Pollack, J.B. (1991) The induction of dynamical recognizers. Machine  Home/Search   Document Details and Download   Summary   Related Articles   Check

....echelons: the weights can be completely replaced with a new set, the weights can be multiplied with a set of values, or finally, a set of values can be added to the weights. A subsuming approach would (temporarily) replace the weights with new values, thereby completely overriding the old ones [5][6] That means that no information is inherited into the new mapping. That is, the new values not only need to reflect the new behavior producing values but also all the old, existing, values in the mapping that might be needed for the correct functioning of the system. This is a wasteful ....

J.B. Pollack, "The induction of dynamical recognizers," Machine Learning, Vol. 7, pp. 227-252, 1991

....the mechanism. A general mechanism may extrapolate beyond the limits of the training set. In Long Short Term Memory (LSTM) networks and some Simple Recurrent Networks (SRNs; 3] simple linear counters are induced [4] for a n b n . In some SRNs and Sequential Cascaded Networks (SCNs; [8]) oscillating or spiralling dynamics is induced [1] As pointed out by Hadley [5] and Marcus [6] generalization in humans sometimes goes beyond the regularities inferred with recurrent networks. As an example, if you 1 Don t care markers can reduce this number. have heard Smith fleedled ....

J. B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:227, 1991.

....to tackle this problem. This approach to the induction of asynchronous translators is discussed in connection with other approaches. 1 Introduction In recent years, there has been a lot of interest in training discrete time recurrent neural networks (DTRNN) to behave as finite state machines [7, 9, 13, 17, 18, 20]. This behavior has recently been formalized [3] in response to hard criticisms [12] So far, all work has focused on training DTRNN to behave as finite state acceptors deterministic finite automata or, more generally, as very simple translators such as Mealy machines, or, equivalently, as ....

....a a a a a a S S S ( Delta Delta Delta Delta Delta Delta Delta Delta Delta j j j j Delta Figure 1: The architecture of the second order DTRNN. lines. We build around a second order, single layer network [17, 9, 20, 2, 7]. The network will have N K input units: N for the previous state, and K = j Sigmaj 1 units for one hot (unary) input of symbols from alphabet Sigma plus one unit for a special symbol representing the empty string (i.e. no input) There will be N M 2 output units: N for the next state ....

Pollack, J.B. (1991) "The induction of dynamical recognizers ", Machine Learning 7, 227--252.

....the mechanism. A general mechanism may extrapolate beyond the limits of the training set. In Long Short Term Memory (LSTM) networks and some Simple Recurrent Networks (SRNs; 3] simple linear counters are induced [4] for a n b n . In some SRNs and Sequential Cascaded Networks (SCNs; [8]) oscillating or spiralling dynamics is induced [1] As pointed out by Hadley [5] and Marcus [6] generalization in humans sometime goes beyond the regularities inferred with recurrent networks. As an example, if you 1 Don t care markers can reduce this number. have heard Smith fleedled ....

J. B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:227, 1991.

.... dilemma models (Lindgren and Nordahl 1994; Hofbauer and Sigmund 1998) The game itself is also not changed over time (see, e.g. Akiyama and Kaneko 2000) for a dynamically changing game) Our model is similar to a model introduced by Taiji and Ikegami (1999) but they use dynamical recognizers (Pollack 1991) instead of genetic programming. We built the model to tackle the following questions: 1. Evaluation of technology Does GP provide a reasonable technique to model the ability of generalization of an actor What kind of beneficial properties posses GP How should the parameter be chosen How ....

Pollack, J. B. (1991). The induction of dynamical recognizers. Machine Learning 7, 227--252.

....makes it highly unlikely that membership in Lin(Z) is P complete, since then we would have NC 2 = P. 30 9 Relationships with other models of analog computation. There are several differences between Blum, Shub and Smale s (BSS) analog machines [2] Siegelmann and Sontag s (SS) neural networks [33], and dynamical recognizers. First, BSS machines can branch on polynomial inequalities during the course of the computation. Except for NLin, our recognizers have completely continuous dynamics except for the final measurement of H yes . SS machines are defined with piecewise linear maps. ....

.... k ) BP(PR ) Blum, Shub and Smale [2] NPiecePoly(R)TIME(O(n k ) SPACE(O(n k ) BP(NDPR ) Cucker and Matamala [8] PieceLin(R)TIME(O(n k ) SPACE(O(n k ) BP(P lin ) Meer [24] and Koiran [19] PieceLin(R)TIME(O(n k ) SPACE(O(1) NET Gamma P (Siegelmann and Sontag [33]) PiecePoly k (Z)TIME(n)SPACE(O(1) PiecePoly k (Z) dynamical recognizers) and similarly for other complexity classes. The last two lines of this table 31 contrast with the discrete case, since Turing machines with constant space can only recognize regular languages. Then there are a ....

