We present a method for training a deep neural network containing sinusoidal activation functions to fit to time-series data. Weights are initialized using a fast Fourier transform, then trained with regularization to improve generalization. A simple dynamic parameter tuning method is employed to adjust both the learning rate and regularization term, such that stability and efficient training are both achieved. We show how deeper layers can be utilized to model the observed sequence using a sparser set of sinusoid units, and how non-uniform regularization can improve generalization by promoting the shifting of weight toward simpler units. The method is demonstrated with time-series problems to show that it leads to effective extrapolation of nonlinear trends.
A more sophisticated group of methods involves neural networks with recurrent connections @cite_34 . These produce their own internal representation of state. (See Figure .B.) This enables them to learn how much to adjust their representations of state based on observed values, and hence operate in a manner more robust against noisy observations.
@cite_34
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Recurrent neural networks show state-of-the-art results in many text analysis tasks but often require a lot of memory to store their weights. Recently proposed Sparse Variational Dropout eliminates the majority of the weights in a feed-forward neural network without significant loss of quality. We apply this technique to sparsify recurrent neural networks. To account for recurrent specifics we also rely on Binary Variational Dropout for RNN. We report 99.5 sparsity level on sentiment analysis task without a quality drop and up to 87 sparsity level on language modeling task with slight loss of accuracy. Training recurrent neural networks to model long term dependencies is difficult. Hence, we propose to use external linguistic knowledge as an explicit signal to inform the model which memories it should utilize. Specifically, external knowledge is used to augment a sequence with typed edges between arbitrarily distant elements, and the resulting graph is decomposed into directed acyclic subgraphs. We introduce a model that encodes such graphs as explicit memory in recurrent neural networks, and use it to model coreference relations in text. We apply our model to several text comprehension tasks and achieve new state-of-the-art results on all considered benchmarks, including CNN, bAbi, and LAMBADA. On the bAbi QA tasks, our model solves 15 out of the 20 tasks with only 1000 training examples per task. Analysis of the learned representations further demonstrates the ability of our model to encode fine-grained entity information across a document. In existing convolutional neural networks (CNNs), both convolution and pooling are locally performed for image regions separately, no contextual dependencies between different image regions have been taken into consideration. Such dependencies represent useful spatial structure information in images. Whereas recurrent neural networks (RNNs) are designed for learning contextual dependencies among sequential data by using the recurrent (feedback) connections. In this work, we propose the convolutional recurrent neural network (C-RNN), which learns the spatial dependencies between image regions to enhance the discriminative power of image representation. The C-RNN is trained in an end-to-end manner from raw pixel images. CNN layers are firstly processed to generate middle level features. RNN layer is then learned to encode spatial dependencies. The C-RNN can learn better image representation, especially for images with obvious spatial contextual dependencies. Our method achieves competitive performance on ILSVRC 2012, SUN 397, and MIT indoor. Recurrent neural networks (RNNs) can learn to perform finite state computations. It is shown that an RNN performing a finite state computation must organize its state space to mimic the states in the minimal deterministic finite state machine that can perform that computation, and a precise description of the attractor structure of such systems is given. This knowledge effectively predicts activation space dynamics, which allows one to understand RNN computation dynamics in spite of complexity in activation dynamics. This theory provides a theoretical framework for understanding finite state machine (FSM) extraction techniques and can be used to improve training methods for RNNs performing FSM computations. This provides an example of a successful approach to understanding a general class of complex systems that has not been explicitly designed, e.g., systems that have evolved or learned their internal structure.