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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...
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...
Surfing a Spike Wave down the Ventral Stream
"... Numerous theories of neural processing, often motivated by experimental observations, have explored the computational properties of neural codes based on the precise or relative occurrence of spikes in a spike train. Spiking neuron models and theories however, as well as their experimental counter ..."
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Cited by 38 (7 self)
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Numerous theories of neural processing, often motivated by experimental observations, have explored the computational properties of neural codes based on the precise or relative occurrence of spikes in a spike train. Spiking neuron models and theories however, as well as their experimental counterparts, have generally been limited to the simulation or observation of isolated neurons, isolated spike trains, or reduced neural populations. Such theories would therefore seem inappropriate to capture the properties of a neural code relying on temporal spike patterns distributed across large neuronal populations. Here we report a range of computer simulations and theoretical considerations that were designed to explore the possibilities of such a code and its relevance for visual processing. In a single, unified framework where the relation between stimulus saliency and spike asynchrony plays the central role, we describe how the ventral stream of the visual system could process natural input scenes and extract meaningful information, both rapidly and reliably. The first wave of spikes generated in the retina in response to a visual stimulation carries information explicitly in its spatiotemporal structure. This spike wave, propagating through a hierarchy of visual areas, is regenerated at each processing stage, where its temporal structure can be modified by (i) the selectivity of the cortical neurons, (ii) lateral interactions and (iii) topdown attentional influences from higher order cortical areas. The concept of temporal asynchrony within a wave of single spikes allows a unique theoretical framework to address the fundamental and complementary notions of neural information coding and representation, visual saliency and attention. 1.
Neural differentiation of expected reward and risk in human subcortical structures, Neuron 51
, 2006
"... In decisionmaking under uncertainty, economic studies emphasize the importance of risk in addition to expected reward. Studies in neuroscience focus on expected reward and learning rather than risk. We combined functional imaging with a simple gambling task to vary expected reward and risk simultan ..."
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Cited by 35 (2 self)
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In decisionmaking under uncertainty, economic studies emphasize the importance of risk in addition to expected reward. Studies in neuroscience focus on expected reward and learning rather than risk. We combined functional imaging with a simple gambling task to vary expected reward and risk simultaneously and in an uncorrelated manner. Drawing on financial decision theory, we modeled expected reward as mathematical expectation of reward, and risk as reward variance. Activations in dopaminoceptive structures correlated with both mathematical parameters. These activations differentiated spatially and temporally. Temporally, the activation related to expected reward was immediate, while the activation related to risk was delayed. Analyses confirmed that our paradigm minimized confounds from learning, motivation, and salience. These results suggest that the primary task of the dopaminergic system is to convey signals of upcoming stochastic rewards, such as expected reward and risk, beyond its role in learning, motivation, and salience.
Reconstruction of Natural Scenes from Ensemble Responses in the Lateral Geniculate Nucleus
 J. Neurosci
, 1999
"... critical test of our understanding of sensory coding, however, is to take an opposite approach: to reconstruct sensory inputs from recorded neuronal responses. The decoding approach can provide an objective assessment of what and how much information is available in the neuronal responses. Although ..."
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Cited by 30 (3 self)
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critical test of our understanding of sensory coding, however, is to take an opposite approach: to reconstruct sensory inputs from recorded neuronal responses. The decoding approach can provide an objective assessment of what and how much information is available in the neuronal responses. Although the f unction of the brain is not necessarily to reconstruct sensory inputs faithfully, these studies may lead to new insights into the f unctions of neuronal circuits in sensory processing (Rieke et al., 1997). The decoding approach has been used to study several sensory systems (Bialek et al., 1991; Theunissen and Miller, 1991; Rieke et al., 1993, 1997; Roddey and Jacobs, 1996; Warland et al., 1997; Dan et al., 1998). Most of these studies aimed to reconstruct temporal signals from the response of a single neuron (Bialek et al., 1991; Rieke et al., 1993, 1995; Roddey and Jacobs, 1996) or a small number of neurons (Warland et al., 1997). An important challenge in understanding the mammalia
Encoding of visual motion information and reliability in spiking and graded potential neurons
 J Neurosci
, 1997
"... We investigated the information about stimulus velocity inherent in the membrane signals of two types of directionally selective, motionsensitive interneurons in the fly visual system. One of the cells, the H1cell, is a spiking neuron, whereas the other, the HScell, encodes sensory information ma ..."
