Jordan, M. I. (1990). Serial order: A parallel distributed processing approach. Tech. Rep., MIT, Cambridge, MA.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....making them more difficult to deal with. For the recognition of those single modalities, only few systems make use of connectionist models [3,7,17,27] for they are not considered well suited to completely address the problem of time alignment and segmentation. However, some neural architecture [10,14,29] has been put forward and successfully exploited to partially solve problems involving the generation, learning or recognition of sequence of patterns. Recently, several research groups have more thoroughly addressed the issue of combining verbal and non verbal behavior. In this context, most of ....

....in space, roughly passing through the base and the tip of the index finger. This line does not usually lie in the target plane, but may intersect it at some point. We recognize pointing gestures by means of a hybrid partial recurrent artificial neural network (RNN) consisting of a Jordan network [14] and a static network with buffered input to handle the temporal structure of the movement underlying the gesture. Concurrently, several speech commands can be issued asynchronously. They are recognized using Dragon 4.0, a commercial speech engine. Speech along with gestures is then used to put ....

[Article contains additional citation context not shown here]

Jordan M., Serial Order: A Parallel Distributed Processing Approach Advances in Connectionist Theory, Lawrence Erlbaum, 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 ....

Michael I. Jordan. Serial order: A parallel distributed processing approach. Technical Report ICS Report 8604, Institute for Cognitive Science, University of California, 1986.

....JIDM, thus better results are expected if the global maximum can be found. Evaluating the performance of the proposed structure, comparisons with classical network structures were performed. The T CombNET structure designed using Approach 2 is compared with Kohonen s LVQ1 [5] Elman and Jordan [3] RNNs trained with the standard Backpropagation algorithm, single 3 layer feedforward backpropagation trained Multi Layer Perceptron (MLP) and original CombNET II structures. The LVQ1, MLP and CombNET II are not recurrent neural networks, so they needed a pre processing stage by the previously ....

Jordan, M. I.: Serial order: A parallel distributed processing approach. Technical Report Nr. 8604, Institute for Cognitive Science, University of California, San Diego (1986)

....Whereas all of the early models were hand wired networks with local representations, some recent production models make use of distributed representations acquired from learning algorithms. In addition, recent architectures allow for the production of true sequences (Eikmeyer Schade, 1991; Jordan, 1986; Gupta, 1996; Hartley Houghton, 1996; Houghton, 1990; MacKay, 1987) In this article, we examine some connectionist models of production. Our aim is not to review the field, but rather to concentrate on our own recent efforts in two areas, lexical access and grammatical encoding. Lexical ....

....we present, the phonological error model, confronts these limitations. The Phonological Error Model The phonological error model (Dell, Juliano, Govindjee, 1993) is an attempt to apply PDP principles specifically to phonological encoding. The model uses a simple recurrent network (Elman, 1990; Jordan, 1986) to map from a static representation of a word to a sequence of phonological features. Figure 3 shows the architecture. The input layer represented the word to be spoken. In different versions of the model, the input was either a random bit vector (which can be viewed as either a lemma or a ....

Jordan, M. I. (1986). Serial order: A parallel distributed processing approach (ICS Technical Report 8604). University of California at San Diego, La Jolla, CA.

....are presented at the advice layer, and this input activity is used to direct the settling of the attractor network at the plan layer. The configuration of activity levels at the plan is then used to modulate the behavior of a task oriented network, much like the plan layer of a Jordan network [ Jordan, 1986 ] The connection weights may be trained using a standard inductive learning technique, such as backpropagation, with an error signal provided only on actual task performance. Such inductive learning may be used both to learn the instructional language and to shape task execution via experience. ....

Michael I. Jordan. Serial order: A parallel distributed processing approach. Technical report, Institute for Cognitive Science, UCSD, 1986.

....is used, which can use a target at each time step (e.g [10, 2] it is not obvious how to provide these targets. For classification purpose often there is only one target for the whole time series. Thus, this single target is used for all time steps or it is only applied to some time steps [7]. In the former case for some time steps (e.g. the first ones) this target is much too strong, which results in inappropriate weight updates. In the later case one needs a strategy to find out which time steps should be given a target. In many cases finding such a strategy is not possible as one ....

