Training recurrent neural networks (RNNs) that possess long-term memory is challenging. We provide insight into the trade-off between the smoothness of the cost function and the memory retention capabilities of the network. We express both aspects in terms of the Lipschitz constant of the dynamics modeled by the network. This allows us to make a distinction between three types of regions in the parameter space. In the first region, the network experiences problems in retaining long-term information, while at the same time the cost function is smooth and easy for gradient descent to navigate in. In the second region, the amount of stored information increases with time and the cost function is intricate and full of local minima. The third region is in between the two other regions and here the RNN is able to retain long-term information. Based on these theoretical findings we present the hypothesis that good parameter choices for the RNN are located in between the well-behaved and the ill-behaved cost function regions. The concepts presented in the paper are illustrated by artificially generated and real examples.
The work in @cite_2 presents a neural network without chaotic behavior. The results presented here, for which the chaotic behavior of LSTMs yield regions in the parameter space where the cost function is highly intricate, densely populated by local minimums and with exploding gradients, is a strong suggestion that this is indeed an interesting line of research that deserves to be further explored.
@cite_2
2572403989 2962711575 2042249109 2024632416
In this paper, a novel architecture for a deep recurrent neural network, residual LSTM is introduced. A plain LSTM has an internal memory cell that can learn long term dependencies of sequential data. It also provides a temporal shortcut path to avoid vanishing or exploding gradients in the temporal domain. The residual LSTM provides an additional spatial shortcut path from lower layers for efficient training of deep networks with multiple LSTM layers. Compared with the previous work, highway LSTM, residual LSTM separates a spatial shortcut path with temporal one by using output layers, which can help to avoid a conflict between spatial and temporal-domain gradient flows. Furthermore, residual LSTM reuses the output projection matrix and the output gate of LSTM to control the spatial information flow instead of additional gate networks, which effectively reduces more than 10 of network parameters. An experiment for distant speech recognition on the AMI SDM corpus shows that 10-layer plain and highway LSTM networks presented 13.7 and 6.2 increase in WER over 3-layer aselines, respectively. On the contrary, 10-layer residual LSTM networks provided the lowest WER 41.0 , which corresponds to 3.3 and 2.8 WER reduction over plain and highway LSTM networks, respectively. Recurrent neural networks, and in particular long short-term memory networks (LSTMs), are a remarkably effective tool for sequence modeling that learn a dense black-box hidden representation of their sequential input. Researchers interested in better understanding these models have studied the changes in hidden state representations over time and noticed some interpretable patterns but also significant noise. In this work, we present LSTMVis a visual analysis tool for recurrent neural networks with a focus on understanding these hidden state dynamics. The tool allows a user to select a hypothesis input range to focus on local state changes, to match these states changes to similar patterns in a large data set, and to align these results with domain specific structural annotations. We further show several use cases of the tool for analyzing specific hidden state properties on datasets containing nesting, phrase structure, and chord progressions, and demonstrate how the tool can be used to isolate patterns for further statistical analysis. There has been a long history of using neural networks for combinatorial optimization and constraint satisfaction problems. Symmetric Hopfield networks and similar approaches use steepest descent dynamics, and they always converge to the closest local minimum of the energy landscape. For finding global minima additional parameter-sensitive techniques are used, such as classical simulated annealing or the so-called chaotic simulated annealing, which induces chaotic dynamics by addition of extra terms to the energy landscape. Here we show that asymmetric continuous-time neural networks can solve constraint satisfaction problems without getting trapped in non-solution attractors. We concentrate on a model solving Boolean satisfiability (k-SAT), which is a quintessential NP-complete problem. There is a one-to-one correspondence between the stable fixed points of the neural network and the k-SAT solutions and we present numerical evidence that limit cycles may also be avoided by appropriately choosing the parameters of the model. This optimal parameter region is fairly independent of the size and hardness of instances, this way parameters can be chosen independently of the properties of problems and no tuning is required during the dynamical process. The model is similar to cellular neural networks already used in CNN computers. On an analog device solving a SAT problem would take a single operation: the connection weights are determined by the k-SAT instance and starting from any initial condition the system searches until finding a solution. In this new approach transient chaotic behavior appears as a natural consequence of optimization hardness and not as an externally induced effect. Neural network based approaches have recently produced record-setting performances in natural language understanding tasks such as word labeling. In the word labeling task, a tagger is used to assign a label to each word in an input sequence. Specifically, simple recurrent neural networks (RNNs) and convolutional neural networks (CNNs) have shown to significantly outperform the previous state-of-the-art - conditional random fields (CRFs). This paper investigates using long short-term memory (LSTM) neural networks, which contain input, output and forgetting gates and are more advanced than simple RNN, for the word labeling task. To explicitly model output-label dependence, we propose a regression model on top of the LSTM un-normalized scores. We also propose to apply deep LSTM to the task. We investigated the relative importance of each gate in the LSTM by setting other gates to a constant and only learning particular gates. Experiments on the ATIS dataset validated the effectiveness of the proposed models.