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 #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 #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 #24966. 	[Title] A Practical Bayesian Framework for Backprop Networks [Abstract] A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible: (1) objective comparisons between solutions using alternative network architectures; (2) objective stopping rules for network pruning or growing procedures; (3) objective choice of magnitude and type of weight decay terms or additive regularisers (for penalising large weights, etc.); (4) a measure of the effective number of well-determined parameters in a model; (5) quantified estimates of the error bars on network parameters and on network output; (6) objective comparisons with alternative learning and interpolation models such as splines and radial basis functions. The Bayesian `evidence' automatically embodies `Occam's razor,' penalising over-flexible and over-complex models. The Bayesian approach helps detect poor underlying assumptions in learning models. For learning models well matched to a problem, a good correlation between generalisation ability and the Bayesian evidence is obtained. This paper makes use of the Bayesian framework for regularisation and model comparison described in the companion paper `Bayesian interpolation' (MacKay, 1991a). This framework is due to Gull and Skilling (Gull, 1989a). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1120138. 	[Title] Volatility of Volatility of Financial Markets [Abstract] We present empirical evidence for considering volatility of Eurodollar futures as a stochastic process, requiring a generalization of the standard Black-Scholes (BS) model which treats volatility as a constant. We use a previous development of a statistical mechanics of financial markets (SMFM) to model these issues. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #643597. 	[Title] A Nonparametric Bayesian Approach to Modelling Nonlinear Time Series [Abstract] The Bayesian multivariate adaptive regression spline (BMARS) methodology of Denison et al. (1997) is extended to cope with nonlinear time series and financial datasets. The nonlinear time series model is closely related to the adaptive spline threshold autoregressive (ASTAR) method of Lewis and Stevens (1991) while the financial models can be thought of as Bayesian versions of both the generalised and simple autoregressive conditional het-eroscadastic (GARCH and ARCH) models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #202639. 	[Title] PREDICTING SUNSPOTS AND EXCHANGE RATES WITH CONNECTIONIST NETWORKS [Abstract] We investigate the effectiveness of connectionist networks for predicting the future continuation of temporal sequences. The problem of overfitting, particularly serious for short records of noisy data, is addressed by the method of weight-elimination: a term penalizing network complexity is added to the usual cost function in back-propagation. The ultimate goal is prediction accuracy. We analyze two time series. On the benchmark sunspot series, the networks outperform traditional statistical approaches. We show that the network performance does not deteriorate when there are more input units than needed. Weight-elimination also manages to extract some part of the dynamics of the notoriously noisy currency exchange rates and makes the network solution interpretable. 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 #94229. 	[Title] Draft Symbolic Representation of Neural Networks [Abstract] An early and shorter version of this paper has been accepted for presenta tion at IJCAI'95. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1129621. 	[Title] Analysis of Dynamical Recognizers [Abstract] Pollack (1991) demonstrated that second-order recurrent neural networks can act as dynamical recognizers for formal languages when trained on positive and negative examples, and observed both phase transitions in learning and IFS-like fractal state sets. Follow-on work focused mainly on the extraction and minimization of a finite state automaton (FSA) from the trained network. However, such networks are capable of inducing languages which are not regular, and therefore not equivalent to any FSA. Indeed, it may be simpler for a small network to fit its training data by inducing such a non-regular language. But when is the network's language not regular? In this paper, using a low dimensional network capable of learning all the Tomita data sets, we present an empirical method for testing whether the language induced by the network is regular or not. We also provide a detailed "-machine analysis of trained networks for both regular and non-regular languages. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #144408. 	[Title] Neural net architectures for temporal sequence processing [Abstract] I present a general taxonomy of neural net architectures for processing time-varying patterns. This taxonomy subsumes many existing architectures in the literature, and points to several promising architectures that have yet to be examined. Any architecture that processes time-varying patterns requires two conceptually distinct components: a short-term memory that holds on to relevant past events and an associator that uses the short-term memory to classify or predict. My taxonomy is based on a characterization of short-term memory models along the dimensions of form, content, and adaptability. Experiments on predicting future values of a financial time series (US dollar-Swiss franc exchange rates) are presented using several alternative memory models. The results of these experiments serve as a baseline against which more sophisticated architectures can be compared. Neural networks have proven to be a promising alternative to traditional techniques for nonlinear temporal prediction tasks (e.g., Curtiss, Brandemuehl, & Kreider, 