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  On computing Boolean functions by a spiking neuron (1998) [11 citations — 2 self]

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by Michael Schmitt
Annals of Mathematics and Artificial Intelligence
http://www.ruhr-uni-bochum.de/lmi/mschmitt/boolspiking.ps.gz
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Abstract:

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 McCulloch-Pitts neurons) and sigma-pi 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 sigma-pi 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 single-cell models with substantially larger computational capabilities. 1

Citations

363 Perceptrons: An Introduction To Computational Geometry – Minsky, Papert - 1969
135 Threshold logic and its applications – Muroga - 1971
86 Networks of Spiking Neurons: The Third Generation of Neural Network Models. Neural Networks 10(9):1659 – Maass - 1997
78 Time structure of the activity in neural network models – Gerstner - 1995
50 Lower Bounds for the Computational Power of Networks of Spiking Neurons – Maass - 1996
41 Fast Sigmoidal Networks via Spiking Neurons. Neural computation 9(2):279 – Maass - 1997
29 Analogue Neural VLSI: A Pulse Stream Approach – Murray, Tarassenko - 1994
25 Aggregation of inequalities in integer programming – CHVÁTAL, HAMMER - 1977
16 Threshold numbers and threshold completions – Hammer, Ibaraki, et al. - 1981
13 On the complexity of learning for spiking neurons with temporal coding, Information and Computation 153 – Maass, Schmitt - 1999
12 On defining sets of vertices of the hypercube by linear inequalities – Jeroslow - 1975
11 On the complexity of learning for a spiking neuron – Maass, Schmitt - 1997
10 Asymptotics of the logarithm of the number of threshold functions of the algebra of logic – Zuev - 1989
6 On the relevance of time in neural computation and learning – Maass - 1997
4 de Ruyter van Steveninck. Spikes: exploring the neural code – Rieke, Warland, et al. - 1996
4 Estimating the efficiency of threshold representations of Boolean functions – Zuev, Lipkin - 1988
2 Single-cell models, in: The Handbook of Brain Theory and Neural – Softky, Koch - 1995
1 The threshold order of a Boolean function, Discrete Applied Mathematics 31 – Wang, Williams - 1991
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