Gerstner, W. and van Hemmen, J. L. (1994). How to describe neuronal activity: Spikes, rates, or assemblies? In Cowan, J. D., Tesauro, G., and Alspector, J., editors, Advances in Neural Information Processing Systems, volume 6, pages 463--470. Morgan Kaufmann Publishers, Inc.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... in order to reach the computational power of a real neural system [Maass, 1997b] As a result of some recent studies, there is a broad agreement that the brain uses simultaneously both mean firing rate as well as spike timing encoding schemes in order to represent information and transfer signals [Gerstner and van Hemmen, 1994, Sejnowski, 1995] Artificial neural networks of spiking neurons which employ the mechanism of precise spike timing for encoding information have been shown to be computationally more powerful than the classical connectionist models [Maass, 1997b] Furthermore, there are several temporal encoding ....

Gerstner, W. and van Hemmen, J. L. (1994). How to describe neuronal activity: Spikes, rates, or assemblies? In Cowan, J. D., Tesauro, G., and Alspector, J., editors, Advances in Neural Information Processing Systems, volume 6, pages 463--470. Morgan Kaufmann Publishers, Inc.

....u to neuron v transforms the output spike train of neuron u (which is of a type as illustrated in Fig. 1 b) into a train of EPSP s or IPSP s in neuron v. One usually assumes that neuron u only causes EPSP s or only causes IPSP s in other neurons v. According to the spike response model (see [Gerstner and van Hemmen, 1994] and [Gerstner, 1998] one can model the response of the membrane potential of neuron v at time t to a spike train with spikes at times t 1 ; t 2 ; from a presynaptic neuron u by a function of the form response vu (t) X i w vu (t) Delta vu (t Gamma t i ) One assumes in this ....

Gerstner, W. and van Hemmen, L. (1994). How to describe neuronal activity: spikes, rates or assemblies? In Advances in Neural Information Processing Systems, volume 6, pages 463--470. Morgan Kaufmann.

....that result in this way are interpreted as the output of N . The complexity of a computation in an SNN is evaluated by counting each spike as a computation step. This formal model is essentially a noise free version of the spike response model as described in [Gerstner 91] Gerstner 92] and [Gerstner 94] One uses the response function u;v in order to describe the potential change or postsynaptic potential ) w u;v Delta u;v (t Gamma s) at the trigger zone of neuron v at time t, as a result of a firing of neuron u at time s. For simplicity the resting value of the membrane potential at the ....

W. Gerstner, J. L. van Hemmen. (1994) How to describe neuronal activity: spikes, rates, or assemblies? Advances in Neural Information Processing Systems, vol. 6, Morgan Kaufmann (San Mateo), 463-470.

....this will increase the slope of the membrane potential P n i=1 h i (t) at the time when it crosses the threshold. As a consequence the output of this neuron in temporal coding will become more noiserobust, both from the point of view of the common mathematical models for noise in spiking neurons (Gerstner, 1994, Maass, 1995, 1996) and from the point of view of experimental results (Mainen, 1995) In an even more noisy setting when synapses and or neurons fail with significant probability, one may replace each single neuron v in our construction by a pool P v of neurons with approximately identical ....

Gerstner, W. and van Hemmen, J. L. (1994) How to describe neuronal activity: spikes, rates, or assemblies? Advances in Neural Information Processing Systems, vol. 6, Morgan Kaufmann (San Mateo) 463-470.

.... value is used to indicate the state of a unit whose inputs have not all yet been available at the beginning of a given computation step (e.g. for units on the l th layer of a net at computation steps t l) The completely different model of a network of m stochastic spiking neurons (see e.g. [Gerstner, van Hemmen, 1994] or [Maass, 1996] is also a special case of our general framework. In this case one wants to set Omega sp : S l j=1 [0; T ) j [ fnot firingg) m , where T 0 is a sufficiently large constant so that it suffices to consider only the firing history of the network during a preceding time ....

W. Gerstner, J. L. van Hemmen, How to describe neuronal activity: spikes, rates or assemblies? Advances in Neural Information Processing Systems 6, 463--470. Morgan Kaufmann, San Mateo, CA, 1994.