....network to recognize the whole series after processing the first time step. Using the overall target in the first time step seems to be a too strong teacher for the network. To overcome this problem one could provide constraints for the output units instead of actual targets, like it is done in [7]. But it is often hard to find such constraints. Thus, an automatic procedure for creating the targets can support the learning. b) For high classification rates the output vector o does not have to reach the value of either t 1 or t 2 . It only has to be in the proper half of the unit square. ....

M. I. Jordan. Serial order: A parallel distributed processing approach. Technical report, Institute for Cognitive Science, University of California, 1986.

....is used, which can use a target at each time step (e.g [10, 1] it is not obvious how to provide these targets. For classi cation purpose often there is only one target for the whole time series. Thus, this single target is used for all time steps or it is only applied to some time steps [7]. In the former case for some time steps (e.g. the rst ones) this target is much too strong, which results in inappropriate weight updates. In the later case one needs a strategy to nd out which time steps should be given a target. In many cases nding such a strategy is not possible as one does ....

....network to recognize the whole series after processing the rst time step, so using the overall target in the rst time step seems to be a too strong teacher for the network. To overcome this problem one could provide constraints for the output units instead of actual targets like it is done in [7]. But it is often hard to nd such constraints. Thus, an automatic procedure for creating the targets could support the learning. b) For high classi cation rates the output vector o does not have to reach the value of either t 1 or t 2 . It only has to be in the proper half of the unit square. ....

M. I. Jordan, \Serial order: A parallel distributed processing approach," Tech. rep., Institute for Cognitive Science, University of California, 1986.

....of the proposed way of learning is provided in Section 5. Finally, Section 6 concludes the paper. 2. Motivation As already pointed out, the choice of the actual values of the targets is an important part of the learning process. Although some techniques and heuristics for choosing targets exist [3, 11, 6, 13], a more general approach addressing the problem is desired. The class information should only be used implicitly during learning, which means that the class information does not have to be encoded into some numerical values, the targets, at all. The class information should only be used during ....

M. I. Jordan. Serial order: A parallel distributed processing approach. Technical report, Institute for Cognitive Science, University of California, 1986.

....a target is needed. For example in the first time step one cannot expect the network to recognize the whole series, so a target in the first step seems too hard for the network. To overcome this problem one could provide constraints for the output units instead of actual targets like it is done in [5]. But it is often hard to find such constraints. So, an automatic procedure for creating the targets could support the learning. b) It is easy to see that for a high classification rate the output vector o does not have to reach the value of either t 1 or t 2 . It only has to be in the proper ....

M. I. Jordan. Serial order: A parallel distributed processing approach. Technical report, Institute for Cognitive Science, University of California, 1986.

....that make a robot arm to follow a desired trajectory. In other cases one may be interested in modeling the dynamic behavior of a plant and an adaptive network may be trained to emulate the input output temporal response. As a last example a recurrent network may be forced to act as an oscillator [17]. Architectures and training strategies may be substantially different depending on the particular applicative field. A typical difficulty that arises in motor control related tasks is that one wants to use the output of the network as control actions such as forces or torques to be applied to ....

....be generated by dynamic programming. They go bejond the scope of this paper and the reader may refer to [19] 20] 21] 22] A recurrent network can generate trajectories also without applying an external input. In such cases the network behaves like an autonomous oscillator. The Jordan net [17] is a first example of a network with feedback connections trained to oscillate on a periodic attractor. In that case feedback weights were fixed 7 and feedforward weights were trained by backpropagation. Of course the approach is not optimal and a gradient can be computed also for the feedback ....

M. Jordan, "Serial order: a parallel distributed processing approach," Tech. Rep. 8604, ICS (Institute for Cognitive Science, University of California), 1986.

