Above are papers related to the following paper: [Paper_ID] Paper #1109891. 	[Title] Interconnected Automata and Linear Systems: A Theoretical Framework in Discrete-Time In Hybrid Systems III: Verification [Abstract] This paper summarizes the definitions and several of the main results of an approach to hybrid systems, which combines finite automata and linear systems, developed by the author in the early 1980s. Some related more recent results are briefly mentioned as well. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #105856. 	[Title] Vapnik-Chervonenkis Dimension of Recurrent Neural Networks [Abstract] Most of the work on the Vapnik-Chervonenkis dimension of neural networks has been focused on feedforward networks. However, recurrent networks are also widely used in learning applications, in particular when time is a relevant parameter. This paper provides lower and upper bounds for the VC dimension of such networks. Several types of activation functions are discussed, including threshold, polynomial, piecewise-polynomial and sigmoidal functions. The bounds depend on two independent parameters: the number w of weights in the network, and the length k of the input sequence. In contrast, for feedforward networks, VC dimension bounds can be expressed as a function of w only. An important difference between recurrent and feedforward nets is that a fixed recurrent net can receive inputs of arbitrary length. Therefore we are particularly interested in the case k w. Ignoring multiplicative constants, the main results say roughly the following: * For architectures with activation = any fixed nonlinear polynomial, the VC dimension is wk. * For architectures with activation = any fixed piecewise polynomial, the VC dimension is between wk and w 2 k. * For architectures with activation = H (threshold nets), the VC dimension is between w log(k=w) and minfwk log wk; w 2 + w log wkg. * For the standard sigmoid (x) = 1=(1 + e x ), the VC dimension is between wk and w 4 k 2 . An earlier version of this paper has appeared in Proc. 3rd European Workshop on Computational Learning Theory, LNCS 1208, pages 223-237, Springer, 1997. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1123087. 	[Title] Noisy Time Series Prediction using Symbolic Representation and Recurrent Neural Network Grammatical Inference [Abstract] Financial forecasting is an example of a signal processing problem which is challenging due to small sample sizes, high noise, non-stationarity, and non-linearity. Neural networks have been very successful in a number of signal processing applications. We discuss fundamental limitations and inherent difficulties when using neural networks for the processing of high noise, small sample size signals. We introduce a new intelligent signal processing method which addresses the difficulties. The method uses conversion into a symbolic representation with a self-organizing map, and grammatical inference with recurrent neural networks. We apply the method to the prediction of daily foreign exchange rates, addressing difficulties with non-stationarity, overfitting, and unequal a priori class probabilities, and we find significant predictability in comprehensive experiments covering 5 different foreign exchange rates. The method correctly predicts the direction of change for the next day with an error rate of 47.1%. The error rate reduces to around 40% when rejecting examples where the system has low confidence in its prediction. The symbolic representation aids the extraction of symbolic knowledge from the recurrent neural networks in the form of deterministic finite state automata. These automata explain the operation of the system and are often relatively simple. Rules related to well known behavior such as trend following and mean reversal are extracted. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1104787. 	[Title] Fault-Tolerant Implementation of Finite-State Automata in Recurrent Neural Networks [Abstract] Recently, we have proven that the dynamics of any deterministic finite-state automata (DFA) with n states and m input symbols can be implemented in a sparse second-order recurrent neural network (SORNN) with n + 1 state neurons and O(mn) second-order weights and sigmoidal discriminant functions [5]. We investigate how that constructive algorithm can be extended to fault-tolerant neural DFA implementations where faults in an analog implementation of neurons or weights do not affect the desired network performance. We show that tolerance to weight perturbation can be achieved easily; tolerance to weight and/or neuron stuck-at-zero faults, however, requires duplication of the network resources. This result has an impact on the construction of neural DFAs with a dense internal representation of DFA states. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #140569. 	[Title] Using Fourier-Neural Recurrent Networks to Fit Sequential Input/Output Data [Abstract] This paper suggests the use of Fourier-type activation functions in fully recurrent neural networks. The main theoretical advantage is that, in principle, the problem of recovering internal coefficients from input/output data is solvable in closed form. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3229. 	[Title] Book Review  Introduction to the Theory of Neural Computation Reviewed by: 2 [Abstract] Neural computation, also called connectionism, parallel distributed processing, neural network modeling or brain-style computation, has grown rapidly in the last decade. Despite this explosion, and ultimately because of impressive applications, there has been a dire need for a concise introduction from a theoretical perspective, analyzing the strengths and weaknesses of connectionist approaches and establishing links to other disciplines, such as statistics or control theory. The Introduction to the Theory of Neural Computation by Hertz, Krogh and Palmer (subsequently referred to as HKP) is written from the perspective of physics, the home discipline of the authors. The book fulfills its mission as an introduction for neural network novices, provided that they have some background in calculus, linear algebra, and statistics. It covers a number of models that are often viewed as disjoint. Critical analyses and fruitful comparisons between these models Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #123556. 	