Hebbian learning and spiking neurons

A correlation-based ~‘‘Hebbian’’ ! learning rule at a spike level with millisecond resolution is formulated, mathematically analyzed, and compared with learning in a firing-rate description. The relative timing of presynaptic and postsynaptic spikes influences synaptic weights via an asymmetric ‘‘learning window.’’ A differential equation for the learning dynamics is derived under the assumption that the time scales of learning and neuronal spike dynamics can be separated. The differential equation is solved for a Poissonian neuron model with stochastic spike arrival. It is shown that correlations between input and output spikes tend to stabilize structure formation. With an appropriate choice of parameters, learning leads to an intrinsic normalization of the average weight and the output firing rate. Noise generates diffusion-like spreading of synaptic weights. @S1063-651X~99!02804-4#

[1]  Heinz Zemanek,et al.  Kybernetik , 1964, Elektron. Rechenanlagen.

[2]  C. Malsburg,et al.  How patterned neural connections can be set up by self-organization , 1976, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[3]  Roman Bek,et al.  Discourse on one way in which a quantum-mechanics language on the classical logical base can be built up , 1978, Kybernetika.

[4]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[5]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[6]  M. Konishi,et al.  Segregation of stimulus phase and intensity coding in the cochlear nucleus of the barn owl , 1984, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[7]  F. Verhulst,et al.  Averaging Methods in Nonlinear Dynamical Systems , 1985 .

[8]  R Linsker,et al.  From basic network principles to neural architecture: emergence of orientation-selective cells. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[9]  R Linsker,et al.  From basic network principles to neural architecture: emergence of spatial-opponent cells. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[10]  L. Optican,et al.  Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. III. Information theoretic analysis. , 1987, Journal of neurophysiology.

[11]  B. Gustafsson,et al.  Long-term potentiation in the hippocampus using depolarizing current pulses as the conditioning stimulus to single volley synaptic potentials , 1987, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[12]  Teuvo Kohonen,et al.  Self-Organization and Associative Memory , 1988 .

[13]  D. O. Hebb,et al.  The organization of behavior , 1988 .

[14]  J. Hemmen,et al.  The Hebb rule: storing static and dynamic objects in an associative neural network , 1988 .

[15]  W. Singer,et al.  Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[16]  William Bialek,et al.  Reading a Neural Code , 1991, NIPS.

[17]  John H. Byrne,et al.  Neural Models of Plasticity: Experimental and Theoretical Approaches , 1989 .

[18]  Kenneth D. Miller,et al.  Derivation of Linear Hebbian Equations from a Nonlinear Hebbian Model of Synaptic Plasticity , 1990, Neural Computation.

[19]  Michael I. Jordan,et al.  Advances in Neural Information Processing Systems 30 , 1995 .

[20]  Georg Dorffner,et al.  Konnektionismus in Artificial Intelligence und Kognitionsforschung. Proceedings 6. Österreichische Artificial Intelligence-Tagung (KONNAI), Salzburg, Österreich, 18. bis 21. September 1990 , 1990, Austrian Conference on Artificial Intelligence.

[21]  D. Mackay,et al.  Analysis of Linsker's application of Hebbian rules to linear networks , 1990 .

[22]  T. H. Brown,et al.  Biophysical model of a Hebbian synapse. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[23]  M. Konishi,et al.  A circuit for detection of interaural time differences in the brain stem of the barn owl , 1990, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[24]  C. Koch,et al.  Synaptic background activity influences spatiotemporal integration in single pyramidal cells. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[25]  Idan Segev,et al.  The Impact of Parallel Fiber Background Activity on the Cable Properties of Cerebellar Purkinje Cells , 1992, Neural Computation.

[26]  W. Singer,et al.  Oscillatory Neuronal Responses in the Visual Cortex of the Awake Macaque Monkey , 1992, The European journal of neuroscience.

[27]  K. Obermayer,et al.  Statistical-mechanical analysis of self-organization and pattern formation during the development of visual maps. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[28]  Catherine E. Carr,et al.  Processing of Temporal Information in the Brain , 1993 .