.... grammar (Hanson and Kegl 1987) However, for the purpose of learning regular string grammars it is more natural to use recurrent networks (which are essentially trainable deterministic finite automata) Various architectures have been used: simple first order recurrent networks (Elman 1990, Jordan 1988); more complex first order networks (Williams and Zipser 1989, Fahlman 1991) and second order recurrent networks (Giles et al. 1992) Elman (1992) has also applied recurrent networks to context free grammars and found that they can represent up to about three levels of recursive embedding; other ....

Jordan, M.I., 1988, Serial Order: A Parallel Distributed Processing Approach.

....presented at the advice layer, and this input activity is used to direct the settling of the attractor network at the plan layer. The stable configuration of activity levels at the plan is then used to modulate the behavior of a task oriented network, much like the plan layer of a Jordan network (Jordan, 1986). The connection weights may be trained using a standard inductive learning technique, such as backpropagation, with an error signal provided only on actual task performance. This allows the language of instruction to be learned in the service of a task (St. John, 1992) Such inductive learning ....

Jordan, M. I. (1986). Serial order: A parallel distributed processing approach. Technical report, Institute for Cognitive Science, UCSD.

....Some architectures of recurrent networks. a) backpropagation through time; b) Jordan net; c) Elman net. 11 BPTT is an efficient algorithm, but it is inherently discrete. We discuss a continuous time analog of BPTT (Pearlmutter) in section II.B.6. II.B. 3 Jordan and Elman nets Jordan style [Jor86] and Elman style [Elm90] networks are basically feedforward nets with their output layer and hidden layer, resp. recycled back as input (Figure II.1) These networks provide limited form of recurrence without a need for new learning algorithms: the recurrent links are not trained, but have a ....

M.I. Jordan. Serial order: a parallel distributed processing approach. Technical Report Technical Report 8604, Institute for Cognitive Science, University of California, San Diego, La Jolla, CA, 1986.

....the corner and then initiate a free from corner routine e.g. by backing up or making a U turn until it finds itself in free space again. Various neural network paradigms incorporate memory themselves by using recurrent links that feed back information. For instance in the Jordan network (Jordan, 1986) output information is fed back to state units that are presented together with the new input. The original Jordan network was created to generate sequences of outputs. In the robot domain it could be used for the generation of trajectories. In Elman s simple recurrent network (SRN, Elman, 1990) ....

Jordan, M. (1986). Serial order: A parallel distributed processing approach. Technical Report 8604, Institute for Cognitive Science.

....net s performance regularly during training. Just as phonemic context is often taken into account in rule sets, it can also be used for classification in neural net al..gorithms. In this case, recurrent networks have to be used. There are two main flavours of recurrent networks: Jordan networks ((Jordan 1988), cited after (Zell 1993) and Elman networks (Elman 1990) In both approaches, the previous state of a layer is fed back into the input layer. With Jordan networks, this is the output layer, with Elman networks, the hidden layer. A sample Jordan network is shown in Fig. 6.7. Recurrent nets have ....

Jordan, M. (1988), Serial order: A parallel distributed processing approach, in J. Elman & D. Rumelhart, eds, `Advances in Connectionist Theory: Speech', Erlbaum, Hillsdale, NJ.

....an FSA in a neural network are (1) representing the state of the automaton, and (2) capturing the notion of scanning an input string. FSKBANN addresses both of these issues. 6 Maintaining Past State FSKBANN uses a neural network structure similar to the networks introduced in both [Elman90, Jordan86] to represent state. The network takes as input the previous state and the input values, and determines the next state. It uses this new state as the previous state input in the next step. This copying back process acts as if there were recurrent links, with fixed weights, from the output units ....

....patterns occurs in work aimed at solving natural language problems [Cleeremans89, Elman90, Mozer91, Porat91, Servan Schreiber91, St. John90] Each of these approaches provides a mechanism for preserving one or more of the past activations of some units for the next input sequence. Jordan [Jordan86] and Elman [Elman90] introduced the particular recurrent network topology we use in FSKBANN. Their networks have a set of hidden units called context units 27 which preserve the state of the network. At each time step the previous value of the context units are copied back as input to the ....