[Title] BACKPROPAGATION SEPARATES WHERE PERCEPTRONS DO [Abstract] Feedforward nets with sigmoidal activation functions are often designed by minimizing a cost criterion. It has been pointed out before that this technique may be outperformed by the classical perceptron learning rule, at least on some problems. In this paper, we show that no such pathologies can arise if the error criterion is of a threshold LMS type, i.e., is zero for values "beyond" the desired target values. More precisely, we show that if the data are linearly separable, and one considers nets with no hidden neurons, then an error function as above cannot have any local minima that are not global. Simulations of networks with hidden units are consistent with these results, in that often data which can be classified when minimizing a threshold LMS criterion may fail to be classified when using instead a simple LMS cost. In addition, the proof gives the following stronger result, under the stated hypotheses: the continuous gradient adjustment procedure is such that from any initial weight configuration a separating set of weights is obtained in finite time. This is a precise analogue of the Perceptron Learning Theorem. The results are then compared with the more classical pattern recognition problem of threshold LMS with linear activations, where no spurious local minima exist even for nonseparable data: here it is shown that even if using the threshold criterion, such bad local minima may occur, if the data are not separable and sigmoids are used. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #286500. 	[Title] Facing The Facts: Necessary Requirements For The Artificial Evolution of Complex Behaviour [Abstract] This paper sets out a conceptual framework for the open-ended artificial evolution of complex behaviour in autonomous agents. If recurrent dynamical neural networks (or similar) are used as phenotypes, then a Genetic Algorithm that employs variable length genotypes, such as Inman Harvey's SAGA, is capable of evolving arbitrary levels of be-havioural complexity. Furthermore, with simple restrictions on the encoding scheme that governs how genotypes develop into phenotypes, it may be guaranteed that if an increase in fitness requires an increase in be-havioural complexity, then it will evolve. In order for this process to be practicable as a design alternative, however, the time periods involved must be acceptable. The final part of this paper looks at general ways in which the encoding scheme may be modified to speed up the process. Experiments are reported in which different categories of scheme were tested against each other, and conclusions are offered as to the most promising type of encoding scheme for a vi able open-ended Evolutionary Robotics. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #133550. 	[Title] OBSERVABILITY IN RECURRENT NEURAL NETWORKS [Abstract] Report SYCON-92-07rev ABSTRACT We obtain a characterization of observability for a class of nonlinear systems which appear in neural networks research. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1120049. 	[Title] Dimension of Recurrent Neural Networks [Abstract] DIMACS Technical Report 96-56 December 1996 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #133553. 	[Title] Sample Complexity for Learning Recurrent Perceptron Mappings [Abstract] Recurrent perceptron classifiers generalize the classical perceptron model. They take into account those correlations and dependences among input coordinates which arise from linear digital filtering. This paper provides tight bounds on sample complexity associated to the fitting of such models to experimental data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12347. 	[Title] First-Order vs. Second-Order Single Layer Recurrent Neural Networks [Abstract] We examine the representational capabilities of first-order and second-order Single Layer Recurrent Neural Networks (SLRNNs) with hard-limiting neurons. We show that a second-order SLRNN is strictly more powerful than a first-order SLRNN. However, if the first-order SLRNN is augmented with output layers of feedforward neurons, it can implement any finite-state recognizer, but only if state-splitting is employed. When a state is split, it is divided into two equivalent states. The judicious use of state-splitting allows for efficient implementation of finite-state recognizers using augmented first-order SLRNNs. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #133566. 	[Title] Recurrent Neural Networks: Some Systems-Theoretic Aspects [Abstract] This paper provides an exposition of some recent research regarding system-theoretic aspects of continuous-time recurrent (dynamic) neural networks with sigmoidal activation functions. The class of systems is introduced and discussed, and a result is cited regarding their universal approximation properties. Known characterizations of controllability, ob-servability, and parameter identifiability are reviewed, as well as a result on minimality. Facts regarding the computational power of recurrent nets are also mentioned. fl Supported in part by US Air Force Grant AFOSR-94-0293 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1105603. 	[Title] Can Recurrent Neural Networks Learn Natural Language Grammars? W&Z recurrent neural networks are able to [Abstract] Recurrent neural networks are complex parametric dynamic systems that can exhibit a wide range of different behavior. We consider the task of grammatical inference with recurrent neural networks. Specifically, we consider the task of classifying natural language sentences as grammatical or ungrammatical can a recurrent neural network be made to exhibit the same kind of discriminatory power which is provided by the Principles and Parameters linguistic framework, or Government and Binding theory? We attempt to train a network, without the bifurcation into learned vs. innate components assumed by Chomsky, to produce the same judgments as native speakers on sharply grammatical/ungrammatical data. We consider how a recurrent neural network could possess linguistic capability, and investigate the properties of Elman, Narendra & Parthasarathy (N&P) and Williams & Zipser (W&Z) recurrent networks, and Frasconi-Gori-Soda (FGS) locally recurrent networks in this setting. We show that both Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #5194. 	