J. Pollack, "The Induction of Dynamical Recognizers." Machine Learning 7 (1991) 227-252.

.... for psychology, it should be clear what its capabilities are when dealing with formal languages which lie at the heart of symbol oriented models [8] We will consider a type of recurrent neural network that has initially been explored by Jordan [4] and more recently by Elman [1] and Pollack [6]. More specifically, we use a second order recurrent network [2, 5] simplified to having only one parameter, and we show by simulation that its nodes can represent the input to the network in a way that captures the essential structure of our context sensitive language. When RNs are applied to ....

J.B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:227--252, 1991.

.... between first order feedback, i.e. the re use of previous neural activation values as extra inputs (e.g. in Elman s (1990) Simple Recurrent Network) and higher order feedback, i.e. the dynamical adaptation modulation of the connection weights embodying the input output mapping (e.g. in Pollack s (1991) Sequential Cascaded Network) In both cases the mapping from input to output will vary with the network s internal state, and thus the machine, depending on its past, can effectively be a different machine in each time step. For the network itself this means that it no longer merely reacts to ....

Pollack, Jordan B. (1991). The induction of dynamical recognizers. Machine Learning, 7:227-252.

.... 1983 ] Following the development of the back propagation algorithm [ Rumelhart and McClelland, 1986 ] various recurrent neural architectures using back propagation have been shown to have some capability for grammatical inference when trained from examples [ Servan Schreiber et al. 1991, Pollack, 1991, Giles et al. 1990 ] The idea of training recurrent neural networks with back propagation was first introduced by Jordan [ 1986 ] In the recurrent neural network, the symbols of a sequence are presented sequentially as network inputs. Also, the output of a higher level layer during one time ....

....of error in time [ Rumelhart and McClelland, 1986 ] It is hard to train a recurrent neural network using this paradigm since the network makes many decisions before it is influenced by the results of those decisions. The classification paradigm has been studied by Giles et al. 1990 ] and Pollack [ 1991 ] The other paradigm is the predictive paradigm. In this case, it is assumed that the desired output at each time interval is known. To use this paradigm in the problem of grammatical inference, the network is trained to predict the next input in any sequence. An on line training algorithm can ....

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Jordan B. Pollack. The induction of dynamical recognizer. Machine Learning, 7(2/3):227--252, 1991.

....region called the Final Region (FR) The term Dynamical Automaton is intentionally like the term Dynamical Recognizer which has been used in closely related contexts. The dynamical automata I describe here are similar to but not quite the same as the dynamical recognizers that Pollack [9], Blair and Pollack, 10] and Moore [6] 7] examine. All of these dynamical computing devices have in common that they perform computations in a real valued space in response to string input and involve iterative computations (a function is repeatedly applied to its own output) Pollack s, ....

....1, 2, 3, etc. 6 Figure 2: A neural network for parenthesis balancing. ffifl fflfi A ffifl fflfi P ffifl fflfi Q w L = 1 2 ffifl fflfi z wR = 2 oe L oe R ffifl fflfi L ffifl fflfi R fractals to keep track of computational processes. 1. 1 A simple case: parenthesis balancing [9] noted that a very simple artificial neural device could recognize the language of balanced parentheses the language in which left parentheses always precede corresponding right parentheses. 4 He describes a machine along the lines of that shown in Figure 2. Initially, the activation of unit ....

Jordan B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:227-- 252, 1991.

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Pollack, J.B. 1991. The Induction of Dynamical Recognizers, Machine Learning 7, 227--252.

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J. B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:227--252, 1991.

....context free has been of particular interest as it demonstrates a certain in nite memory capacity. Rodrigez, Wiles and Elman [64] have explored how the dynamics of a predictor network allow it to recognize a context free language, a . Moore [56] showed how to construct Dynamical Recognizers [61] that can recognize arbitrary contextfree languages using the Cantor sets [82] In this work we look at a RAAM decoder model whose network is identical to the one used in chapter 4. Using understanding of the underlying dynamics of this network, Pollack has reformulated the original RAAM model in ....

....there is no obvious interpretation of computation. As such, there have been numerous interpretations of the function that dynamics serve in recurrent network computation. The Hop eld network uses the xed points of the network dynamics to represent memory elements. Networks studied by Pollack [61], Giles [28] and Casey [16] use the current activation of the network as a state in a state machine while using the dynamics of the network as the transition map. Some try to model existing dynamical systems with recurrent neural networks [89] RAAMs [60] as seen in the next chapter) use the ....

J.B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:227252, 1991.

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Pollack, J.B. (1991) The induction of dynamical recognizers. Machine

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Pollack, J. B. (1991). The induction of dynamical recognizers.

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J. B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:227, 1991.

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J. B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:227, 1991.

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Pollack, J. B. (1991), `The induction of dynamical recognizers', Machine Learning 7, 227--252.

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Jordan B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:227, 1991.

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J. B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:227, 1991. 16

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Jordan B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:227, 1991. 21

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J. B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:123--148, 1991.

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Jordan B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:227--252, 1991.

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Pollack, Jordan B. The Induction of Dynamical Recognizers. In Machine Learning, 7, 227-252. Kluwer Academic Publishers, Boston, 1991.

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J.B. Pollack. The induction of dynamical recognizers. Machine Learning, 7:227-- 252, 1991.

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