.... activation function fl : R [0; fl] defined by fl (y) 8 : 0 ; if y 0 y ; if 0 y fl fl ; if y fl : As a model for a spiking neuron we take the common model of a leaky integrate and fire neuron with noise, respectively the somewhat more general spike response model of (Gerstner, van Hemmen, 1994). The only specific assumption that is needed for the construction in this article is that postsynaptic potentials can be described (respectively approximated) by a linear function during some initial segment. Actually, the constructions of this article appear to be of interest even if this ....

.... systematic noise ) In a simpler model for a noisy spiking neuron one assumes that a neuron v fires exactly at those time points t when P noisy v (t) reaches from below the value Theta noisy v (t Gamma t 0 ) We consider in this article a biologically more realistic model, where as in (Gerstner, van Hemmen, 1994) the size of the difference P noisy v (t) Gamma Theta noisy v (t Gamma t 0 ) just governs the probability that neuron v fires. The choice of the exact firing times is left up to some unknown stochastic processes, and it may for example occur that v does not fire in a time interval I during ....

[Article contains additional citation context not shown here]

Gerstner, W. and van Hemmen, J. L. (1994) How to describe neuronal activity: spikes, rates, or assemblies? Advances in Neural Information Processing Systems, vol. 6, Morgan Kaufmann (San Mateo) 463-470.

....out that result in this way are interpreted as the output of N . The complexity of a computation in an SNN is evaluated by counting each spike as a computation step. This formal model is essentially a noise free version of the spike response model as described in [Gerstner 91] Gerstner 92] and [Gerstner 94] One uses the response function u;v in order to describe the potential change or postsynaptic potential w u;v Delta u;v (t Gamma s) at the trigger zone of neuron v at time t, as a result of a firing of neuron u at time s. For simplicity the resting value of the membrane potential at the ....

W. Gerstner, J. L. van Hemmen. (1994) How to describe neuronal activity: spikes, rates, or assemblies? Advances in Neural Information Processing Systems, vol. 6, Morgan Kaufmann (San Mateo), 463-470.

.... segmentation (for an overview see Gerstner et al. 1993) Very recently one has also started to build artificial neural nets that model networks of spiking neurons (see e.g. Murray and Tarassenko, 1994, Watts, 1994) Some aspects of these models have also been studied analytically (see e.g. Gerstner and van Hemmen, 1994, Gerstner, 1995) but almost nothing is known about their computational complexity (see Judd and Aihara, 1993, for some first results in this direction) In this article we investigate a simple formal model SNN for networks of spiking neurons that allows us to model the most important timing ....

....selects a single one of the incoming stimulations of maximal size, and determines on the basis of that stimulation whether it should fire. Consequently, computations in this model PPN proceed quite differently from computations in models of spiking neurons such as the spike response model of Gerstner and van Hemmen, 1994, or the here considered model SNN. Judd and Aihara, 1993, construct PPN s which can simulate Turing machines that use at most a constant number s of cells on their tapes, where s is bounded by the number of neurons in the simulating PPN. However a Turing machine with a constant bound s on its ....

W. Gerstner, J. L. van Hemmen. (1994) How to describe neuronal activity: spikes, rates, or assemblies? appears in: Advances in Neural Information Processing Systems, vol. 6, Morgan Kaufmann: 463-470.

....their computation on single firing events. In this article we consider spiking neuron networks (SNN s) as introduced by Maass [6] where each neuron is basically a leaky integrateand fire neuron and can be considered as a noise free version of the spike response model by Gerstner and van Hemmen [4]. These SNN s are besides their biological realism also because of their computational power of great interest. In [7, 5] it has been shown that SNN s are computationally more powerful than McCulloch Pitts neurons (i.e. threshold gates) and also than sigmoidal gates. It has turned out that espe ....

Gerstner, W. and van Hemmen, L.H.: How to describe neuronal activity: spikes, rates, or assemblies? Advances in Neural Information Processing Systems 6, Morgan Kaufmann, San Mateo (1994) 463--470.

