R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1:270-280, 1989.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....state) at the next time step, c i (t 1) are computed as follows: c i (t 1) oe w ij (t)d j (t) m ik (t)c k (t) # (8) The threshold term is denoted by # i . At each time step t, the RNN is trained to predict the next symbol in the sequence. Training is performed via the RTRL [8] minimization of the error function: E(t) 1 (r m (t) Gamma om (t) 9) where the desired (required) output vector r(t) fr m (t)g is the binary code of the next symbol in the training sequence. 4 Building predictive models First we trained both RBCMN and RNN on a long sequence of ....

Williams R.J. and Zipser D. (1989) A learning algorithm for continually running fully recurrent neural networks. Neural Computation 1, 270--280.

....BPTT, m = n, and Rtime = O(m) BPTT s disadvantage is that it requires O(ntime) storage which means that Rspace is infinite: BPTT is not a fixed size storage algorithm. The most well known fixed size storage learning algorithm for minimizing E ttal (ntime) with fully recurrent nets is RTRL [2] [8]. With RTRL, m = n, Rtime = O(m 3) much worse than with BPTT) and Rspace = O(m 2) much better than with BPTT) Contribution of this paper. The contribution of this paper is an extension of the conventional dynamics (as in equation (1) plus a corresponding exact gradient based learning algorithm ....

....changes) such that it creates appropriate intra sequence weight changes at appropriate time steps. 3 SUPERVISED LEARNING ALGORITHM The following algorithm for minimizing E ttal is partly inspired by conventional recurrent network algorithms (e.g. 2] 7] The notation is partly inspired by [8]. Derivation. Before training, all initial weights Wab(1) are randomly initialized. The chain rule serves to compute weight increments (to be performed after each training sequence) for all initial weights according to OE ttal (ntime ) Wab(1) wab(1) q , 5) 0wab(1) where q is a constant ....

R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent networks. Neural Computation, 1(2):270-280, 1989.

....patterns and sequences. Notwithstanding the importance of these networks, a major problem in their deployment in practice is the complexity of training due to the presence of recurrent and feedback connections. The problem is further exacerbated if gradient descent learning algorithms [1,2] that require the computation of error gradients for the necessary updating are used, often forcing one to resort to approximations that may in turn reduce the training efficiency [3] More recently, some efforts have been made to tailor alternate training schemes (such as reinforcement learning ....

....a trajectory defined on a certain feature space is often the task for a robot in industrial and manufacturing settings and the accurate generation of such a trajectory is typically required in the satisfactory control of such robots. Due to the importance of this problem, a number of recent works [2, 4 7] have focused on designing efficient schemes for training recurrent neural nets to produce periodic trajectories of desired forms. Two specific benchmark trajectories that have received wide attention in performance evaluations of these learning schemes are the circle trajectory and a figure ....

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R. Williams and D. Zipser, "A Learning Algorithm For Continually Running Fully Recurrent Neural Networks," Neural Computation, vol. 1, pp. 270-280, 1989.

....not possible to solve many of the dynamical problems with the same degree of success with which neural networks have been used in static problems. It has been proven that a RNN can approximate any known dynamical system [16] and several techniques for training RNNs have been developed [17] 18] [19], 20] 21] 22] 23] 24] 25] 26] 27] 28] 29] 30] 31] 32] 33] 34] 35] 36] 37] 38] 39] 40] A subset of these works directed to the trajectory generation problem have shown that a RNN can indeed be trained to produce desired trajectory behavior, and have ....

R.J. William and D. Zipser, "A learning algorithm for continually running fully recurrent neural networks," Neural Computation, vol. 1, pp. 270-280, 1989.

....number of context units is equal to the number of hidden units [CK01, p. 21 2] propagation through time, in which the temporal history is not considered [CK01, p. 22] Similar types of time delay recurrent neural networks are developed in parallel by Jordan, Williams and Zipser or Giles et al. [Elm90, WiZi89, Gil91]. Jordan invented a traditional three layer feedforward architecture with a set of context units that mirror the output layer activation and feed it back into the hidden layer [CK01, p. 19] A comprehensive description of Jordan s network is provided in Churchland and Sejnowski (1997) CS97, p. ....