M. Jordan, "Serial order: A parallel distributed processing approach," Technical Report 8604, University of California, Institute for Cognitive Science, San Diego, 1986.

....of input units map representations to hidden units which in turn map representations to output units. Since no specific assumptions are made regarding the nature of the order pair representation, three layered feedforward networks are weakly systematic of inference. Jordan s recurrent network Jordan s (1990) recurrent network (see Figure 9(a) differs from the simple recurrent network in that context is copied from the output unit activations rather than the hidden unit activations of the previous time step. Like the simple recurrent network, this network requires two hidden units to discriminate ....

Jordan, M. I. (1990). Serial order: A parallel distributed processing approach. Tech. Rep., MIT, Cambridge, MA.

....the future. Furthermore, encoding may also serve as an alternative way to handle overlapping sequences. Folding requires a set of separated SDMs, whereas an architecture independent representation of sequences of arbitrary length is desirable. Encoding of system history like in Jordan nets (cf. [6]) combines the sufficiency of one single unfolded SDM with an intuitively more plausible handling of overlapping sequences: long overlaps are harder to discriminate than short ones. Experiments on encoding are currently beeing prepared. 15 This simulator is used in the WINA project ....

M. Jordan. Serial Order: A Parallel Distributed Processing Approach. ICS-UCSD, Report No. 8604, 1986.

....error sum over all episodes is equal to the sum of the corresponding gradients, for convenience we renounce on indices for different episodes. In general the task above requires to memorize past events. Previous approaches to solving this problem employed either gradient descent in recurrent nets [1] [3] 11] 2] 12] adaptive critic like methods [5] 6] or (more recently) adaptive fast weights [8] All these approaches have severe limitations when it comes to long time lags between relevant input events. This can be seen e.g. with examples from grammar learning: With a given grammar G, ....

M. I. Jordan. Serial order: A parallel distributed processing approach. Technical Report ICS Report 8604, Institute for Cognitive Science, University of California, San Diego, 1986.

.... [26] 28] 17] and the recent fast weight algorithm [19] All these approaches are non local for a restricted class of recurrent networks, however, there is a local gradient based algorithm [6] Local (but much weaker) approximations of the general supervised algorithms have been proposed (e.g. [3][1] Local approaches to reinforcement learning in recurrent networks [25] 15] 5] unfortunately are not very practicable in realistic applications. Although non local gradient based recurrent nets are general and can sometimes learn to perform quite complicated algorithms, they tend to fail when ....

M. I. Jordan. Serial order: A parallel distributed processing approach. Technical Report ICS Report 8604, Institute for Cognitive Science, University of California, San Diego, 1986.

....and Warren 1992, Adamson and Damper 1996) neural networks can be designed to posit several candidate possibilities for a given input. For example, Deshmukh et al. 1996) describe a neural network implementation designed to provide n best pronunciations for proper nouns. Hare (1990) used a Jordan (1986) style neural network to investigate Hungarian vowel harmony, in particular, transparent vowels which neither display harmony themselves, nor block the spread of the harmonizing feature to other vowels. Since the same vowels can be harmonic in some contexts and transparent to harmony in others, ....

Jordan, M. 1986. Serial order: a parallel distributed processing approach. ICS Report No. 8604. UC San Diego.

....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 ....

Michael I. Jordan. Serial order: A parallel distributed processing approach. Technical Report ICS Report 8604, Institute for Cognitive Science, University of California, 1986.

....or neurocomputing. The discovery (or re discovery) of Backpropagation learning for Multi layer Perceptrons by Rumelhart et al. in 1986 [36] led the way for a raft of new learning methods; mainly architectural variations of the feedforward networks for which Backpropagation was designed, e.g. [12, 20, 32]. The problem with supervised learning for robotics is that a precise teaching signal is required to form the error terms. It is a data fitting or function approximation method in which the error signal is derived from a comparison of the output vector to an ideal vector (teaching signal) It is a ....

