Abstract
In this paper we focus on the stochastic kinetic extension of the well-known Hodgkin-Huxley model of a biological neuron. We show the gradient descent algorithm for training of the neuron model. In comparison with training of the Hodgkin-Huxley model we use only three weights instead of nine. We show that the trained stochastic kinetic model gives equally good results as the trained Hodgkin-Huxley model, while we gain on more concise mathematical description of the training procedure. The trained stochastic kinetic model of neuron is tested in solving the problem of approximation, where for the approximated function the membrane potential obtained using different models of a biological neuron was chosen. Additionally, we present a simple application, in which the trained models of neuron connected with the outputs of a recurrent neural network form a system, which is used to calculate the Euler angles of an object’s position in space, based on linear and angular acceleration, direction and the magnitude of Earth’s magnetic field.
Highlights
Neuron models which precisely describe the processes that take place on the membrane can be expressed in the form commonly used for artificial neural networks
The biological neuron model consists of a current input and a voltage output which is coupled with the input; there are parameters that can be treated as weights [5,6,7] and sigmoid functions that determine the activation functions
As the target of the training we use the potential obtained from different models of a biological neuron
Summary
Neuron models which precisely describe the processes that take place on the membrane (in particular the HodgkinHuxley model and its kinetic extensions) can be expressed in the form commonly used for artificial neural networks. Researchers use models of a biological neuron in a number of applications, very often in the field of automatics and robotics These models exhibit only the spiking nature of a neural cell, without taking into account all of the ionic processes that take place in the neuron. J Intell Robot Syst (2020) 98:615–626 we will consider the stochastic kinetic model of biological neuron, which besides the spiking nature of neuron, takes into account ionic processes that take place on the membrane. In this paper we present the gradient descent algorithm for training the stochastic kinetic model of neuron. The same algorithm of gradient descent was already used for the training of a model of a dendritic structure of the biological neuron given with the following equation [12]:. We will provide a short description of the Hodgkin-Huxley neuron model and its deterministic and stochastic kinetic extensions
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