Williams R. J. and Zipser D.: A learning algorithm for continually running fully recurrent neural networks, in: Neural Computation, Vol. 1, No. 2, 1989, pp. 270-280.

.... cannot be stored naturally (unless encoded explicitly, e.g. through the use of tapped delay inputs [74,78] To circumvent the above drawback, recurrent neural networks (RNNs) have been introduced by a number of researchers, e.g. Elman [15] Jordan [36] Pineda [64] and Williams and Zipser [84], to name but a few. These networks have feedback connections so that they can preserve their past activities for future computation. As a result, the current network state depends on the previous ones over a potentially unbounded period of time (up to the time at which the network is started to ....

R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1:270--280, 1989.

....engineering viewpoint, time varying behaviors are probably of greater importance among the nonlinear dynamic behaviors that recurrent neural networks manifest. Many authors have studied recurrent neural network models of various types of perceptual processes and applications [1] 2] 31, 41, [5], 61, 71. One of the dynamic behaviors concerned by many works [8] 9] 10] 11] 12] is that the existence and the location of equilibrium points, and with the qualitative properties of the equilibria. The stability analysis and applications of a class of single layered, fully or sparsely ....

. R. J. Williams and D. Zipset, "A Learning Algorithm for Continually Running Fully Recurrent Neural Networks", Neural Computation, Vol. 2, pp. 490-501, 1990.

....Hence in many real problems the BPTT cannot be used to adapt the network, but on line learning algorithms are needed. In order to develop on line algorithms there are two classical choices: approximating BPTT [8] or using the computationally very expensive Real Time Recurrent Learning (RTRL) [9]. In this paper we propose a new learning algorithm, called Truncated Recursive Back Propagation (TRBP) which can be easily implemented on line with good performance. Moreover it genemlises the algorithm proposed by Waibel et al. in [4] for TDNN, and includes the Back and Tsoi algorithm [3] as ....

....is necessary. Therefore we want to derive a new method to approximate this batch mode algorithm whose inspiration comes from the algorithm proposed by Williams and Peng for fully recurrent neural networks [8] Must be stressed that the RBP algc ithm is not a version of BPTr [7,8] nor one of RTRL [9] even if in the first papers [10,11] we used the name BPTT. However, for the first time, it implements some features of both algorithms: the backward error propagation of BPTT is used in expressions (3) 5) and (8) the recursive forward derivatives calculation commonly used in the RTRL and ....

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R.J. Williams, D. Zipser, "A Learning Algorithm for Continually Running Fully Recurrent Neural Networks", Neural Computation 1: 270-280, 1989.

....instead of the true network outputs. In Infinite Impulse Response This research was supported by the Italian MURST. 2 (IIR) adaptive filter theory this is the equation error approximation of the true output error approach [10] in neural network theory this is the teacher forced technique [2]. Extension of Back Propagation to recurrent networks was firstly proposed by F. Pineda and L. B. Almeida, e.g. 26] only in the case when the recurrent network behaviour relaxes to a fixed point. However, if a general temporal processing is needed, two main gradient based learning approaches ....

....the case when the recurrent network behaviour relaxes to a fixed point. However, if a general temporal processing is needed, two main gradient based learning approaches exist for recurrent networks [15,16,20] Back Propagation Through Time (BPTT) 6,1,27,15] and Real Time Recurrent Learning (RTRL) [2,18,22,27,15]. BPTT is a family of algorithms which extends the BP paradigm to dynamic networks. There are two major points of view to understand what BPTT is. The first is an intuitive one: time unfolding of the recurrent network, i.e. for single layer single feedback delay fully recurrent networks one can ....

