grossberg Hopfield networks. Unlike the proposal of Rumelhart, Hinton, and Williams, this generalization does not require the storage of intermediate iterations to deal with continuous recurrence. This generalization was applied in 1981 to a model of natural gas markets, where it located sources of forecast uncertainty related to the use of least squares to estimate the model parameters in the first place.
@cite_5: Neural machine translation is a relatively new approach to statistical machine translation based purely on neural networks. The neural machine translation models often consist of an encoder and a decoder. The encoder extracts a fixed-length representation from a variable-length input sentence, and the decoder generates a correct translation from this representation. In this paper, we focus on analyzing the properties of the neural machine translation using two models; RNN Encoder--Decoder and a newly proposed gated recursive convolutional neural network. We show that the neural machine translation performs relatively well on short sentences without unknown words, but its performance degrades rapidly as the length of the sentence and the number of unknown words increase. Furthermore, we find that the proposed gated recursive convolutional network learns a grammatical structure of a sentence automatically.
@cite_12: In recent years, deep artificial neural networks (including recurrent ones) have won numerous contests in pattern recognition and machine learning. This historical survey compactly summarizes relevant work, much of it from the previous millennium. Shallow and Deep Learners are distinguished by the depth of their credit assignment paths, which are chains of possibly learnable, causal links between actions and effects. I review deep supervised learning (also recapitulating the history of backpropagation), unsupervised learning, reinforcement learning & evolutionary computation, and indirect search for short programs encoding deep and large networks.
@cite_17: 
. Recurrent Neural Networks (RNNs) have a long history of applications in various sequence learning tasks @cite_19 @cite_12 @cite_29 . Despite their early successes, the difficulty of training simple recurrent networks @cite_9 @cite_3 has encouraged various proposals for improvements to their basic architecture. Among the most successful variants are the Long Short Term Memory networks @cite_17 , which can in principle store and retrieve information over long time periods with explicit gating mechanisms and a built-in constant error carousel. In the recent years there has been a renewed interest in further improving on the basic architecture by modifying the functional form as seen with Gated Recurrent Units @cite_5 , incorporating content-based soft attention mechanisms @cite_0 @cite_28 , push-pop stacks @cite_22 , or more generally external memory arrays with both content-based and relative addressing mechanisms @cite_6 . In this work we focus the majority of our analysis on the LSTM due to its widespread popularity and a proven track record.