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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 138 (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...
Pointtopoint connectivity between neuromorphic chips using addressevents
 IEEE Trans. Circuits Syst. II
, 2000
"... Abstract — I discuss connectivity between neuromorphic chips, which use the timing of fixedheight, fixedwidth, pulses to encode information. Addressevents—log2 (N)bit packets that uniquely identify one of N neurons—are used to transmit these pulses in realtime on a randomaccess, timemultiplex ..."
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Cited by 89 (17 self)
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Abstract — I discuss connectivity between neuromorphic chips, which use the timing of fixedheight, fixedwidth, pulses to encode information. Addressevents—log2 (N)bit packets that uniquely identify one of N neurons—are used to transmit these pulses in realtime on a randomaccess, timemultiplexed, communication channel. Activity is assumed to consist of neuronal ensembles—spikes clustered in space and in time. I quantify tradeoffs faced in allocating bandwidth, granting access, and queuing, as well as throughput requirements, and conclude that an arbitered channel design is the best choice. I implement the arbitered channel with a formal design methodology for asynchronous digital VLSI CMOS systems, after introducing the reader to this topdown synthesis technique. Following the evolution of three generations of designs, I show how the overhead of arbitrating, and encoding and decoding, can be reduced in area (from N to √ N) by organizing neurons into rows and columns, and reduced in time (from log2 (N) to 2) by exploiting locality in the arbiter tree and in the row–column architecture, and clustered activity. Throughput is boosted by pipelining and by reading spikes in parallel. Simple techniques that reduce crosstalk in these mixed analog–digital systems are described.
Communication neuronal ensembles between neuromorphic chips
 In preparation
"... Abstract. I describe an interchip communication system that reads out pulse trains from a 64 64 array of neurons on one chip, and transmits them to corresponding locations in a 64 64 array of neurons on a second chip. It uses a randomaccess, timemultiplexed, asynchronous digital bus to transmit lo ..."
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Cited by 58 (5 self)
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Abstract. I describe an interchip communication system that reads out pulse trains from a 64 64 array of neurons on one chip, and transmits them to corresponding locations in a 64 64 array of neurons on a second chip. It uses a randomaccess, timemultiplexed, asynchronous digital bus to transmit log2 Nbit addresses that uniquely identify each of the N neurons in the sending population. A peak transmission rate of 2.5MSpikes/s is achieved by pipelining the operation of the channel. I discuss how the communication channel design is optimized for sporadic stimulustriggered activity which causes some small subpopulation to re in synchrony, by adopting an arbitered, eventdriven architecture. I derive the bandwidth required to transmit this neuronal ensemble, without temporal dispersion, in terms of the number of neurons, the probability that a neuron is part of the ensemble, and the degree of synchrony.
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 (11 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., ...
Fast Sigmoidal Networks via Spiking Neurons
 Neural Computation
, 1997
"... 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 ..."
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Cited by 52 (8 self)
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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...
A burstmode wordserial addressevent LinkIII: Analysis and test results
 IEEE Trans. Circuits Syst. I, Reg. Papers
, 2004
"... Abstract—We present a transmitter for a scalable multipleaccess interchip link that communicates binary activity between twodimensional arrays fabricated in deep submicrometer CMOS. Transmission is initiated by active cells but cells are not read individually. An entire row is read in parallel; t ..."
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Cited by 25 (7 self)
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Abstract—We present a transmitter for a scalable multipleaccess interchip link that communicates binary activity between twodimensional arrays fabricated in deep submicrometer CMOS. Transmission is initiated by active cells but cells are not read individually. An entire row is read in parallel; this increases communication capacity with integration density. Access is random but not inequitable. A row is not reread until all those waiting are serviced; this increases parallelism as more of its cells become active in the mean time. Row and column addresses identify active cells but they are not transmitted simultaneously. The row address is followed sequentially by a column address for each active cell; this cuts pad count in half without sacrificing capacity. We synthesized an asynchronous implementation by performing a series of program decompositions, starting from a highlevel description. Links using this design have been implemented successfully in
On the Complexity of Learning for Spiking Neurons with Temporal Coding
, 1999
"... Spiking neurons axe models for the computational units in biological neural systems where information is considered to be encoded mainly in the temporal patterns of their activity. In a network of spiking neurons a new set of paxameters becomes relevant which has no counterpaxt in traditional neu ..."
