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Networks of Spiking Neurons: The Third Generation of Neural Network Models
 Neural Networks
, 1997
"... 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 powe ..."
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Cited by 152 (12 self)
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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...
Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking
 NEURAL COMPUTATION
, 2000
"... An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrateandfire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analy ..."
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Cited by 139 (24 self)
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An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrateandfire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analyzed in terms of the noise level and transmission delay and a bifurcation diagram is derived. The response of a population of noisy integrateandfire neurons to an input current of small amplitude is calculated and characterized by a linear filter L. The stability of perfectly synchronized `locked' solutions is analyzed.
Lower Bounds for the Computational Power of Networks of Spiking Neurons
 Neural Computation
, 1995
"... We investigate the computational power of a formal model for networks of spiking neurons. It is shown that simple operations on phasedifferences between spiketrains provide a very powerful computational tool that can in principle be used to carry out highly complex computations on a small network o ..."
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Cited by 53 (10 self)
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We investigate the computational power of a formal model for networks of spiking neurons. It is shown that simple operations on phasedifferences between spiketrains provide a very powerful computational tool that can in principle be used to carry out highly complex computations on a small network of spiking neurons. We construct networks of spiking neurons that simulate arbitrary threshold circuits, Turing machines, and a certain type of random access machines with real valued inputs. We also show that relatively weak basic assumptions about the response and thresholdfunctions of the spiking neurons are sufficient in order to employ them for such computations. 1 Introduction and Basic Definitions There exists substantial evidence that timing phenomena such as temporal differences between spikes and frequencies of oscillating subsystems are integral parts of various information processing mechanisms in biological neural systems (for a survey and references see e.g. Kandel et al., ...
What Matters in Neuronal Locking?
"... Present and permanent address: PhysikDepartment der TU Munchen Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessa ..."
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Cited by 45 (10 self)
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Present and permanent address: PhysikDepartment der TU Munchen Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessary and in the limit of a large number of interacting neighbors also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire. If the postsynaptic potential is decreasing, oscillations are bound to be unstable. This is a kind of locking theorem and boils down to a subtle interplay of axonal delays, postsynaptic potentials, and refractory behavior. The theorem also allows for mixtures of excitatory and inhibitory interactions. On the basis of the locking theorem we present a simple geometric method to verify existence and local stability of a coherent oscillation. 2 1
Networks of spiking neurons can emulate arbitrary hopfield nets in temporal coding
 Neural Systems
, 1997
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Pattern Separation and Synchronization in Spiking Associative Memories and Visual Areas
 Neural Networks
, 2001
"... Scene analysis in the mammalian visual system, conceived as a distributed and parallel process, faces the socalled binding problem. As a possible solution, the temporal correlation hypothesis has been suggested and implemented in phasecoding models. ..."
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Cited by 26 (12 self)
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Scene analysis in the mammalian visual system, conceived as a distributed and parallel process, faces the socalled binding problem. As a possible solution, the temporal correlation hypothesis has been suggested and implemented in phasecoding models.
Scene Segmentation by Spike Synchronization in Reciprocally Connected Visual Areas I. Local Effects of Cortical Feedback
 Biological Cybernetics
, 2002
"... To investigate scene segmentation in the visual system we present a model of two reciprocally connected visual areas using spiking neurons. Area P corresponds to the orientation selective subsystem of the primary visual cortex, while the central visual area C is modeled as associative memory represe ..."
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Cited by 21 (4 self)
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To investigate scene segmentation in the visual system we present a model of two reciprocally connected visual areas using spiking neurons. Area P corresponds to the orientation selective subsystem of the primary visual cortex, while the central visual area C is modeled as associative memory representing stimulus objects according to Hebbian learning. Without feedback from area C, a single stimulus results in relatively slow and irregular activity, synchronized only for neighboring patches (slow state), while in the complete model activity is faster with enlarged synchronization range (fast state). Presenting a superposition of several stimulus objects, scene segmentation happens on a time scale of hundreds of milliseconds by alternating epochs of the slow and fast state, where neurons representing the same object are simultaneously in the fast state. Correlation analysis reveals synchronization on different time scales as found in experiments (T,C,H peaks). On the fast time scale (T peaks, gamma frequency range), recordings from two sites coding either different or the same object lead to correlograms that are either at or exhibit oscillatory modulations with a central peak. This is in agreement with experimental findings while standard phase coding models would predict shifted peaks in the case of different objects.
Role of the Temporal Domain for Response Selection and Perceptual Binding
, 1997
"... Most cognitive functions are based on highly parallel and distributed information processing by the brain. A paradigmatic example is provided by the vertebrate visual system where numerous cortical areas have been described which analyse different types of visual information. At present, it is uncle ..."
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Cited by 20 (3 self)
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Most cognitive functions are based on highly parallel and distributed information processing by the brain. A paradigmatic example is provided by the vertebrate visual system where numerous cortical areas have been described which analyse different types of visual information. At present, it is unclear how information can be integrated and how coherent representational states can be established in such distributed systems. We suggest that this socalled ‘binding problem ’ may be solved in the temporal domain. The hypothesis is that synchronization of neuronal discharges can serve for the integration of distributed neurons into cell assemblies and that this process may underlie the selection of perceptually and behaviourally relevant information. We review experimental results, mainly obtained in the visual system, which support this temporal binding hypothesis.
Extracting Oscillations: Neuronal Coincidence Detection with Noisy Periodic Spike Input
, 1998
"... How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidencedetection properties of an integra ..."
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Cited by 20 (6 self)
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How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidencedetection properties of an integrateandfire neuron. We derive an expression indicating how coincidence detection depends on neuronal parameters. Specifically, we show how coincidence detection depends on the shape of the postsynaptic response function, the number of synapses, and the input statistics, and 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.
On the computational complexity of networks of spiking neurons
 Advances in Neural Information Processing Systems
, 1995
"... 2 Abstract We investigate the computational power of a formal model for networks of spiking neurons. It is shown that simple operations on phasedifferences between spiketrains provide a very powerful computational tool that can in principle be used to carry out highly complex computations on a sma ..."
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Cited by 19 (7 self)
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2 Abstract We investigate the computational power of a formal model for networks of spiking neurons. It is shown that simple operations on phasedifferences between spiketrains provide a very powerful computational tool that can in principle be used to carry out highly complex computations on a small network of spiking neurons. We construct networks of spiking neurons that simulate arbitrary threshold circuits, Turing machines, and a certain type of random access machines with real valued inputs. We also show that relatively weak basic assumptions about the response and thresholdfunctions of the spiking neurons are sufficient in order to employ them for such computations. Furthermore we prove upper bounds for the computational power of networks of spiking neurons with arbitrary piecewise linear responseand thresholdfunctions, and show that they are with regard to realtime simulations computationally equivalent to a certain type of random access machine, and to recurrent analog neural nets with piecewise linear activation functions. In addition we give corresponding results for networks of spiking neurons with a limited timing precision, and we prove upper and lower bounds for the VCdimension and pseudodimension of networks of spiking neurons. 3 1