1992; Lapedes & Farber, 1987; Weigend, Huberman, & Rumelhart, 1992). However, temporal prediction is a particularly challenging problem because conventional neural net architectures and algorithms are not well suited for patterns that vary over time. The prototypical use of neural nets is in structural pattern recognition. In such a task, a collection of features|visual, semantic, or otherwise|is presented to a network and the network must categorize the input feature pattern as belonging to one or more classes. For example, a network might be trained to classify animal species based on a set of attributes describing living creatures such as "has tail", "lives in water", or "is carnivorous"; or a network could be trained to recognize visual patterns over a two-dimensional pixel array as a letter in fA; B; . . . ; Zg. In such tasks, the network is presented with all relevant information simultaneously. In contrast, temporal pattern recognition involves processing of patterns that evolve over time. The appropriate response at a particular point in time depends not only on the current input, but potentially all previous inputs. This is illustrated in Figure 1, which shows the basic framework for a temporal prediction problem. I assume that time is quantized into discrete steps, a sensible assumption because many time series of interest are intrinsically discrete, and continuous series can be sampled at a fixed interval. The input at time t is denoted x(t). For univariate series, this input Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #33818. 	[Title] Statistical Mechanics of Nonlinear Nonequilibrium Financial Markets: Applications to Optimized Trading [Abstract] A paradigm of statistical mechanics of financial markets (SMFM) using nonlinear nonequilibrium algorithms, first published in L. Ingber, Mathematical Modelling, 5, 343-361 (1984), is fit to multi-variate financial markets using Adaptive Simulated Annealing (ASA), a global optimization algorithm, to perform maximum likelihood fits of Lagrangians defined by path integrals of multivariate conditional probabilities. Canonical momenta are thereby derived and used as technical indicators in a recursive ASA optimization process to tune trading rules. These trading rules are then used on out-of-sample data, to demonstrate that they can profit from the SMFM model, to illustrate that these markets are likely not efficient. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #33823. 	[Title] Statistical mechanics of neocortical interactions: Training and testing canonical momenta indicators of EEG [Abstract] A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electrical-chemical properties of synaptic interactions. While not useful to yield insights at the single neuron level, SMNI has demonstrated its capability in describing large-scale properties of short-term memory and electroencephalographic (EEG) systematics. The necessity of including nonlinear and stochastic structures in this development has been stressed. Sets of EEG and evoked potential data were fit, collected to investigate genetic predispositions to alcoholism and to extract brain signatures of short-term memory. Adaptive Simulated Annealing (ASA), a global optimization algorithm, was used to perform maximum likelihood fits of Lagrangians defined by path integrals of multivariate conditional probabilities. Canonical momenta indicators (CMI) are thereby derived for individual's EEG data. The CMI give better signal recognition than the raw data, and can be used to advantage as correlates of behavioral states. These results give strong quantitative support for an accurate intuitive picture, portraying neocortical interactions as having common algebraic or physics mechanisms that scale across quite disparate spatial scales and functional or behavioral phenomena, i.e., describing interactions among neurons, columns of neurons, and regional masses of neurons. This paper adds to these previous investigations two important aspects, a description of how the CMI may be used in source localization, and calculations using previously ASA-fitted parameters in out-of-sample data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #22563. 	[Title] A Comparative Study of ID3 and Backpropagation for English Text-to-Speech Mapping [Abstract] The performance of the error backpropagation (BP) and ID3 learning algorithms was compared on the task of mapping English text to phonemes and stresses. Under the distributed output code developed by Sejnowski and Rosenberg, it is shown that BP consistently out-performs ID3 on this task by several percentage points. Three hypotheses explaining this difference were explored: (a) ID3 is overfitting the training data, (b) BP is able to share hidden units across several output units and hence can learn the output units better, and (c) BP captures statistical information that ID3 does not. We conclude that only hypothesis (c) is correct. By augmenting ID3 with a simple statistical learning procedure, the performance of BP can be approached but not matched. More complex statistical procedures can improve the performance of both BP and ID3 substantially. A study of the residual errors suggests that there is still substantial room for improvement in learning methods for text-to-speech mapping. 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 #1117348. 	[Title] MIXED MEMORY MARKOV MODELS FOR TIME SERIES ANALYSIS [Abstract] This paper presents a method for analyzing coupled time series using Markov models in a domain where the state space is immense. To make the parameter estimation tractable, the large state space is represented as the Cartesian product of smaller state spaces, a paradigm known as factorial Markov models. The transition matrix for this model is represented as a mixture of the transition matrices of the underlying dynamical processes. This formulation is know as mixed memory Markov models. Using this framework, we analyze the daily exchange rates for five currencies - British pound, Canadian dollar, Deutsch mark, Japanese yen, and Swiss franc as measured against the U.S. dollar. 