R.J. Williams, D. Zipser. A Learning Algorithm for Continually Running Fully Recurrent Neural Networks. Neural Computation 1: 270-280, 1989.

.... forecasting recognition, and identification control of general non linear dynamic systems by Neural Networks (NN) feedforward structures are not adequate, several architectures of Recurrent NN (RNN) have been proposed for them [4,11,12] the two major classes being Fully Recurrent NNs (FRNNs) [1,2] and Locally Recurrent Globally Feedforward NNs [3,4,6,7] In order to train adaptively a recurrent NN with a given architecture, an online learning algorithm must be derived. Considering gradient based learning algorithms, we must estimate the gradient of a cost function and then use it in the ....

....depends upon the past output of the RNN, so the present error depends not only on the present parameters set but also on the past parameters values, and this dependence has to be considered in the calculation of the gradient. The works on recurrent NNs being trained on line are quite few, e.g. [1,2,6,7,8,11,12]. There are two different ways to calculate the gradient: the forward computation approach and backward computation approach. Real Time Recurrent Learning (RTRL) algorithm [2] and truncated Back Propagation Through Time (truncated BPTT) 1] implement the forward and backward computation ....

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R.J. Williams, D. Zipser, "A Learning Algorithm for Continually Running Fully Recurrent Neural Networks", Neural Computation 1: 270-280, 1989.

....layer with four nodes. Recurrent neural networks are often used for modeling syntactic processing [3] Second order networks are suited for processing languages generated by FSMs [4] Learning is carried out by the weight update rule for recurrent networks developed by Williams and Zipser ([7]) extended to second order connections ( 4] where necessary. The learning rate and the momentum are 0.2 and 0.8, respectively. High and low thresholds are initialized to 0.20 and 0.17 respectively and are adapted after the network have processed the test sentences as follows. The high threshold ....

Williams, R. J. and Zipser, D. (1989) A learning algorithm for continually running fully recurrent neural networks, Neural Computation, 1 (2), 270.

....of neural network models [62] the xed width limitation seems especially problematic. The second problem has been addressed by a host of connectionists who have over the past fteen years investigated network models which support generativity through recurrent (feedback) connections [29] 50][113]. As in nite state automata [44] such connections enable a neural network to travel through an unbounded number of states, and hence to recognize and generate strings of arbitrary length. Not surprisingly, then, one focus of recurrent net research has been on the formal properties of the ....

R.J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1:270280, 1989.

....operator is encountered, the error is evaluated, its derivative is computed, and the chain rule applied to update the parameters of all contributing function approximators. This credit assignment mechanism is a version of gradient descent, similar to the real time Backpropagation algorithm [35, 112], where gradients are propagated through CES program code. Gradients are only propagated for variables whose learning flag is set (c.f. Section 3.1) 3.3 The Importance of Probabilities for Learning Probabilistic computation is a key enabling factor for the learning mechanism in CES. ....

R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1(2):270--280, 1989.

....in a sequence given the previous context [8] 17] 18] At the beginning of each training epoch the network is re set with the same initial state . The initial state is randomly chosen prior to the training session. Recurrent networks were trained with both real time recurrent learning (RTRL) [26] [3] and extended Kalman lter (EKF) 27] 28] methodologies. A. Neural Prediction Machines After training RNNs on symbolic sequences, the main e ort is often concentrated on analyzing the resulting activation patterns in the recurrent layer R . We make an explicit use of the induced ....

....of variable memory depth are necessary. Recursive structures, however, cannot in principle be grasped by nite memory models and trained RNNs should be able to outperform their initial nite memory predictive capabilities. A. RNN training We trained RNNs using Real Time Recurrent Learning (RTRL) [26] and Extended Kalman Filtering (EKF) 27] 28] Unlike RTRL, EKF does not update all RNN weights with the same learning rate. The Kalman gain matrix adjusts the learning rate individually for each RNN weight parameter. Although compared with RTRL, EKF usually converges in a much smaller number of ....

