Introduction Research on integrated neural-symbolic systems has made significant progress in the recent past. In particular the understanding of ways to deal with symbolic knowledge within connectionist systems (also called artificial neural networks) has reached a critical mass which enables the community to strive for applicable implementations and use cases. Recent work has covered a great variety of logics used in artificial intelligence and provides a multitude of techniques for dealing with them within the context of artificial neural networks. Already in the pioneering days of computational models of neural cognition, the question was raised how symbolic knowledge can be represented and dealt with within neural networks. The landmark paper [McCulloch and Pitts, 1943] provides fundamental insights how propositional logic can be processed using simple artificial neural networks. Within the following decades, however, the topic did not receive much attention as research in arti

Abstract not found

To continue the tradition of the previous brainstorming weeks on membrane computing, I am collecting here a series of open problems and research topics, not about membrane computing in general, but about one of the directions of research which were pretty much investigated in the last year: spiking neural P systems. In general, one mentions issues which look of a broader nature, but also some precise problems are formulated. As usual with such lists of problems, the selection is subjective, by no means exhaustive. Of course, choosing only problems related to spiking neural P systems does not mean that there are no longer enough problems waiting to be solved in the general framework of membrane computing – on contrarily (e.g., separate lists can refer to computational complexity issues, to dynamical systems approaches, etc.), but such problems tend to become rather specialized and technical at the present stage of the development of membrane computing. Instead, the membrane computing models with a neural inspiration are at the beginning of a systematic exploration, and, as claimed below, this area of research looks very promising. 2

INTRODUCTION The two main streams of neural networks research consider neural networks either as a powerful family of nonlinear statistical models, to be used in for example pattern recognition applications [6], or as formal models to help develop a computational understanding of the brain [10]. Historically, the brain theory interest was primary [32], but with the advances in computer technology, the application potential of the statistical modeling techniques has shifted the balance. 1 The study of neural networks as general computational devices does not strictly follow this division of interests: rather, it provides a general framework outlining the limitations and possibilities aecting both research domains. The prime historic example here is obviously Minsky's and Papert's 1969 study of the computational limitations of singlelayer perceptrons [34], which was a major inuence in turning away interest from neural network learning to symbolic AI techniques for more

We present a mechanism of unsupervised competitive learning and development of topology preserving self-organizing maps of spiking neurons. The information encoding is based on the precise timing of single spike events. The work provides a competitive learning algorithm that is based on the relative timing of the pre- and post-synaptic spikes, local synapse competitions within a single neuron and global competition via lateral connections. Furthermore, we present part of the experimental work on the capability of the suggested mechanism to perform topology preserving mapping and competitive learning. The results show that our model covers the main characteristic behaviour of the standard SOM but uses a computationally more powerful timing-dependent spike encoding.

This paper gives an introduction to spiking neural networks, some biological background, and will present two models of spiking neurons that employ pulse coding. Networks of spiking neurons are more powerful than their non-spiking predecessors as they can encode temporal information in their signals, but therefore do also need dilferent and biologically more plausible rules for synaptic plasticity

In this review we focus our attention on supervised learning methods for spike time coding in Spiking Neural Networks (SNNs). This study is motivated by recent experimental results regarding information coding in biological neural systems, which suggest that precise timing of individual spikes may be essential for efficient computation in the brain. We are concerned with the fundamental question: What paradigms of neural temporal coding can be implemented with the recent learning methods? In order to answer this question, we discuss various approaches to the learning task considered. We shortly describe the particular learning algorithms and report the results of experiments. Finally, we discuss the properties, assumptions and limitations of each method. We complete this review with a comprehensive list of pointers to the literature.

Summary. After a quick introduction of spiking neural P systems (a class of P systems inspired from the way neurons communicate by means of spikes, electrical impulses of identical shape), and presentation of typical results (in general equivalence with Turing machines as number computing devices, but also other issues, such as the possibility of handling strings or infinite sequences), we present a long list of open problems and research topics in this area, also mentioning recent attempts to address some of them. The bibliography completes the information offered to the reader interested in this research area. 1

A description of neuronal activity on the level of ion channels, as in the Hodgkin-Huxley model, leads to a set of coupled nonlinear differential equations which are difficult to analyze. In this paper, we present a conceptual framework for a reduction of the nonlinear spike dynamics to a threshold process. Spikes occur if the membrane potential u(t) reaches a threshold #. The voltage response to spike input is described by the postsynaptic potential ffl. Postsynaptic potentials of several input spikes are added linearly until u reaches #. The output pulse itself and the reset/refractory period which follow the pulse are described by a function j. Since ffl and j can be interpreted as response kernels, the resulting model is called the Spike Response Model (SRM). After a short review of the Hodgkin-Huxley model we show that (i) Hodgkin-Huxley dynamics with time-dependent input can be reproduced to a high degree of accuracy by the SRM; (ii) the simple integrate-and-fire neuron is a spe...

Abstract. A real-time, large scale, leaky-integrate-and-fire neural network processor realized using FPGA is presented. This has been designed, as part of a collaborative project, to investigate and implement biologically plausible models of the rodent vibrissae based somatosensory system to control a robot. An emphasis has been made on hard real-time performance of the processor, as it is to be used as part of a feedback control system. This has led to a revision of some of the established modelling protocols used in other hardware spiking neural network processors. The underlying neuron model has the ability to model synaptic noise and inter-neural propagation delays to provide a greater degree of biological plausibility. The processor has been demonstrated modelling real neural circuitry in real-time, independent of the underlying neural network activity. 1 Introduction and