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 #1111733. 	[Title] Evaluation and Ordering of Rules Extracted from Feedforward Networks [Abstract] Rules extracted from trained feedforward networks can be used for explanation, validation, and cross-referencing of network output decisions. This paper introduces a rule evaluation and ordering mechanism that orders rules extracted from feedforward networks based on three performance measures. Detailed experiments using three rule extraction techniques as applied to the Wisconsin breast cancer database, illustrate the power of the proposed methods. Moreover, a method of integrating the output decisions of both the extracted rule-based system and the corresponding trained network is proposed. The integrated system provides further improvements. 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 #672064. 	[Title] Direct Multi-Step Time Series Prediction Using TD() [Abstract] This paper explores the application of Temporal Difference (TD) learning (Sutton, 1988) to forecasting the behavior of dynamical systems with real-valued outputs (as opposed to game-like situations). The performance of TD learning in comparison to standard supervised learning depends on the amount of noise present in the data. In this paper, we use a deterministic chaotic time series from a low-noise laser. For the task of direct five-step ahead predictions, our experiments show that standard supervised learning is better than TD learning. The TD algorithm can be viewed as linking adjacent predictions. A similar effect can be obtained by sharing the internal representation in the network. We thus compare two architectures for both paradigms: the first architecture (separate hidden units) consists of individual networks for each of the five direct multi-step prediction tasks, the second (shared hidden units) has a single (larger) hidden layer that finds a representation from which all five predictions for the next five steps are generated. For this data set we do not find any significant difference between the two architectures. fl http://www.cs.colorado.edu/~andreas/Home.html. This paper is available as ftp://ftp.cs.colorado.edu/pub/Time-Series/MyPapers/kazlas.weigend nips7.ps.Z 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 #40131. 	[Title] A comparison of neural net and conventional techniques for lighting control [Abstract] We compare two techniques for lighting control in an actual room equipped with seven banks of lights and photoresistors to detect the lighting level at four sensing points. Each bank of lights can be independently set to one of sixteen intensity levels. The task is to determine the device intensity levels that achieve a particular configuration of sensor readings. One technique we explored uses a neural network to approximate the mapping between sensor readings and device intensity levels. The other technique we examined uses a conventional feedback control loop. The neural network approach appears superior both in that it does not require experimentation on the fly (and hence fluctuating light intensity levels during settling, and lengthy settling times) and in that it can deal with complex interactions that conventional control techniques do not handle well. This comparison was performed as part of the "Adaptive House" project, which is described briefly. Further directions for control in the Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12359. 	[Title] Pruning Recurrent Neural Networks for Improved Generalization Performance [Abstract] Determining the architecture of a neural network is an important issue for any learning task. For recurrent neural networks no general methods exist that permit the estimation of the number of layers of hidden neurons, the size of layers or the number of weights. We present a simple pruning heuristic which significantly improves the generalization performance of trained recurrent networks. We illustrate this heuristic by training a fully recurrent neural network on positive and negative strings of a regular grammar. We also show that if rules are extracted from networks trained to recognize these strings, that rules extracted after pruning are more consistent with the rules to be learned. This performance improvement is obtained by pruning and retraining the networks. Simulations are shown for training and pruning a recurrent neural net on strings generated by two regular grammars, a randomly-generated 10-state grammar and an 8-state triple parity grammar. Further simulations indicate that this pruning method can gives generalization performance superior to that obtained by training with weight decay. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1154123. 	[Title]  [Abstract] Most connectionist modeling assumes noise-free inputs. This assumption is often violated. This paper introduces the idea of clearning, of simultaneously cleaning the data and learning the underlying structure. The cleaning step can be viewed as top-down processing (where the model modifies the data), and the learning step can be viewed as bottom-up processing (where the data modifies the model). Clearning is used in conjunction with standard pruning. This paper discusses the statistical foundation of clearning, gives an interpretation in terms of a mechanical model, describes how to obtain both point predictions and conditional densities for the output, and shows how the resulting model can be used to discover properties of the data otherwise not accessible (such as the signal-to-noise ratio of the inputs). This paper uses clearning to predict foreign exchange rates, a noisy time series problem with well-known benchmark performances. On the out-of-sample 1993-1994 test period, clearning obtains an annualized return on investment above 30%, significantly better than an otherwise identical network. The final ultra-sparse network with 36 remaining non-zero input-to-hidden weights (of the 1035 initial weights between 69 inputs and 15 hidden units) is very robust against overfitting. This small network also lends itself to interpretation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1154124. 	