R.J. Williams and D. Zipser, \A learning algorithm for continually running fully recurrent neural networks," Neural Computation, vol. 1, no. 2, pp. 270-280, 1989.

....Encoding of prior knowledge in feed forward networks (Knowledge Based Neural Networks) 8] has been predominantly done using Horn clauses. In recurrent neural networks, prior knowledge in the form of DFAs has been encoded[9] A network is then trained using either real time recurrent learning (RTRL)[7] or back propagation trough time (BPTT) 10] The advantages to using prior knowledge are thus as follows: 1) The learning performance may lead to a faster convergence to a solution, 2) networks that are trained with hints may generalize better on future unseen examples (3) revision of current ....

Williams, R., Zipser, D.: A learning algorithm for continually running fully recurrent neural networks. Neural Computation 1 (1989) 270-280

....results are presented. 2. Conventional Learning Algorithm Two typical learning algorithms for the recurrent neural network are proposed One is BPTT (Back Propagation Through Time) 1] etc. for discrete time, 2] etc. for continuous time) and the other is RTRL (Real Time Recurrent Learning) [3] etc. for discrete time, 4] etc. for continuous time) In BPTT, it is necessary to make the error propagate to the past. This means that the past states of the neural network have to be stored. If the propagation is truncatedat T time step, that is called truncated BPTT(T) the neural network ....

Williams, R. J. and Zipser, D., "A learning algorithm for continually running fully recurrent neural networks", Neural Computation, Vol. 1, pp.270-280 (1989)

....[10] have been executed with fully satisfactory results. III. TIE APPLICATION FOR TRAINING NEtreAL NETS We consider two paradigmaUc systems in the area of neural networks: the MulU Layer Perceptron (MLP , see the applications considered in Sections IV A IV B, and the recurrent neural network of [43], see Section IV C. The notation for the MLP system an the tranformaUon into a combinatorial opUmizaUon task are described in this secUon, the feedback system considered will be illustrated in Section IV C. Input units of an MLP are denoted by h, hidden units by Hi (we consider a single hidden ....

R.J. Williams and D. Zipser, "A Learning Algorithm for Contin- ually Running Fully Recurrent Neural Networks," Neural Computation, vol.1 , pp. 270 280, 1989.

....lter, whose parameters are being estimated by the weight lter, has a recurrent architecture, i.e. x k is a function of x k 1 , and both are functions of w. Thus, the linearization must be computed using recurrent derivatives with a routine similar to real time recurrent learning (RTRL) [46]. Taking the derivative of the signal Note that a linearization is also required for the state EKF, but this derivative, F( x k 1 ; w , can be computed with a simple technique (such as backpropagation) because w k is not itself a function of x k 1 . Initialize with: x 0 = ....

R. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1:270-80, 1989.

....reward, if this delay is bounded above by a known upper bound N. In [20] and [56] look ahead planning based on neural networks is successfully applied to real time control of a robot arm. For example, in [56] the task is to touch a rolling ball with a robot arm. Recurrent neural networks [10, 15, 61] are trained to predict the robot arm behavior as well as the movement of the ball, and look ahead planning with N = 5 allowed for touching the ball in real time in about 70 of the cases. However, planning with larger horizons suffered significantly from local minima due to gradient descent, as ....

R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1(2):270 280, 1989.

....abilities in theory exceed those of FFNs by far. Hitherto little work has been done, however, on this topic [1, 2] One of the reasons for the conventional focus on FFNs may be the relative maturity of this architecture, and the algorithms used to train it. Compared to FFNs, traditional RNNs [3 5] are notoriously difficult to train, especially when the interval between relevant events in the input sequence exceeds about 10 time steps [6 8] Recent progress in RNN research, however, has overcome some of these problems [8, 9] and may pave the way for a fresh look at unsupervised sequence ....

R. J. Williams and D. Zipser, "A learning algorithm for continually running fully recurrent networks," Tech. Rep. ICS 8805, Univ. of California, San Diego, 1988.

