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.
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Bouganis, A., Shanahan, M.: Training a spiking neural network to control a 4-dof robotic arm based on spike timing-dependent plasticity. In: Proceedings of the 2010 International Joint Conference on Neural Networks (IJCNN), pp 1–8 (2010)
Bower, J.M., Beeman, D.: The Book of GENESIS, Exploring Realistic Neural Models with the GEneral NEural SImulation System. Internet Edition (2003)
Cai, G., Chen, B.M., Lee, T.H.: Unmanned Rotocraft Systems. Advances in Industrial Control. Springer, Berlin (2011)
Destexhe, A., Mainen, Z.F., Sejnowski, T.J.: Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. J. Comput. Neurosci. 3(1), 195–230 (1994)
Doi, S., Onoda, Y., Kumagai, S.: Parameter estimation of various Hodgkin-Huxley-type neuronal models using a gradient-descent learning method. In: SICE 2002, Proceedings of the 41st SICE Annual Conference, vol. 3, pp 1685–1688 (2002)
Doya, K., Selverston, A.I.: A learning algorithm for Hodgkin-Huxley type neuron models. In: Proceedings of 1993 International Joint Conference on Neural Networks, 1993. IJCNN ’9293-Nagoya., vol. 2, pp 1108–1111 (1993)
Doya, K., Selverston, A.I., Rowat, P.F.: A Hodgkin-Huxley type neuron model that learns slow non-spike oscillations. In: NIPS’9293, pp 566–573 (1993)
Feller, W.: An Introduction to Probability Theory and its Applications, volume 1, chapter VII. Wiley, New York (1968)
Gerstner, W., Kistler, W.: Spiking Neuron Models. Single Neurons. Populations, Plasticity, Cambridge (2000)
Gugała, K., Figas, A., Jurkowlaniec, A., Rybarczyk, A.: Parallel simulation of stochastic denritic neurons using nvidia gpus with cuda c. In: 2011 Proceedings of the 18th International Conference Mixed Design of Integrated Circuits and Systems (MIXDES) (2011)
Gugała, K., Świetlicka, A., Burdajewicz, M., Rybarczyk, A.: Random number generation system improving simulations of stochastic models of neural cells. Computing 95(1), 259–275 (2013)
Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Phys. 117(4), 500–544 (1952)
Hopfield, J.J.: Neurodynamics of mental exploration. Proc. Natl. Acad. Sci. USA 107(4), 1648–1653 (2010)
Izhikevich, E.M.: Simple model of spiking neurons. IEEE Trans. Neural Netw. 14(6), 1569–1572 (2003)
Kapela, R., Świetlicka, A., Kolanowski, K., Pochmara, J., Rybarczyk, A.: A set of dynamic artificial neural networks for robot sensor failure detection. In: 11th International Workshop on Robot Motion and Control 2017 (RoMoCo), pp 199–204 (2017)
Keener, J., Sneyd, J.: Mathematical Physiology, volume 8 of Mathematical Biology. Springer, Berlin (1998)
Koch, C.: Biophysics of Computation: Information Processing in Single Neurons, chapter, VI. Oxford University Press, New York (1999)
Kolanowski, K., Świetlicka, A., Kapela, R., Pochmara, J., Rybarczyk, A.: Multisensor data fusion using elman neural networks. Appl. Math. Comput. 319, 236–244 (2018)
Kolanowski, K., Świetlicka, A., Majchrzycki, M., Gugała, K., Karoń, I., Rybarczyk, A.: Nine-axis imu sensor fusion using the ahrs algorithm and neural networks. In: ISTET International Symposiumon Theoretical Electrical Engineering, Pilsen, Czech Republic, pp III–23–III–24, 24th–26th June 2013 (2013)
Maass, W.: Networks of spiking neurons: the third generation of neural networks models. Neural Netw. 10, 1659–1671 (1997)
Saffari, A.: Unknown environment representation for mobile robot using spiking neural networks. Trans. Eng. Comput. Technol. 6, 49–52 (2005)
Schneidman, E., Freedman, B., Segev, I.: Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comput. 10, 1679–1703 (1998)
Świetlicka, A.: Trained stochastic model of biological neural network used in image processing task. Appl. Math. Comput. 267, 716–726 (2015)
Świetlicka, A., Gugała, K., Jurkowlaniec, A., Śniatała, P., Rybarczyk, A.: The stochastic, markovian, Hodgkin-Huxley type of mathematical model of the neuron. Neural Netw. World 25(1), 219–239 (2015)
Świetlicka, A., Gugała, K., Karoń, I., Kolanowski, K., Majchrzycki, M., Rybarczyk, A.: Gradient method of learning for stochastic kinetic model of neuron. In: ISTET International Symposiumon Theoretical Electrical Engineering, Pilsen, Czech Republic, pages III–17–III–18, 24th – 26th June 2013 (2013)
Świetlicka, A., Gugała, K., Pedrycz, W., Rybarczyk, A.: Development of the deterministic and stochastic markovian model of a dendritic neuron. Biocybernetics Biomed. Eng. 37, 201–216 (2017)
Świetlicka, A., Kolanowski, K., Kapela, R., Galicki, M., Rybarczyk, A.: Investigation of generalization ability of a trained stochastic kinetic model of neuron. Appl. Math. Comput. 319, 115–124 (2018)
Webb, A., Davies, S., Lester, D.: Spiking neural PID controllers. Neural Inf. Process Lect. Notes Comput. Sci 7064, 259–267 (2011)
Wu, Q.X., McGinnity, T.M., Maguire, L., Cai, R., Chen, M.: A visual attention model based on hierarchical spiking neural networks. Neurocomputing 16, 3–12 (2013)
Yanduo, Z., Kun, W.: Application of liquid state machines in robot path planning. J. Comput. 4(11), 1182–1186 (2009)
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Świetlicka, A., Kolanowski, K. & Kapela, R. Training the Stochastic Kinetic Model of Neuron for Calculation of an Object’s Position in Space. J Intell Robot Syst 98, 615–626 (2020). https://doi.org/10.1007/s10846-019-01068-0
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DOI: https://doi.org/10.1007/s10846-019-01068-0