[Title]  [Abstract] Most connectionist modeling assumes noise-free inputs. This assumption is often violated. This paper introduces the idea of clearning, of simultaneously cleaning the data and learning the underlying structure. The cleaning step can be viewed as top-down processing (where the model modifies the data), and the learning step can be viewed as bottom-up processing (where the data modifies the model). Clearning is used in conjunction with standard pruning. This paper discusses the statistical foundation of clearning, gives an interpretation in terms of a mechanical model, describes how to obtain both point predictions and conditional densities for the output, and shows how the resulting model can be used to discover properties of the data otherwise not accessible (such as the signal-to-noise ratio of the inputs). This paper uses clearning to predict foreign exchange rates, a noisy time series problem with well-known benchmark performances. On the out-of-sample 1993-1994 test period, clearning obtains an annualized return on investment above 30%, significantly better than an otherwise identical network. The final ultra-sparse network with 36 remaining non-zero input-to-hidden weights (of the 1035 initial weights between 69 inputs and 15 hidden units) is very robust against overfitting. This small network also lends itself to interpretation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #242637. 	[Title] A Delay Damage Model Selection Algorithm for NARX Neural Networks [Abstract] Recurrent neural networks have become popular models for system identification and time series prediction. NARX (Nonlinear AutoRegressive models with eXogenous inputs) neural network models are a popular subclass of recurrent networks and have been used in many applications. Though embedded memory can be found in all recurrent network models, it is particularly prominent in NARX models. We show that using intelligent memory order selection through pruning and good initial heuristics significantly improves the generalization and predictive performance of these nonlinear systems on problems as diverse as grammatical inference and time series prediction. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #78549. 	[Title] Path-integral evolution of chaos embedded in noise: Duffing neocortical analog [Abstract] A two dimensional time-dependent Duffing oscillator model of macroscopic neocortex exhibits chaos for some ranges of parameters. We embed this model in moderate noise, typical of the context presented in real neocortex, using PATHINT, a non-Monte-Carlo path-integral algorithm that is particularly adept in handling nonlinear Fokker-Planck systems. This approach shows promise to investigate whether chaos in neocortex, as predicted by such models, can survive in noisy contexts. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #78552. 	[Title] STATISTICAL MECHANICS OF COMBAT WITH HUMAN FACTORS [Abstract] This highly interdisciplinary project extends previous work in combat modeling and in control-theoretic descriptions of decision-making human factors in complex activities. A previous paper has established the first theory of the statistical mechanics of combat (SMC), developed using modern methods of statistical mechanics, baselined to empirical data gleaned from the National Training Center (NTC). This previous project has also established a JANUS(T)-NTC computer simulation/wargame of NTC, providing a statistical ``what-if '' capability for NTC scenarios. This mathematical formulation is ripe for control-theoretic extension to include human factors, a methodology previously developed in the context of teleoperated vehicles. Similar NTC scenarios differing at crucial decision points will be used for data to model the inuence of decision making on combat. The results may then be used to improve present human factors and C 2 algorithms in computer simulations/wargames. Our approach is to ``subordinate'' the SMC nonlinear stochastic equations, fitted to NTC scenarios, to establish the zeroth order description of that combat. In practice, an equivalent mathematical-physics representation is used, more suitable for numerical and formal work, i.e., a Lagrangian representation. Theoretically, these equations are nested within a larger set of nonlinear stochastic operator-equations which include C 3 human factors, e.g., supervisory decisions. In this study, we propose to perturb this operator theory about the SMC zeroth order set of equations. Then, subsets of scenarios fit to zeroth order, originally considered to be similarly degenerate, can be further split perturbatively to distinguish C 3 decision-making inuences. New methods of Very Fast Simulated Re-Annealing (VFSR), developed in the previous project, will be used for fitting these models to empirical data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #16474. 	