M.I. Jordan. Serial order: A parallel distributed processing approach. Technical Report 8604, Institute for Cognitive Science, 1986.

....neural networks. In addition, an empirical study using the MONK s problems and a robot arm kinematics problem as a testbed is described in order to characterize how the proposed rule extraction scheme works in practice. While it is clear that these mechanism do not estab 10 See for example [Jordan, 1986] , Elman, 1988] and [Williams and Zipser, 1989] for literature on recurrent networks Extracting Symbolic Knowledge from Artificial Neural Networks 43 lish a final solution to the problem of extracting rules, we are confident that rule extraction via VI Analysis can shed light into a variety ....

Michael I. Jordan. Serial order: A parallel distributed processing approach. Technical Report ICS Report 8604, Institute for Cognitive Science, University of California, 1986.

....scalability inherent in mechanisms based on backpropagation can be overcome, this view offers a way forward to a kind of system that embodies both rules and sub symbolic representations in a principled way. 2 Recurrent Networks and Finite State Disambiguators The recurrent networks proposed by Jordan (1989) and Elman (1990) use an auxiliary bank of state or context units to store information about the previous state of an otherwise standard three level feed forward network using backpropagation to adjust a hidden layer of units. The recurrence consists of copying either the output units or the ....

Jordan, Michael, 1989. "Serial Order: a Parallel Distributed Processing Approach." In Jeffrey Elman and David Rumelhart (eds.), Advances in Connectionist Theory: Speech, Hillsdale, NJ: Erlbaum. xxx--xxx.

....important when one wants to randomize learning by always choosing an arbitrary window from the time series, instead of stepping thorugh the series sequentially. The network in figure 4 can be considered a special case of the recurrent network type in figure 5, usually called Jordan network after [26]. It consists of a multilayer perceptron with one hidden layer and a feedback loop from the output layer to an additional input (or context) layer. In addition, 26] introduced self recurrent loops on each unit in the context layer, i.e. each unit in the context layer is connected with itself, ....

....network in figure 4 can be considered a special case of the recurrent network type in figure 5, usually called Jordan network after [26] It consists of a multilayer perceptron with one hidden layer and a feedback loop from the output layer to an additional input (or context) layer. In addition, [26] introduced self recurrent loops on each unit in the context layer, i.e. each unit in the context layer is connected with itself, with a weight v i smaller than 1. Without such self recurrent loops, the network forms a non linear function of p past sequence elements and q past estimates: x(t) ....

Jordan M.I.: Serial Order: A Parallel Distributed Processing Approach, ICS- UCSD, Report No. 8604, 1986.

....3.4 Truncated learning equations One simple way to avoid the instability of the learning equations is to use non recurrent learning equations. Actually, learning rules in which recurrent connections are neglected in error gradient calculation have been successfully applied to sequence generation [5, 14] and sequence prediction tasks [2, 7] In the algorithm called truncated back propagation through time [26] the adjoint equation (7) is calculated only for some limited steps backward in time. Although this algorithm was developed mainly to reduce the amount of computation, it also avoids the ....

M. I. Jordan. Serial order: A parallel distributed processing approach. In J. L. Elman and D. E. Rumelhart, editors, Advances in Connectionist Theory: Speech. Erlbaum, 1989.

....with supervised learning are very popular for applications which use static representations, but time is important in many domains e.g. vision, speech and motor control. Dynamic neural networks can be constructed by adding recurrent connections to form a contextual memory for prediction in time (Jordan 1989, Elman 1990, Mozer 1993) These partially recurrent neural networks can be trained using back propagation but there may be problems with stability and very long training sequences when using dynamic representations. Instead, we use simple Time Delay (TD) in conjunction with Radial Basis Function ....

Jordan, M. (1989), Serial order: A parallel distributed processing approach, in `Advances in Connectionist Theory', Erlbaum.