[29]  T. Bliss,et al.  A synaptic model of memory: long-term potentiation in the hippocampus , 1993, Nature.

[30]  C. Gielen,et al.  Neural computation and self-organizing maps, an introduction , 1993 .

[31]  William R. Softky,et al.  The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[32]  Kenneth D. Miller,et al.  The Role of Constraints in Hebbian Learning , 1994, Neural Computation.

[33]  Michael N. Shadlen,et al.  Noise, neural codes and cortical organization , 1994, Current Opinion in Neurobiology.

[34]  D. Debanne,et al.  Asynchronous pre- and postsynaptic activity induces associative long-term depression in area CA1 of the rat hippocampus in vitro. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[35]  D. Baylor,et al.  Concerted Signaling by Retinal Ganglion Cells , 1995, Science.

[36]  J. J. Hopfield,et al.  Pattern recognition computation using action potential timing for stimulus representation , 1995, Nature.

[37]  Wulfram Gerstner,et al.  A neuronal learning rule for sub-millisecond temporal coding , 1996, Nature.

[38]  R. Christopher deCharms,et al.  Primary cortical representation of sounds by the coordination of action-potential timing , 1996, Nature.

[39]  M. Meister.  Multineuronal codes in retinal signaling. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[40]  H. Sompolinsky,et al.  Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity , 1996, Science.

[41]  Paul Antoine Salin,et al.  Cyclic AMP Mediates a Presynaptic Form of LTP at Cerebellar Parallel Fiber Synapses , 1996, Neuron.

[42]  K. I. Blum,et al.  Functional significance of long-term potentiation for sequence learning and prediction. , 1996, Cerebral cortex.

[43]  V. Han,et al.  Synaptic plasticity in a cerebellum-like structure depends on temporal order , 1997, Nature.

[44]  C. Köppl.  Phase Locking to High Frequencies in the Auditory Nerve and Cochlear Nucleus Magnocellularis of the Barn Owl, Tyto alba , 1997, The Journal of Neuroscience.

[45]  H. Markram,et al.  Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EPSPs , 1997, Science.

[46]  J. Leo van Hemmen,et al.  Development of spatiotemporal receptive fields of simple cells: I. Model formulation , 1997, Biological Cybernetics.

[47]  T. Sejnowski,et al.  Synchronous oscillatory activity in sensory systems: new vistas on mechanisms , 1997, Current Opinion in Neurobiology.

[48]  J. Leo van Hemmen,et al.  Development of spatiotemporal receptive fields of simple cells: II. Simulation and analysis , 1997, Biological Cybernetics.

[49]  Michael J. Berry,et al.  The structure and precision of retinal spike trains. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[50]  Martin Stemmler.  Models of Neural Networks III: Association, Generalization, and Representation.E. Domany , J. L. van Hemmen , K. Schulten , 1997 .

[51]  R. Tsien,et al.  Synergies and Coincidence Requirements between NO, cGMP, and Ca2+ in the Induction of Cerebellar Long-Term Depression , 1997, Neuron.

[52]  B. Sakmann,et al.  Calcium dynamics in single spines during coincident pre- and postsynaptic activity depend on relative timing of back-propagating action potentials and subthreshold excitatory postsynaptic potentials. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[53]  Günther Palm,et al.  Synaptic Delay Learning in Pulse-Coupled Neurons , 1998, Neural Computation.

[54]  Wulfram Gerstner,et al.  Extracting Oscillations: Neuronal Coincidence Detection with Noisy Periodic Spike Input , 1998, Neural Computation.

[55]  Terrence J. Sejnowski,et al.  Constrained Optimization for Neural Map Formation: A Unifying Framework for Weight Growth and Normalization , 1998, Neural Computation.

[56]  Li I. Zhang,et al.  A critical window for cooperation and competition among developing retinotectal synapses , 1998, Nature.

[57]  D. Wilkin,et al.  Neuron , 2001, Brain Research.