Search

Abstract: One of the phenomena that can be observed when using neural networks for time series prediction is that the quality of the forecasts obtained is correlated with the dimensionality of the data. Higher data dimensionality leads, in most cases, to higher prediction errors. This phenomenon is connected by some authors to the decrease in variance of the distances between the data points, which occurs when the lengths of the predicted vectors increase. In this paper, a proof is given that the variance of the distances between data points also decreases with the so-called correlation dimension of the data. Therefore, a drop in forecast quality might be expected not only when the lengths of the data vectors are increased, but also when using vectors of the same length to represent data of increasing dimensionality. We also present some experimental results that illustrate the dependence between data dimensionality and the variance of the distances between the data points, and the forecast error obtained when using a multilayer perceptron to predict future values of some time series. [Copyright &y& Elsevier]

Abstract: Modal logics are amongst the most successful applied logical systems. Neural networks were proved to be effective learning systems. In this paper, we propose to combine the strengths of modal logics and neural networks by introducing Connectionist Modal Logics (CML). CML belongs to the domain of neural-symbolic integration, which concerns the application of problem-specific symbolic knowledge within the neurocomputing paradigm. In CML, one may represent, reason or learn modal logics using a neural network. This is achieved by a Modalities Algorithm that translates modal logic programs into neural network ensembles. We show that the translation is sound, i.e. the network ensemble computes a fixed-point meaning of the original modal program, acting as a distributed computational model for modal logic. We also show that the fixed-point computation terminates whenever the modal program is well-behaved. Finally, we validate CML as a computational model for integrated knowledge representation and learning by applying it to a well-known testbed for distributed knowledge representation. This paves the way for a range of applications on integrated knowledge representation and learning, from practical reasoning to evolving multi-agent systems. [Copyright &y& Elsevier]

Abstract: The construction of computational models with provision for effective learning and added reasoning is a fundamental problem in computer science. In this paper, we present a new computational model for integrated reasoning and learning that combines intuitionistic reasoning and neural networks. We use ensembles of neural networks to represent intuitionistic theories, and show that for each intuitionistic theory and intuitionistic modal theory there exists a corresponding neural network ensemble that computes a fixed-point semantics of the theory. This provides a massively parallel model for intuitionistic reasoning. In our model, the neural networks can be trained from examples to adapt to new situations using standard neural learning algorithms, thus providing a unifying foundation for intuitionistic reasoning, knowledge representation, and learning. [Copyright &y& Elsevier]