....of this work must be the number of postures covered. With five, unsimilar postures, problems of overlapping classes will not occur, an issue that needs to be addressed. A method for using neural networks to recognise gestures is also mentioned. The approach uses recurrent networks, by Jordan [20], whose architectures encode the temporal information about prior network states. 2.4 Statistical Classification In statistical matching, the statistics of example feature vectors are used to derive deciders, usually called classifiers. Functionally, statistical classifiers operate in the same ....

M Jordan. Serial order: A parallel distributed processing approach. Technical Report 8604, Institute for Cognitive Science, University of California, San Diego, 1986.

....Actually, it is easy to show that a two layered network with delay elements in the feedback loop (Figure 1 (a) can approximate any dynamical system because a two layer network can approximate any map or vector field. Such multi layer recurrent networks have been used in modeling sequence learning [6] and more elaborate architectures have been considered for modeling various classes of dynamical systems [7] Note that the state of such networks is updated sequentially from the input layer to the output layer. Another approach to modeling dynamical systems is the use of fully connected ....

M. I. Jordan. Serial order: A parallel distributed processing approach. In J. L. Elman and D. E. Rumelhart, editors, Advances in Connectionist Theory: Speech. Erlbaum, 1989.

....networks have both feedforward and feedback connections. Here we consider only partially recurrent networks in which the majority of connections are feedforward and adaptable with a few selected fixed feedback connections to a set of context units. Several architectures have been suggested [2, 6, 8] which have in common this use of a set of context units to receive the feedback signals and act as memory for the recent past required in dynamic tasks. outputs inputs OUTPUT HIDDEN INPUT CONTEXT outputs inputs OUTPUT HIDDEN INPUT CONTEXT exponential memory Fig. 1: The basic Elman network ....

M. Jordan. "Serial Order: A Parallel Distributed Processing Approach". In Advances in Connectionist Theory. Erlbaum, 1989.

.... multilayer version of a AR(20) model) ffl NAR: a two layer perceptron with an input window of size 20 and 10 nonlinear hidden units with sigmoid activation functions (a general nonlinear NAR(20) autoregressive model) ffl JORDAN: a Jordan type recurrent perceptron (based on the one proposed in [ Jordan, 1986 ] with an input of size 1, a sigmoidal hidden layer of size 55, and a feedback from the output unit to an extra context layer with a self recurrent loop. ffl JORDAN2: a Jordan type recurrent perceptron with an input of size 1, two sigmoidal hidden layers of size 13 each, and a feedback from the ....

Jordan M.I.: Serial Order: A Parallel Distributed Processing Approach, ICS- UCSD, Report No. 8604, 1986.

....approach may address systematicity of representation, in the next section it is shown that they cannot address systematicity of inference. 3 Systematicity of inference Recurrent networks, used to demonstrate generalization over structured domains (e.g. the architectures of Elman [3] Jordan [10], and Pollack [14] all share a common feature. That is, they all additively combine some non linear transformation of representations at the input and context layers. It is argued that this feature prevents these architectures from demonstrating strong systematicity. The argument proceeds by ....

M I Jordan. Serial order: A parallel distributed processing approach. Technical report, MIT, Cambridge, MA, 1990.

....concepts be updated after each training instance. Few symbolic learning algorithms are able to meet both of these requirements. Sequential and temporal prediction tasks provide another type of problem for which neural networks are often more appropriate than symbolic algorithms. Recurrent networks (Jordan, 1986; Pineda, 1987) which are often applied to these problems, employ input units that represent the state of the hidden units at the previous time step. Recurrent networks use their own representations of the problem at the previous time step to generate predictions for the current time step. ....

Jordan, M. (1986). Serial order: A parallel distributed processing approach. Technical Report 8604, University of California, Institute for Cognitive Science, San Diego.

....of time delay elements to feedforward connections: One of the examples is the Time Delay Neural Networks (TDNN) 2, 3, 4] The longest time length to be dealt is limited by the longest delayed path. 3. Addition of time delay elements to feedback connections: Recurrent networks are their examples [5, 6, 7, 8]. Several learning algorithms have been proposed [9, 10, 11] This technique has an ability to deal with longer temporal sequences because of the recurrent signal flow. However, the number of connections increases as the network becomes large. In addition, the learning algorithm also tends to be ....