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Cited by 18 (4 self)
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Spiking neurons axe models for the computational units in biological neural systems where information is considered to be encoded mainly in the temporal patterns of their activity. In a network of spiking neurons a new set of paxameters becomes relevant which has no counterpaxt in traditional neural network models: the time that a pulse needs to travel through a connection between two neurons (also known as delay of a connection). It is known that these delays axe tuned in biological neural systems through a vaxiety of mechanisms. In this
SelfOrganization of Spiking Neurons Using Action Potential Timing
, 1998
"... We propose a mechanism for unsupervised learning in networks of spiking neurons which is based on the timing of single firing events. Our results show that a topology preserving behaviour quite similar to that of Kohonen's selforganizing map can be achieved using temporal coding. In contrast to pre ..."
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Cited by 18 (0 self)
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We propose a mechanism for unsupervised learning in networks of spiking neurons which is based on the timing of single firing events. Our results show that a topology preserving behaviour quite similar to that of Kohonen's selforganizing map can be achieved using temporal coding. In contrast to previous approaches, which use rate coding, the winner among competing neurons can be determined fast and locally. Our model is a further step towards a more realistic description of unsupervised learning in biological neural systems. Furthermore, it may provide a basis for fast implementations in pulsed VLSI. Keywords Selforganizing map, spiking neurons, temporal coding, unsupervised learning. I. 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. [1], [2], [3], [4]). Discrete models, such as threshold gates or McCullochPitts neurons, are undoubtedly very simplis...
On the Complexity of Learning for a Spiking Neuron
, 1997
"... ) Wolfgang Maass and Michael Schmitt Abstract Spiking neurons are models for the computational units in biological neural systems where information is considered to be encoded mainly in the temporal patterns of their activity. They provide a way of analyzing neural computation that is not captu ..."
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Cited by 16 (7 self)
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) Wolfgang Maass and Michael Schmitt Abstract Spiking neurons are models for the computational units in biological neural systems where information is considered to be encoded mainly in the temporal patterns of their activity. They provide a way of analyzing neural computation that is not captured by the traditional neuron models such as sigmoidal and threshold gates (or "Perceptrons"). We introduce a simple model of a spiking neuron that, in addition to the weights that model the plasticity of synaptic strength, also has variable transmission delays between neurons as programmable parameters. For coding of input and output values two modes are taken into account: binary coding for the Boolean and analog coding for the realvalued domain. We investigate the complexity of learning for a single spiking neuron within the framework of PAClearnability. With regard to sample complexity, we prove that the VCdimension is \Theta(n log n) and, hence, strictly larger than that of a thresho...
On Computing Boolean Functions by a Spiking Neuron
 Annals of Mathematics and Artificial Intelligence
, 1998
"... Computations by spiking neurons are performed using the timing of action potentials. We investigate the computational power of a simple model for such a spiking neuron in the Boolean domain by comparing it with traditional neuron models such as threshold gates (or McCullochPitts neurons) and sigma ..."
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Cited by 16 (2 self)
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Computations by spiking neurons are performed using the timing of action potentials. We investigate the computational power of a simple model for such a spiking neuron in the Boolean domain by comparing it with traditional neuron models such as threshold gates (or McCullochPitts neurons) and sigmapi units (or polynomial threshold gates). In particular, we estimate the number of gates required to simulate a spiking neuron by a disjunction of threshold gates and we establish tight bounds for this threshold number. Furthermore, we analyze the degree of the polynomials that a sigmapi unit must use for the simulation of a spiking neuron. We show that this degree cannot be bounded by any fixed value. Our results give evidence that the use of continuous time as a computational resource endows singlecell models with substantially larger computational capabilities. 1 Introduction Biological neurons communicate by sending spikes among themselves. A spike is a discrete event in continuous ti...