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Cited by 18 (1 self)
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We investigated the information about stimulus velocity inherent in the membrane signals of two types of directionally selective, motionsensitive interneurons in the fly visual system. One of the cells, the H1cell, is a spiking neuron, whereas the other, the HScell, encodes sensory information mainly by a graded shift of its membrane potential. Using a pseudorandom 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 steplike 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 H1cells: For HScells the coherence value amounts to �70%, and for H1cells this value is �60%. ComDeciphering 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
On computation with pulses
 Information and Computation
, 1999
"... We explore the computational power of formal models for computation with pulses. Such models are motivated by realistic models for biological neurons, and by related new types of VLSI (\pulse stream VLSI"). In preceding work it was shown that the computational power of formal models for computa ..."
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Cited by 14 (0 self)
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We explore the computational power of formal models for computation with pulses. Such models are motivated by realistic models for biological neurons, and by related new types of VLSI (\pulse stream VLSI"). In preceding work it was shown that the computational power of formal models for computation with pulses is quite high if the pulses arriving at a computational unit have an approximately linearly rising or linearly decreasing initial segment. This property is satis ed by common models for biological neurons. On the other hand several implementations of pulse stream VLSI employ pulses that are approximately piecewise constant (i.e. step functions). In this article we investigate the relevance of the shape of pulses in formal models for computation with pulses. It turns out that the computational power drops signi cantly if one replaces pulses with linearly rising or decreasing initial segments by piecewise constant pulses. We provide an exact characterization of the latter model in terms of a weak version of a random access machine (RAM). We also compare the language recognition capability of a recurrent version of this model with that of deterministic nite automata and Turing machines. 1
Neural representation of probabilistic information
 Neural Computation
, 2003
"... It has been proposed that populations of neurons process information in terms of probability density functions (PDFs) of analog variables. Such analog variables range, for example, from target luminance and depth on the sensory interface to eye position and joint angles on the motor output side. The ..."
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Cited by 14 (0 self)
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It has been proposed that populations of neurons process information in terms of probability density functions (PDFs) of analog variables. Such analog variables range, for example, from target luminance and depth on the sensory interface to eye position and joint angles on the motor output side. The requirement that analog variables must be processed leads inevitably to a probabilistic description, while the limited precision and lifetime of the neuronal processing units leads naturally to a population representation of information. We show how a timedependent probability density ρ(x; t) over variable x, residing in a specified function space of dimension D, may be decoded from the neuronal activities in a population as a linear combination of certain decoding functions φi(x), with coefficients given by the N firing rates ai(t) (generally with D << N). We show how the neuronal encoding process may be described by projecting a set of complementary encoding functions ˆ φi(x) on the probability density ρ(x; t), and passing the result through a rectifying nonlinear activation function. We show how both encoders ˆ φi(x) and decoders φi(x) may be determined by minimizing cost functions that quantify the inaccuracy of the representation. Expressing a given computation in terms of manipulation and transformation of probabilities, we show how this representation leads to a neural circuit that can carry out the required computation within a consistent Bayesian framework, with the synaptic weights being explicitly generated in terms of encoders, decoders, conditional probabilities, and priors.
Phaseresponse curves give the responses of neurons to transient inputs
 Journal of Neurophysiology
, 2005
"... You might find this additional information useful... This article cites 65 articles, 45 of which you can access free at: ..."
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Cited by 13 (0 self)
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You might find this additional information useful... This article cites 65 articles, 45 of which you can access free at:
An Efficient Implementation of Sigmoidal Neural Nets in Temporal Coding with Noisy Spiking Neurons
, 1995
"... 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 ..."
Abstract

Cited by 11 (4 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...