.... have been explored by numerous authors [3] 8] 14] 16] 18] 37] 60] 64] 66] 67] 82] 87] 102] There has been considerable work on extending the computational capabilities of recurrent neural network models by providing some form of external memory in the form of a tape [103] or a stack [5] 11] 29] 55] 74] 84] 90] 93] 105] To the best of our knowledge, to date, most of the research on neural architectures for syntax analysis has focused on the investigation of neural networks that are designed to learn to parse particular classes of syntactic ....

R. J. Williams and D. Zipser, "A learning algorithm for continually running fully recurrent neural networks," Neural Comput., vol. 1, pp. 270--280, 1989.

....and symbolic data. We will deal with this third setting and consider the principal capability of recurrent networks to approximate an unknown function. This capability together with the principle learnability of recurrent networks established e.g. in [3] and the existence of learning algorithm [14, 5] will justify the use of recurrent networks in practical applications. Now we will proceed as follows: After defining recurrent networks formally we will proof their approximation capability in the L 1 norm, i.e. in probability. It will be shown that sequences with entries from a finite alphabet ....

R. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1, 1989.

....or hybrid data [4] Here we deal with the third setting and consider the capability of recurrent networks of approximating an unknown function in principle. This capability together with the learnability of recurrent networks established for example in [6] and the existence of learning algorithms [21, 8] justify the use of recurrent networks in practical applications. Now we proceed as follows: After defining recurrent networks formally we proof their capability of approximating any measurable mapping in probability. If only a finite set of data is dealt with, explicit bounds on the number of ....

R. Williams and D. Zipser, A learning algorithm for continually running fully recurrent neural networks, Neural Computation 1 (1989) 270--280. 17

....function is the standard logistic sigmoid (u) 1= 1 e u ) The output nodes are then updated as o i (t) Q ij h j (t) T where Q ij and T i are weights and thresholds, respectively. We train the network to predict the next symbol using full real time recurrent learning [20] with a momentum term. We use sum of squared errors measure SSE = i=1 (o i (t) x i (t 1) 4) Assuming the length of the training sequence is N . Also note that the code x(t 1) of the next symbol s t 1 forms the desired output at time t. as well as the relative entropy error ....

R.J. Williams and D. Zipser, \A learning algorithm for continually running fully recurrent neural networks," Neural Computation, vol. 1, no. 2, pp. 270-280, 1989. 27

....are diverse approaches like Hidden Markov Models and Finite States Machines, which are able to do the modeling of time series. The Neural Network (NN) approach is a natural one due to its inherent capability of extracting the structure present in a data set and its universal approximating property [4]. In this work, we are interested in extracting temporal structure from data temporal series. Many researches have dedicated efforts to create neural network models capable of analyzing these kinds of problems. Structures like the Time Delay Neural Networks (TDNN) use the spatialization of the ....

....states and or outputs. Layered approaches like Elman [7] and Jordan structures have been 1 is an Assistant Professor at the Federal University of Paran a DELT CIEL Brazil proved to be as efficient and powerful as fully connected networks like Hopfield [3] and William and Zipser structures [4], 12] Layered networks have simpler training and utilization stages, without the risk of instability that is present in the fully connected networks. This work presents a new neural network structure, called T CombNET, which is able to do a temporal analysis and fine classification of ....

R. J. Williams and D. Zipser, "A Learning Algorithm for Continually Running Fully Recurrent Neural Networks", ICS Report 8805, Oct. 1988.

....shortcomings, still represent a significant success for artificial intelligence. Perceptrons, which can be seen as simple neural nets, were originally described by Minsky and Papert [MP69] in terms of gradient descent algorithms. Gradient descent methods play a huge role in training algorithms [WZ89], MMR97] AGPC90] Logic programming enjoys an advantage over neural networks by being able to equip the object corresponding to the neural net, namely the program, with a declarative semantics. The lack of declarative semantics for neural nets is sometimes enthusiastically regarded as some ....