....neurons are interconnected. The latter one is similar to the proposed MNCF, because a complex neuron is composed of a real neuron and an imaginary neuron and they are interconnected. 3. Elman s Network: There is a context layer which is copied from a hidden layer. We did not use Jordan s network [5] because the problem is not suited to the Jordan s network. Learning algorithms for the networks (1) 3) are derived from Eq. 4) Figure 3 and Figure 4 show the learning curves, where m = 5 and n = 3 in both cases. Each line is based on average of 100 trials. It can be observed from these figures ....

Jordan, M. I.: "Serial Order: a parallel distributed processing approach", ICS Report 8604, UC San Diego (1986).

....4.5.2. Predicting the future The existence and recognition of these problems is slowly causing a change in the direction of nearterm connectionist research. There are many ongoing efforts now on more serial approaches to recognition and generation problems (Elman, 1988; Gasser Dyer, 1988; Jordan, 1986; Pollack, 1987) which may help overcome the problem of massive duplication in dealing with time. There is also research in progress along the lines of Hinton s (unpublished) proposal for reduced descriptions as a way out of the superposition concatenation difficulty for distributed ....

Jordan, M. I. (1986). Serial Order: A Parallel Distributed Processing Approach. ICS report 8608, La Jolla: Institute for Cognitive Science, UCSD.

No context found.

Jordan, M. I. (1990). Serial order: A parallel distributed processing approach. Tech. Rep., MIT, Cambridge, MA.

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M. I. Jordan 1989, "Serial order: A parallel, distributed processing approach," in Advances in Connectionist Theory: Speech,eds.J.L.ElmanandD. E. Rumelhart (Erlbaum, Hillsdale).

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M. I. Jordan. Serial order: A parallel distributed processing approach. Technical Report ICS Report 8604, Institute for Cognitive Science, University of California, 1986.

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M. I. Jordan, Serial Order: A Parallel Distributed Processing Approach. Technical Report ICS Report 8604, Institute for Cognitive Science, University of California, B1986

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M. Jordan. Serial Order: A Parallel Distributed Processing Approach. In J. Elman and D. Rumelhart, editors, Advances in Connectionist Theory, San Diego, La Jolla, CA, 1989. Institute for Cognitive Science, University of California.

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M. I. Jordan. Serial order: a parallel distributed processing approach. Technical Report 86044, Institute for Cognitive Science, University of California San Diego, 1986.

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Jordan, M. I. [1986], Serial order: A parallel distributed processing approach, ICS Report 8604, Institute for Cognitive Science, University of California, San Diego.

No context found.

M. I. Jordan 1989, "Serial order: A parallel, distributed processing approach," in Advances in Connectionist Theory: Speech,eds.J.L.ElmanandD. E. Rumelhart (Erlbaum, Hillsdale).

No context found.

Michael Jordan. Serial order: a parallel distributed processing approach. Technical Report ICS Report No. 8604, Institute for Cognitive Science; University of California at San Diego, 1986.

No context found.

Jordan, M. (1986). Serial Order: a Parallel Distributed Processing Approach. ICS Report No. 8604, Institute for Cognitive Science, University of California at San Diego.

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Jordan, M. I. (1986). Serial order: A parallel distributed processing approach (ICS Report 8604). La Jolla: University of California, San Diego, Institute for Cognitive Science.

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Jordan, M. I. (1986). Serial order: A parallel distributed processing approach. Technical Report ICS Report 8604, Institute for Cognitive Science, University of California, San Diego.

No context found.

M. Jordan, "Serial Order: A Parallel Distributed Processing Approach," University of California at San Diego ICS Report 8604, 1986.

No context found.

Jordan, M. I. [1986], Serial order: A parallel distributed processing approach, ICS Report 8604, Institute for Cognitive Science, University of California, San Diego.

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