Random Neural Networks with Synchronized Interactions

Large-scale distributed systems, such as natural neuronal and artificial systems, have many local interconnections, but they often also have the ability to propagate information very fast over relatively large distances. Mechanisms that enable such behavior include very long physical signaling paths and possibly saccades of synchronous behavior that may propagate across a network. This letter studies the modeling of such behaviors in neuronal networks and develops a related learning algorithm. This is done in the context of the random neural network (RNN), a probabilistic model with a well-developed mathematical theory, which was inspired by the apparently stochastic spiking behavior of certain natural neuronal systems. Thus, we develop an extension of the RNN to the case when synchronous interactions can occur, leading to synchronous firing by large ensembles of cells. We also present an O(N3) gradient descent learning algorithm for an N-cell recurrent network having both conventional excitatory-inhibitory interactions and synchronous interactions. Finally, the model and its learning algorithm are applied to a resource allocation problem that is NP-hard and requires fast approximate decisions.

[1]  E. Gelende.  Réseaux stochastiques ouverts avec clients négatifs et positifs, et réseaux neuronaux , 1989 .

[2]  Erol Gelenbe,et al.  Traffic and video quality with adaptive neural compression , 1996, Multimedia Systems.

[3]  Erol Gelenbe,et al.  Random Neural Networks with Multiple Classes of Signals , 1999, Neural Computation.

[4]  Erol Gelenbe.  Dealing with software viruses: A biological paradigm , 2007, Inf. Secur. Tech. Rep..

[5]  Erol Gelenbe,et al.  Stability of the Random Neural Network Model , 1990, Neural Computation.

[6]  Erol Gelenbe,et al.  Random Neural Networks with Negative and Positive Signals and Product Form Solution , 1989, Neural Computation.

[7]  Erol Gelenbe,et al.  Learning neural networks for detection and classification of synchronous recurrent transient signals , 1998, Signal Process..

[8]  Erol Gelenbe,et al.  Neural network methods for volumetric magnetic resonance imaging of the human brain , 1996 .

[9]  Erol Gelenbe,et al.  Area-based results for mine detection , 2000, IEEE Trans. Geosci. Remote. Sens..

[10]  Erol Gelenbe.  Réseaux neuronaux aléatoires stables , 1990 .

[11]  Zhi-Hong Mao,et al.  Function Approximation by Random Neural Networks with a Bounded Number of Layers , 2006 .

[12]  Erol Gelenbe,et al.  Learning in the multiple class random neural network , 2002, IEEE Trans. Neural Networks.

[13]  Erol Gelenbe,et al.  Learning in the Recurrent Random Neural Network , 1992, Neural Computation.

[14]  Pik-Yin Lai,et al.  Connectivities and synchronous firing in cortical neuronal networks. , 2004, Physical review letters.

[15]  Ferhan Pekergin,et al.  Dynamical random neural network approach to the traveling salesman problem , 1993, Proceedings of IEEE Systems Man and Cybernetics Conference - SMC.

[16]  Erol Gelenbe,et al.  The Random Neural Network Model for Texture Generation , 1992, Int. J. Pattern Recognit. Artif. Intell..

[17]  Erol Gelenbe,et al.  Low bit-rate video compression with neural networks and temporal subsampling , 1996, Proc. IEEE.

[18]  A Kawana,et al.  Periodic synchronized bursting and intracellular calcium transients elicited by low magnesium in cultured cortical neurons. , 1993, Journal of neurophysiology.

[19]  Y Yarom,et al.  Electrotonic Coupling Interacts with Intrinsic Properties to Generate Synchronized Activity in Cerebellar Networks of Inhibitory Interneurons , 1999, The Journal of Neuroscience.

[20]  Erol Gelenbe,et al.  Task Assignment and Transaction Clustering Heuristics for Distributed Systems , 1997, Inf. Sci..

[21]  Erol Gelenbe,et al.  Measurement and performance of a cognitive packet network , 2001, Comput. Networks.

[22]  Erol Gelenbe,et al.  Image processing with the random neural network , 1998, Electronic Imaging.

[23]  Ronen Segev,et al.  Formation of electrically active clusterized neural networks. , 2003, Physical review letters.

[24]  Erol Gelenbe,et al.  Steady-state solution of probabilistic gene regulatory networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Erol Gelenbe,et al.  Video quality and traffic QoS in learning-based subsampled and receiver-interpolated video sequences , 2000, IEEE Journal on Selected Areas in Communications.

[26]  E. Gelenbe.  G-networks by triggered customer movement , 1993 .

[27]  Erol Gelenbe,et al.  Self-aware networks and QoS , 2004, Proceedings of the IEEE.

[28]  Y Shapira,et al.  Observations and modeling of synchronized bursting in two-dimensional neural networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Anoop Ghanwani,et al.  Improved Neural Heuristics for Multicast Routing , 1997, IEEE J. Sel. Areas Commun..

[30]  Zhi-Hong Mao,et al.  Function approximation with spiked random networks , 1999, IEEE Trans. Neural Networks.

[31]  Kazuo Kobayashi,et al.  Functional synapse formation between cultured neurons of rat cerebral cortex. Block by a protein kinase inhibitor which does not permeate the cell membrane.:Block by a Protein Kinase Inhibitor which does not Permeate the Cell Membrane , 1988 .

[32]  P. König,et al.  Correlated firing in sensory-motor systems , 1995, Current Opinion in Neurobiology.

[33]  E Gelenbe,et al.  Oscillatory corticothalamic response to somatosensory input. , 1998, Bio Systems.

[34]  Erol Gelenbe,et al.  Wafer surface reconstruction from top–down scanning electron microscope images , 2004 .

[35]  E. Gelenbe.  Une généralisation probabiliste du problème SAT , 1992 .

[36]  Erol Gelenbe,et al.  A class of genetic algorithms with analytical solution , 1997, Robotics Auton. Syst..