[Title] Rule Revision with Recurrent Neural Networks [Abstract] Recurrent neural networks readily process, recognize and generate temporal sequences. By encoding grammatical strings as temporal sequences, recurrent neural networks can be trained to behave like deterministic sequential finite-state automata. Algorithms have been developed for extracting grammatical rules from trained networks. Using a simple method for inserting prior knowledge (or rules) into recurrent neural networks, we show that recurrent neural networks are able to perform rule revision. Rule revision is performed by comparing the inserted rules with the rules in the finite-state automata extracted from trained networks. The results from training a recurrent neural network to recognize a known non-trivial, randomly generated regular grammar show that not only do the networks preserve correct rules but that they are able to correct through training inserted rules which were initially incorrect. (By incorrect, we mean that the rules were not the ones in the randomly generated grammar.) Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #78555. 	[Title] NONLINEAR NONEQUILIBRIUM NONQUANTUM NONCHAOTIC STATISTICAL MECHANICS OF NEOCORTICAL INTERACTIONS [Abstract] The work in progress reported by Wright & Liley shows great promise, primarily because of their experimental and simulation paradigms. However, their tentative conclusion that macroscopic neocortex may be considered (approximately) a linear near-equilibrium system is premature and does not correspond to tentative conclusions drawn from other studies of neocortex. At this time, there exists an interdisciplinary multidimensional gradation on published studies of neocortex, with one primary dimension of mathematical physics represented by two extremes. At one extreme, there is much scientifically unsupported talk of chaos and quantum physics being responsible for many important macroscopic neocortical processes (involving many thousands to millions of neurons) (Wilczek, 1994). At another extreme, many non-mathematically trained neuroscientists uncritically lump all neocortical mathematical theory into one file, and consider only statistical averages of citations for opinions on the quality of that research (Nunez, 1995). In this context, it is important to appreciate that Wright and Liley (W&L) report on their scientifically sound studies on macroscopic neocortical function, based on simulation and a blend of sound theory and reproducible experiments. However, their pioneering work, given the absence of much knowledge of neocortex at this time, is open to criticism, especially with respect to their present inferences and conclusions. Their conclusion that EEG data exhibit linear near-equilibrium dynamics may very well be true, but only in the sense of focusing only on one local minima, possibly with individual-specific and physiological-state dependent Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #16476. 	[Title] Extraction of Rules from Discrete-Time Recurrent Neural Networks [Abstract] The extraction of symbolic knowledge from trained neural networks and the direct encoding of (partial) knowledge into networks prior to training are important issues. They allow the exchange of information between symbolic and connectionist knowledge representations. The focus of this paper is on the quality of the rules that are extracted from recurrent neural networks. Discrete-time recurrent neural networks can be trained to correctly classify strings of a regular language. Rules defining the learned grammar can be extracted from networks in the form of deterministic finite-state automata (DFA's) by applying clustering algorithms in the output space of recurrent state neurons. Our algorithm can extract different finite-state automata that are consistent with a training set from the same network. We compare the generalization performances of these different models and the trained network and we introduce a heuristic that permits us to choose among the consistent DFA's the model which best approximates the learned regular grammar. Keywords: Recurrent Neural Networks, Grammatical Inference, Regular Languages, Deterministic Finite-State Automata, Rule Extraction, Generalization Performance, Model Selection, Occam's Razor. fl Technical Report CS-TR-3465 and UMIACS-TR-95-54, University of Maryland, College Park, MD 20742. Ac cepted for publication in Neural Networks. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #78557. 	[Title] Application of statistical mechanics methodol- ogy to term-structure bond-pricing models, Mathl. Comput. Modelling Application of [Abstract]  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 #25702. 	[Title] Nonlinear Prediction of Chaotic Time Series Using Support Vector Machines [Abstract] A novel method for regression has been recently proposed by V. Vapnik et al. [8, 9]. The technique, called Support Vector Machine (SVM), is very well founded from the mathematical point of view and seems to provide a new insight in function approximation. We implemented the SVM and tested it on the same data base of chaotic time series that was used in [1] to compare the performances of different approximation techniques, including polynomial and rational approximation, local polynomial techniques, Radial Basis Functions, and Neural Networks. The SVM performs better than the approaches presented in [1]. We also study, for a particular time series, the variability in performance with respect to the few free parameters of SVM. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #9586. 	[Title] %A L. Ingber %T Adaptive simulated annealing (ASA): Lessons learned %J Control and Cybernetics Annealing [Abstract]  Please summarise all the given information.

Paper #1123087 has the title `Noisy Time Series Prediction using Symbolic Representation and Recurrent Neural Network Grammatical Inference  
` and the 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. 
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Question: Which category should Paper #1123087 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1123087 has the title `Noisy Time Series Prediction using Symbolic Representation and Recurrent Neural Network Grammatical Inference  
` and the 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. 
`.
Question: Which category should Paper #1123087 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