Algorithm learning is a core problem in artificial intelligence with significant implications on automation level that can be achieved by machines. Recently deep learning methods are emerging for synthesizing an algorithm from its input-output examples, the most successful being the Neural GPU, capable of learning multiplication. We present several improvements to the Neural GPU that substantially reduces training time and improves generalization. We introduce a new technique - hard nonlinearities with saturation costs- that has general applicability. We also introduce a technique of diagonal gates that can be applied to active-memory models. The proposed architecture is the first capable of learning decimal multiplication end-to-end.
Grid LSTM @cite_13 allow explicit unrolling along time and memory dimension and are able to learn such tasks as addition and memorization.
@cite_13
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Learning to store information over extended time intervals by recurrent backpropagation takes a very long time, mostly because of insufficient, decaying error backflow. We briefly review Hochreiter's (1991) analysis of this problem, then address it by introducing a novel, efficient, gradient based method called long short-term memory (LSTM). Truncating the gradient where this does not do harm, LSTM can learn to bridge minimal time lags in excess of 1000 discrete-time steps by enforcing constant error flow through constant error carousels within special units. Multiplicative gate units learn to open and close access to the constant error flow. LSTM is local in space and time; its computational complexity per time step and weight is O. 1. Our experiments with artificial data involve local, distributed, real-valued, and noisy pattern representations. In comparisons with real-time recurrent learning, back propagation through time, recurrent cascade correlation, Elman nets, and neural sequence chunking, LSTM leads to many more successful runs, and learns much faster. LSTM also solves complex, artificial long-time-lag tasks that have never been solved by previous recurrent network algorithms. This paper introduces Grid Long Short-Term Memory, a network of LSTM cells arranged in a multidimensional grid that can be applied to vectors, sequences or higher dimensional data such as images. The network differs from existing deep LSTM architectures in that the cells are connected between network layers as well as along the spatiotemporal dimensions of the data. The network provides a unified way of using LSTM for both deep and sequential computation. We apply the model to algorithmic tasks such as 15-digit integer addition and sequence memorization, where it is able to significantly outperform the standard LSTM. We then give results for two empirical tasks. We find that 2D Grid LSTM achieves 1.47 bits per character on the Wikipedia character prediction benchmark, which is state-of-the-art among neural approaches. In addition, we use the Grid LSTM to define a novel two-dimensional translation model, the Reencoder, and show that it outperforms a phrase-based reference system on a Chinese-to-English translation task. In this paper, we extend the deep long short-term memory (DLSTM) recurrent neural networks by introducing gated direct connections between memory cells in adjacent layers. These direct links, called highway connections, enable unimpeded information flow across different layers and thus alleviate the gradient vanishing problem when building deeper LSTMs. We further introduce the latency-controlled bidirectional LSTMs (BLSTMs) which can exploit the whole history while keeping the latency under control. Efficient algorithms are proposed to train these novel networks using both frame and sequence discriminative criteria. Experiments on the AMI distant speech recognition (DSR) task indicate that we can train deeper LSTMs and achieve better improvement from sequence training with highway LSTMs (HLSTMs). Our novel model obtains @math WER on AMI (SDM) dev and eval sets, outperforming all previous works. It beats the strong DNN and DLSTM baselines with @math and @math relative improvement respectively. In this paper, we present bidirectional Long Short Term Memory (LSTM) networks, and a modified, full gradient version of the LSTM learning algorithm. We evaluate Bidirectional LSTM (BLSTM) and several other network architectures on the benchmark task of framewise phoneme classification, using the TIMIT database. Our main findings are that bidirectional networks outperform unidirectional ones, and Long Short Term Memory (LSTM) is much faster and also more accurate than both standard Recurrent Neural Nets (RNNs) and time-windowed Multilayer Perceptrons (MLPs). Our results support the view that contextual information is crucial to speech processing, and suggest that BLSTM is an effective architecture with which to exploit it'.