The computational power of formal models for networks of spiking neurons is compared with that of other neural network models based on McCulloch Pitts neurons (i.e. threshold gates) respectively sigmoidal gates. In particular it is shown that networks of spiking neurons are computationally more powerful than these other neural network models. A concrete biologically relevant function is exhibited which can be computed by a single spiking neuron (for biologically reasonable values of its parameters), but which requires hundreds of hidden units on a sigmoidal neural net. This article does not assume prior knowledge about spiking neurons, and it contains an extensive list of references to the currently available literature on computations in networks of spiking neurons and relevant results from neurobiology. 1 Definitions and Motivations If one classifies neural network models according to their computational units, one can distinguish three different generations. The first generation i...

We show that networks of relatively realistic mathematical models for biological neurons can in principle simulate arbitrary feedforward sigmoidal neural nets in a way which has previously not been considered. This new approach is based on temporal coding by single spikes (respectively by the timing of synchronous firing in pools of neurons), rather than on the traditional interpretation of analog variables in terms of firing rates. The resulting new simulation is substantially faster and hence more consistent with experimental results about the maximal speed of information processing in cortical neural systems. As a consequence we can show that networks of noisy spiking neurons are "universal approximators" in the sense that they can approximate with regard to temporal coding any given continuous function of several variables. This result holds for a fairly large class of schemes for coding analog variables by firing times of spiking neurons. Our new proposal for the possible organiza...

This paper describes a novel theoretical framework of how the position of a letter within a string is encoded, the SERIOL model (sequential encoding regulated by inputs to oscillations within letter units). Letter order is represented by a temporal activation pattern across letter units, as is consistent with current theories of information coding based on the precise timing of neural spikes. The framework specifies how this pattern is invoked via an activation gradient that interacts with subthreshold oscillations and how it is decoded via contextual units that activate word units. Using mathematical modeling, this theoretical framework is shown to account for the experimental data from a wide variety of string-processing studies, including hemispheric asymmetries, the optimal viewing position, and positional priming effects

Abstract. We describe a set of preliminary experiments to evolve spiking neural controllers for a vision-based mobile robot. All the evolutionary experiments are carried out on physical robots without human intervention. After discussing how to implement and interface these neurons with a physical robot, we show that evolution finds relatively quickly functional spiking controllers capable of navigating in irregularly textured environments without hitting obstacles using a very simple genetic encoding and fitness function. Neuroethological analysis of the network activity let us understand the functioning of evolved controllers and tell the relative importance of single neurons independently of their observed firing rate. Finally, a number of systematic lesion experiments indicate that evolved spiking controllers are very robust to synaptic strength decay that typically occurs in hardware implementations of spiking circuits. 1 Spiking Neural Circuits The great majority of biological neurons communicate by sending pulses along

this technical difficulty by considering for example in a simplified setting only correlation variables

. Spiking neurons, receiving temporally encoded inputs, can compute radial basis functions (RBFs) by storing the relevant information in their delays. In this paper we show how these delays can be learned using exclusively locally available information (basically the time difference between the pre- and postsynaptic spike). Our approach gives rise to a biologically plausible algorithm for finding clusters in a high dimensional input space with networks of spiking neurons, even if the environment is changing dynamically. Furthermore, we show that our learning mechanism makes it possible that such RBF neurons can perform some kind of feature extraction where they recognize that only certain input coordinates carry relevant information. Finally we demonstrate that this model allows the recognition of temporal sequences even if they are distorted in various ways. 1. Introduction Radial basis functions (RBFs) have turned out to be among the most powerful artificial neural network types, e....

We have investigated the possibility that rapid processing in the visual system could be achieved by using the order of firing in different neurones as a code, rather than more conventional firing rate schemes. Using SPIKENET, a neural net simulator based on integrate-and-fire neurones and in which neurones in the input layer function as analogto-delay converters, we have modeled the initial stages of visual processing. Initial results are extremely promising. Even with activity in retinal output cells limited to one spike per neuron per image (effectively ruling out any form of rate coding), sophisticated processing based on asynchronous activation was nonetheless possible. 1.

A theoretical model for analog computation in networks of spiking neurons with temporal coding is introduced and tested through simulations in GENESIS. It turns out that the use of multiple synapses yields very noise robust mechanisms for analog computations via the timing of single spikes in networks of detailed compartmental neuron models. One arrives in this way at a method for emulating arbitrary Hopfield nets with spiking neurons in temporal coding, yielding new models for associative recall of spatio-temporal firing patterns. We also show that it suffices to store these patterns in the efficacies of excitatory synapses. A corresponding layered architecture yields a refinement of the synfire-chain model that can assume a fairly large set of different stable firing patterns for different inputs.

This memory is embedded in the distribution of channel states in the spike initiation site. The nature and resolution of this memory depend on the size of the channel pool and on the kinetics and number of states of the channels. We hypothesize that the number of channels in the spike initiation zone may be optimized in some sense to give the reliability and accuracy discussed above, together with a short-term memory of the neuron's activity. In this context, it is interesting to mention the work of Marder, Abbott, Turrigiano, Liu, and Golowasch (1996) and Abbott et al. (1996), which demonstrates activity-dependent long-term changes in the properties of intrinsic membrane currents.

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