# Feedforward and Feedback Control in Neural Networks

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Excitation and inhibition are two of the fundamental interactions between neurons. In neural networks, these processes allow for competition and learning, and lead to the diverse variety of output behaviors found in biology. Two simple network control systems based on these interactions are the feedforward and feedback inhibitory networks. Feedforward inhibition limits activity at the output depending on the *input* *activity*. Feedback networks induce inhibition at the output as a result of activity at the *output *[1].

Contributed by: Oliver K. Ernst (June 2015)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: example of feedforward inhibition, where the repeated spiking of neuron 2 causes continual inhibition in neuron 3

Snapshot 2: example of feedback inhibition, where spiking activity in neuron 3 leads to later self-inhibition in neuron 3, which in turn allows for excitation again

Snapshot 3: fine-tuning of the synaptic currents may be used to explore the transition between inhibitory and excitatory realms

The networks in this Demonstration consist of neurons modeled by Hodgkin–Huxley kinetics, connected with either -mediated excitatory synapses or -mediated inhibitory synapses. The first neuron in the network is depolarized with a constant current of adjustable amplitude . Spikes in presynaptic cells trigger postsynaptic currents

,

,

where and are the reversal potentials, is the potential of the postsynaptic cell, is the fraction of active ion channels, and are the maximum conductances that you can vary. A simple model for describing the dynamics of is a two-state (open or closed) system, described by

,

where is the concentration of neurotransmitters (in this case either or ), and and are the rate constants. As a simplification, it is assumed that a spike in the presynaptic cell triggers a pulse of neurotransmitter during which the concentration is constant, , for a duration of , and is zero otherwise. In this case, an analytic expression for exists [2]. The values of the rate constants used were , , , and [2].

References

[1] R. C. O'Reilly, Y. Munakata, M. J. Frank, T. E. Hazy, and Contributors. *Computational Cognitive Neuroscience*, 1st ed., WikiBook, 2012. http://ccnbook.colorado.edu.

[2] A. Destexhe, Z. F. Mainen, and T. J. Sejnowski, "An Efficient Method for Computing Synaptic Conductances Based on a Kinetic Model of Receptor Binding," *Neural Computation, *6(1), 1994 pp. 14–18. doi:10.1162/neco.1994.6.1.14.

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