Coherence detection in a spiking neuron via Hebbian learning
Section snippets
Coding scheme
We will represent (as in [2]) the signal Si at synapse i by the sum of Dirac pulses located at the spiking times tik drawn from the lists of spikes Γi (see Fig. 1-left).Synfire patterns are generated in analogy with the response of a retina to flashed binary images. The input of the synapses is characterized as the output of single-synapse IF neurons responding to a specific binary input. This response may be described as the sum of two random point processes with different
Definition of the cost function
Based on neurophysiological studies, we set the following principles:
- (1)
the learning is associated with a spiking response: the nth learning step occurs at the nth output firing time tn,
- (2)
to discriminate between the different input patterns, the output voltage should be close to a winner-take-all configuration: the potential of the winning neuron (which we index j=jn) should be above threshold whereas other neurons should be hyperpolarized,
- (3)
economy of the total synaptic efficacy and current use
Numerical results
We implemented this model using discrete versions of the differential equations (forward Euler method) on a MATLAB system.
Conclusion
We have presented an original gradient descent method to find a learning rule for a layer of spiking neurons. The simplicity of the rule gives a new insight into the comprehension of the mechanism behind the observed STDHP. Further work is done for the detection of asynchronous patterns.
However, this study should be extended to more realistic spike trains (e.g. bursts), account for more complex behavior (e.g. facilitation and depression) and may be extended to population of neurons and
Acknowledgements
This work has been initiated during the EU Advanced Course in Computational Neuroscience. LP wish to thank its organizers, the teachers, the course-mates and my tutor, S. Panzeri.
Laurent Perrinet is a Ph.D. student in Computational Neuroscience, under the direction of Manuel Samuelides at the CERT-ONERA, Toulouse and in narrow collaboration with the team of Simon Thorpe at the CERCO-CNRS, Toulouse. He works on theoretical and simulated aspects of neural coding, especially on the implication of fast-categorization visual experiments. Working areas span learning (especially in spike timing dependant plasticity) and the statistics of natural images.
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Cited by (3)
Emergence of filters from natural scenes in a sparse spike coding scheme
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2023, Brain Sciences
Laurent Perrinet is a Ph.D. student in Computational Neuroscience, under the direction of Manuel Samuelides at the CERT-ONERA, Toulouse and in narrow collaboration with the team of Simon Thorpe at the CERCO-CNRS, Toulouse. He works on theoretical and simulated aspects of neural coding, especially on the implication of fast-categorization visual experiments. Working areas span learning (especially in spike timing dependant plasticity) and the statistics of natural images.