this paper we propose that the irregular ISI arises as a consequence of a specific problem that cortical neurons must solve: the problem of dynamic range or gain control. Cortical neurons receive 3000--10,000 synaptic contacts, 85% of which are asymmetric and hence presumably excitatory (Peters, 1987; Braitenberg and Schuz, 1991). More than half of these contacts are thought to arise from neurons within a 100--200 #m radius of the target cell, reflecting the stereotypical columnar organization of neocortex. Because neurons within a cortical column typically share similar physiological properties, the conditions that excite one neuron are likely to excite a considerable fraction of its afferent input as well (Mountcastle, 1978; Peters and Sethares, 1991), creating a scenario in which saturation of the neuron's firing rate could easily occur. This problem is exacerbated by the fact that EPSPs from individual axons appear to exert substantial impact on the membrane potential (Mason et al., 1991; Otmakhov Received Sept. 15, 1997; revised Feb. 25, 1998; accepted March 3, 1998.

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...

This article describes the concepts and strategies that have guided the design and implementation of this simulator, with emphasis on those features that are particularly relevant to its most efficient use. 1.1 The problem domain

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...

It is not clear how information related to cognitive or psychological processes is carried by or represented in the responses of single neurons. One provocative proposal is that precisely timed spike patterns play a role in carrying such information. This would require that these spike patterns have the potential for carrying information that would not be available from other measures such as spike count or latency. We examined exactly timed (1-ms precision) triplets and quadruplets of spikes in the stimulus-elicited responses of lateral geniculate nucleus (LGN) and primary visual cortex (V1) neurons of the awake fixating rhesus monkey. Large numbers of these precisely timed spike patterns were found. Information theoretical analysis showed that the precisely timed spike patterns carried only information already available from spike count, suggesting that the number of precisely timed spike

We show that spike timing adds to the information content of spike trains for transiently presented stimuli but not for comparable steady-state stimuli, even if the latter elicit transient responses. Contrast responses of 22 single neurons in macaque V1 to periodic presentation of steady-state stimuli (drifting sinusoidal gratings) and transient stimuli (drifting edges) of optimal spatiotemporal parameters were recorded extracellularly. The responses were analyzed for contrast-dependent clustering in spaces determined by metrics sensitive to the temporal structure of spike trains. Two types of metrics, costbased spike time metrics and metrics based on Fourier harmonics of the response, were used. With both families of metrics, temporal coding of contrast is lacking in responses to drifting sinusoidal gratings of most (simple and complex) V1 A prevailing view of neural coding is that the meaningful signal

The distribution of responses of sensory neurons to ecological stimulation has been proposed to be designed to maximize information transmission, which according to a simple model would imply an exponential distribution of spike counts in a given time window. We have used recordings from inferior temporal cortex neurons responding to quasi-natural visual stimulation (presented using a video of everyday lab scenes, and a large number of static images of faces and natural scenes) to assess the validity of this exponential model and to develop an alternative simple model of spike count distributions. We find that the exponential model has to be rejected in 84% of cases (at the P ! 0:01 level). A new model, which accounts for the firing rate distribution found in terms of slow and fast variability in the inputs which produce neuronal activation, is rejected statistically in only 16% of cases. Finally, we show that the neurons are moderately efficient at transmitting information, ...

How does a neuron vary its mean output firing rate if the input changes from random to coherent activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidence detection properties of an integrate-and-fire neuron. We derive an expression indicating how coincidence detection depends on neuronal parameters. Specifically, (i) we show how coincidence detection depends on the shape of the postsynaptic response function, the number of synapses, and the input statistics, and (ii) we demonstrate that there is an optimal threshold. Our considerations can be used to predict from neuronal parameters whether and to what extent a neuron can act as a coincidence detector and thus can convert a temporal code into a rate code. Physik-Department der TU Munchen (T35), D-85747 Garching bei Munchen, Germany y Swiss Federal Institute of Technology, Center of Neuromimetic Systems, EPFL-DI, CH-1015 Lausanne, Switz...

We investigated the information about stimulus velocity inherent in the membrane signals of two types of directionally selective, motion-sensitive interneurons in the fly visual system. One of the cells, the H1-cell, is a spiking neuron, whereas the other, the HS-cell, encodes sensory information mainly by a graded shift of its membrane potential. Using a pseudo-random velocity waveform by which a visual grating is moving along the horizontal axis of the eye, both cell types follow the stimulus velocity at higher precision than in response to a step-like velocity function. To measure how much information about the stimulus velocity is preserved in the cellular responses, we calculated the coherence between the stimulus and the neural signals as a function of stimulus frequency. At frequencies up to �10 Hz motion information is well contained in the electrical signals of HS- and H1-cells: For HS-cells the coherence value amounts to �70%, and for H1-cells this value is �60%. Com-Deciphering the neural code nerve cells are using to signal information within the nervous system represents a major prerequisite for our understanding of the brain in terms of informationprocessing machinery. In particular it has been questioned to what extent information is represented in the precise time of occurrence of individual action potentials (de Ruyter van Steveninck

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...