"Recurrent backprop" for learning to store information over extended time intervals takes too long. The main reason is insufficient, decaying error back flow. We briefly review Hochreiter's 1991 analysis of this problem. Then we overcome it by introducing a novel, efficient method called "Long Short Term Memory" (LSTM). LSTM can learn to bridge minimal time lags in excess of 1000 time steps by enforcing constant error flow through internal states of special units. Multiplicative gate units learn to open and close access to constant error flow. LSTM's update

motivation: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using highthroughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of co-expression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiple-cluster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e. who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and non-linear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain a deeper insight into living organisms, therapeutic targeting and bioengineering.

Recently, there has been much interest in reverse engineering genetic networks from time series data. In this paper, we show that most of the proposed discrete time models — including the boolean network model [Kau93, SS96], the linear model of D’haeseleer et al. [DWFS99], and the nonlinear model of Weaver et al. [WWS99] — are all special cases of a general class of models called Dynamic Bayesian Networks (DBNs). The advantages of DBNs include the ability to model stochasticity, to incorporate prior knowledge, and to handle hidden variables and missing data in a principled way. This paper provides a review of techniques for learning DBNs. Keywords: Genetic networks, boolean networks, Bayesian networks, neural networks, reverse engineering, machine learning. 1

This article investigates the neural mechanisms underlying salamander locomotion, and develops a biologically plausible connectionist model of a central pattern generator capable of producing the typical aquatic and terrestrial gaits of the salamander. It investigates, in particular, what type of neural circuitry can produce and modulate the two locomotor programs identified within the salamander's spinal cord, namely, a traveling wave of neural activity for swimming and a standing wave for trotting. A two-dimensional biomechanical simulation of the salamander's body is developed whose muscle contraction is determined by the locomotion controller simulated as a leaky-integrator neural network. While the connectivity of the neural circuitry underlying locomotion in the salamander has not been decoded for the moment, this article presents the design of a neural circuit which has a general organization corresponding to that hypothesized by neurobiologists. In particular, the locomotion c...

Long Short-Term Memory (LSTM, Hochreiter & Schmidhuber, 1997) can solve numerous tasks not solvable by previous learning algorithms for recurrent neural networks (RNNs). We identify a weakness of LSTM networks processing continual input streams that are not a priori segmented into subsequences with explicitly marked ends at which the network's internal state could be reset. Without resets, the state may grow indenitely and eventually cause the network to break down. Our remedy is a novel, adaptive \forget gate" that enables an LSTM cell to learn to reset itself at appropriate times, thus releasing internal resources. We review illustrative benchmark problems on which standard LSTM outperforms other RNN algorithms. All algorithms (including LSTM) fail to solve continual versions of these problems. LSTM with forget gates, however, easily solves them in an elegant way.

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We introduce a new learning rule for fully recurrent neural networks which we call Backpropagation-Decorrelation rule (BPDC). It combines important principles: one-step backpropagation of errors and the usage of temporal memory in the network dynamics by means of decorrelation of activations. The BPDC rule is derived and theoretically justified from regarding learning as a constraint optimization problem and applies uniformly in discrete and continuous time. It is very easy to implement, and has a minimal complexity of 2N multiplications per time-step in the single output case. Nevertheless we obtain fast tracking and excellent performance in some benchmark problems including the Mackey-Glass time-series.

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The temporal distance between events conveys information essential for numerous sequential tasks such as motor control and rhythm detection. While Hidden Markov Models tend to ignore this information, recurrent neural networks (RNNs) can in principle learn to make use of it. We focus on Long Short-Term Memory (LSTM) because it has been shown to outperform other RNNs on tasks involving long time lags. We find that LSTM augmented by "peephole connections" from its internal cells to its multiplicative gates can learn the fine distinction between sequences of spikes spaced either 50 or 49 time steps apart without the help of any short training exemplars. Without external resets or teacher forcing, our LSTM variant also learns to generate stable streams of precisely timed spikes and other highly nonlinear periodic patterns. This makes LSTM a promising approach for tasks that require the accurate measurement or generation of time intervals.