Williams, R.J. & Zipser, D. "A Learning Algorithm for Continually Running Fully Recurrent Neural Networks", Neural Computation, 1:270-280, 1989.

....abilities in theory exceed those of FFNs by far. Hitherto little work has been done, however, on this topic [1, 2] One of the reasons for the conventional focus on FFNs may be the relative maturity of this architecture, and the algorithms used to train it. Compared to FFNs, traditional RNNs [3 5] are notoriously dicult to train, especially when the interval between relevant events in the input sequence exceeds about 10 time steps [6 8] Recent progress in RNN research, however, has overcome some of these problems [8, 9] and may pave the way for a fresh look at unsupervised sequence ....

R. J. Williams and D. Zipser, \A learning algorithm for continually running fully recurrent networks," Tech. Rep. ICS 8805, Univ. of California, San Diego, 1988.

....) and the current and previous estimates of the blood glucose. To be specific, the second order 3 2 Note that since the blood glucose prediction is fed back as an input to the system, a recurrent learning rule has to be used for adaptation. We applied the real time recurrent learning rule (RTRL) [20] using a quadratic error function, see Appendix A. 3 The second order RNN model outperformed higher order RNN models in the experiments. May 6, 1999 DRAFT NEURAL NETWORK MODELS FOR THE BLOOD GLUCOSE METABOLISM OF A DIABETIC nonlinear neural network model is y t = y t Gamma1 fw (y t Gamma1 ....

Williams R. J. and Zipser D., "A learning algorithm for continually running fully recurrent neural networks," Neural Computation, vol. 1, pp. 270--280, 1989.

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R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1:270-280, 1989.

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R. J. Williams and D. Zipser, "A learning algorithm for continually running fully recurrent neural networks," Neural Computation, vol. 1, pp. 270--280, 1989.

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Williams, R.J. & D. Zipser, 1989. A learning algorithm for continually running fully recurrent neural networks, Neural Computation 1(2), 270.

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Williams, R., & Zipser, D. (1989). A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1, 270--280.

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R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1(2):270--280, 1989.

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R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Technical Report ICS Report 8805, Institute for Cognitive Science, University of California, San Diego, CA, 1988.

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R. J. Williams and D. Zipser, A learning algorithm for continually running fully recurrent neural networks, Neural Computation, 1(2), pp. 270-280, 1989.

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R. J. Williams, D. Zipser, A Learning Algorithm for Continually Running Fully Recurrent Networks. ICS Report 8805, 1988

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R. J. Williams and D. Zipser, "A learning algorithm for continually running fully recurrent neural networks," Neural Comput., vol. 1, pp. 270--280, 1989.

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Williams, R. J. and Zipser, D. A Learning Algorithm for Continually Running Fully Recurrent Neural Networks. Neural Computation, vol. 1 (1989), pp. 270--280. Also appeared as: Technical Report ICS Report 8805, Institute for Cognitive Science, University of California, San Diego, CA, 1988.

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R. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Report 8805, Institute for Cognitive Science, University of California, San Diego, La Jolla, CA, 1988.

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R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent networks. Technical Report ICS 8805, Univ. of Cal., La Jolla, 1988.

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R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1(2):270--280, 1989. 17

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R. Williams and D. Zipser, \A learning algorithm for continually running fully recurrent neural networks", Neural Computation, 1:270-280, 1989.

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R.J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1:270--280, 1989.

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R. J. Williams and D. Zipser, "A learning algorithm for continually running fully recurrent neural networks," Neural Computation, vol. 1, pp. pp.270-- 1989.

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R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1:270--280, 1989.

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R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1(2):270--280, 1989.

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R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1(2):270--280, 1989.

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R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1:270--280, 1989. 3.1

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Williams R.J. and Zipser D., "A learning algorithm for continually run- ning fully recurrent networks," Neural Coraputation, Vol. 1 (1989), 270- 280. 14

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R. J. Williams and D. Zipser. A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1(2):270--280, 1989.

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