....their computation on single firing events. In this article we consider spiking neuron networks (SNN s) as introduced by Maass [6] where each neuron is basically a leaky integrate and fire neuron and can be considered as a noise free version of the spike response model by Gerstner and van Hemmen [4]. These SNN s are besides their biological realism also because of their computational power of great interest. In [7, 5] it has been shown that SNN s are computationally more powerful than McCulloch Pitts neurons (i.e. threshold gates) and also than sigmoidal gates. It has turned out that ....

Gerstner, W. and van Hemmen, L.H.: How to describe neuronal activity: spikes, rates, or assemblies? Advances in Neural Information Processing Systems 6, Morgan Kaufmann, San Mateo (1994) 463--470.

....is a further step towards a more realistic description of unsupervised learning in biological neural systems. 1 Introduction In the area of modelling information processing in biological neural systems, there is an ongoing debate about which essentials have to be taken into account (see e.g. [3,13,11,9]) Discrete models, such as threshold gates or McCullochPitts neurons, are undoubtedly very simplistic descriptions of biological neurons. Models with real valued output, such as the sigmoidal gate, where analogue values are interpreted as firing rates of biological neurons, are more suitable for ....

Gerstner, W., van Hemmen, L. H.: How to describe neuronal activity: spikes, rates, or assemblies? In Advances in Neural Information Processing Systems 6, Morgan Kaufmann, San Mateo (1994) 463--470.

.... memory, binding, and pattern segmentation (for an overview see Gerstner et al. 1992) Very recently one has also started to build artificial neural nets that model networks of spiking neurons (see e.g. Watts, 1994) Some aspects of these models have also been studied analytically (see e.g. Gerstner and van Hemmen, 1994), but almost nothing is known about their computational complexity (see Judd and Aihara, 1993, for some first results in this direction) In this article we investigate a simple formal model SNN for networks of spiking neurons that allows us to model the most important timing phenomena of neural ....

....time in a small interval around time i Delta . The model SNN that we consider in this article is very closely related to the model that was previously considered by Buhmann and Schulten, 1986, and especially to the spike response model of Gerstner, 1991, Gerstner, Ritz, van Hemmen, 1992, and Gerstner, van Hemmen, 1994. Similarly as in Buhmann and Schulten, 1986, we consider in this article only the deterministic case (which corresponds to the limit case fi 1 in the stochastic spike response model of Gerstner et al. However in contrast to these preceding models we do not fix particular (necessarily somewhat ....

[Article contains additional citation context not shown here]

W. Gerstner, J. L. van Hemmen. (1994) How to describe neuronal activity: spikes, rates, or assemblies?. Advances in Neural Information Processing Systems, vol. 6, Morgan Kaufmann: 463-470.

.... value is used to indicate the state of a unit whose inputs have not all yet been available at the beginning of a given computation step (e.g. for units on the l th layer of a net at computation steps t l) The completely different model of a network of m stochastic spiking neurons (see e.g. [Gerstner, van Hemmen, 1994] or [Maass, 1997] is also a special case of our general framework. In this case one wants to set Omega sp : S l j=1 [0; T ) j [ fnot firingg) m , where T 0 is a sufficiently large constant so that it suffices to consider only the firing history of the network during a preceding time ....

W. Gerstner, J. L. van Hemmen, How to describe neuronal activity: spikes, rates or assemblies? Advances in Neural Information Processing Systems 6, 463--470. Morgan Kaufmann, San Mateo, CA, 1994.

....u to neuron v transforms the output spike train of neuron u (which is of a type as illustrated in Fig. 1 b) into a train of EPSP s or IPSP s in neuron v. One usually assumes that neuron u only causes EPSP s or only causes IPSP s in other neurons v. According to the spike response model (see [Gerstner and van Hemmen, 1994] and [Gerstner, 1998] one can model the response of the membrane potential of neuron v at time t to a spike train with spikes at times t 1 ; t 2 ; from a presynaptic neuron u by a function of the form response vu (t) X i w vu (t) Delta vu (t Gamma t i ) 5 . neuron v time ....

Gerstner, W. and van Hemmen, L. (1994). How to describe neuronal activity: spikes, rates or assemblies? In Advances in Neural Information Processing Systems, volume 6, pages 463--470. Morgan Kaufmann.

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