[Title] NETWORKS, FUNCTION DETERMINES FORM [Abstract] Report SYCON-92-03 ABSTRACT This paper shows that the weights of continuous-time feedback neural networks are uniquely identifiable from input/output measurements. Under very weak genericity assumptions, the following is true: Assume given two nets, whose neurons all have the same nonlinear activation function ; if the two nets have equal behaviors as "black boxes" then necessarily they must have the same number of neurons and |except at most for sign reversals at each node| the same weights. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131345. 	[Title] Lemma 2.3 The system is reachable and observable and realizes the same input/output behavior as [Abstract] Here we show a similar construction for multiple-output systems, with some modifications. Let = (A; B; C) s be a discrete-time sign-linear system with state space IR n and p outputs. Perform a change of ; where A 1 (n 1 fi n 1 ) is invertible and A 2 (n 2 fi n 2 ) is nilpotent. If (A; B) is a reachable pair and (A; C) is an observable pair, then is minimal in the sense that any other sign-linear system with the same input/output behavior has dimension at least n. But, if n 1 &lt; n, then det A = 0 and is not observable and hence not canonical. Let us find another system ~ (necessarily not sign-linear) which has the same input/output behavior as , but is canonical. Let i be the relative degree of the ith row of the Markov sequence A, and = minf i : i = 1; : : : ; pg. Let the initial state be x. There is a difference between the case when the smallest relative degree is greater or equal to n 2 and the case when &lt; n 2 . Roughly speaking, when n 2 the outputs of the sign-linear system give us information about sign (Cx), sign (CAx), : : : , sign (CA 1 x), which are the first outputs of the sys tem. After that, we can use the inputs and outputs to learn only about x 1 (the first n 1 components of x). When &lt; n 2 , we may be able to use some controls to learn more about x 2 (the last n 2 components of x) before time n 2 when the nilpotency of A 2 has finally Lemma 2.4 Two states x and z are indistinguishable for if and only if (x) = (z). Proof. In the case n 2 , we have only the equations x 1 = z 1 and the equality of the 's. The first ` output terms for are exactly the terms of . So these equalities are satisfied if and only if the first ` output terms coincide for x and z, for any input. Equality of everything but the first n 1 components is equivalent to the first n 2 output terms coinciding for x and z, since the jth row of the qth output, for initial state x, for example, is either sign (c j A q x) if j &gt; q, or sign (c j A q x + + A j j u q j +1 + ) if j q in which case we may use the control u q j +1 to identify c j A q x (using Remark 3.3 in [1]). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #16485. 	[Title] POWER OF NEURAL NETS [Abstract] Report SYCON-91-11 ABSTRACT This paper deals with the simulation of Turing machines by neural networks. Such networks are made up of interconnections of synchronously evolving processors, each of which updates its state according to a "sigmoidal" linear combination of the previous states of all units. The main result states that one may simulate all Turing machines by nets, in linear time. In particular, it is possible to give a net made up of about 1,000 processors which computes a universal partial-recursive function. (This is an update of Report SYCON-91-08; new results include the simulation in linear time of binary-tape machines, as opposed to the unary alphabets used in the previous version.) Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #141160. 	[Title] LINEAR SYSTEMS WITH SIGN-OBSERVATIONS [Abstract] This paper deals with systems that are obtained from linear time-invariant continuous-or discrete-time devices followed by a function that just provides the sign of each output. Such systems appear naturally in the study of quantized observations as well as in signal processing and neural network theory. Results are given on observability, minimal realizations, and other system-theoretic concepts. Certain major differences exist with the linear case, and other results generalize in a surprisingly straightforward manner. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #917493. 	[Title] Observability of Linear Systems with Saturated Outputs [Abstract] In this paper, we present necessary and sufficient conditions for observability of the class of output-saturated systems. These are linear systems whose output passes through a saturation function before it can be measured. Please summarise all the given information.

Paper #1109891 has the title `Interconnected Automata and Linear Systems: A Theoretical Framework in Discrete-Time In Hybrid Systems III: Verification
` and the abstract `This paper summarizes the definitions and several of the main results of an approach to hybrid systems, which combines finite automata and linear systems, developed by the author in the early 1980s. Some related more recent results are briefly mentioned as well. 
`.
Question: Which category should Paper #1109891 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1109891 has the title `Interconnected Automata and Linear Systems: A Theoretical Framework in Discrete-Time In Hybrid Systems III: Verification
` and the abstract `This paper summarizes the definitions and several of the main results of an approach to hybrid systems, which combines finite automata and linear systems, developed by the author in the early 1980s. Some related more recent results are briefly mentioned as well. 
`.
Question: Which category should Paper #1109891 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks