Synchronization in Spiking Neural Networks
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1 CS 790R Seminar Modeling & Simulation Synchronization in Spiking Neural Networks ~ Lecture 8 ~ René Doursat Department of Computer Science & Engineering University of Nevada, Reno Spring 2005
2 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 2
3 Synchronization in Spiking Neural Networks 1. Temporal Coding Neural networks The neural code Questions of representation 2. Coupled Oscillators 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 3
4 Synchronization in Spiking Neural Networks 1. Temporal Coding Neural networks Structure of neural networks Structure of a neuron Propagation of a spike Model of neural network The neural code Questions of representation 2. Coupled Oscillators 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 4
5 Neural networks Structure of neural networks Cortical layers Medial surface of the brain (Virtual Hospital, University of Iowa) Phenomenon neurons together form... the brain! (and peripheral nervous system) perception, cognition, action emotions, consciousness behavior, learning autonomic regulation: organs, glands ~10 11 neurons in humans Pyramidal neurons and interneurons (Ramón y Cajal 1900) communicate with each other through (mostly) electrical potentials neural activity exhibits specific patterns of spatial and temporal synchronization ( temporal code ) 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 5
6 Neural networks Structure of a neuron Ionic channels opening and closing depolarization of the membrane ( Pyramidal neurons and interneurons (Ramón y Cajal 1900) A typical neuron ( 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 6
7 Neural networks Propagation of a spike ( Propagation of the depolarization along the axon called action potential, or spike ( 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 7
8 Neural networks Model of neural network Schematic neurons (adapted from CS 791S Neural Networks, Dr. George Bebis, UNR) A binary neural network Mechanism each neuron receives signals from many other neurons through its dendrites the signals converge to the soma (cell body) and are integrated if the integration exceeds a threshold, the neuron fires a spike on its axon 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 8
9 Synchronization in Spiking Neural Networks 1. Temporal Coding Neural networks The neural code Rate vs. temporal coding Synchronization and correlations Interest for temporal coding Questions of representation 2. Coupled Oscillators 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 9
10 The neural code Rate vs. temporal coding Rate coding: average firing rate (mean activity) Temporal coding: correlations, possibly delayed von der Malsburg, C. (1981) The correlation theory of brain function. Internal Report 81-2, Max Planck Institute for Biophysical Chemistry, Göttingen. 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 10
11 The neural code Synchronization and correlations high activity rate high activity rate high activity rate low activity rate low activity rate low activity rate 1 and 2 more in sync than 1 and 3 4, 5 and 6 correlated through delays 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 11
12 The neural code Interest for temporal coding Historical motivation for rate coding Adrian (1926): the firing rate of mechanoreceptor neurons in frog leg is proportional to the stretch applied Hubel & Wiesel (1959): selective response of visual cells; e.g., the firing rate is a function of edge orientation rate coding is confirmed in sensory system and primary cortical areas, however increasingly considered insufficient for integrating the information Recent temporal coding boom : a few milestones Abeles (1982, 1991): precise, reproducible spatiotemporal spike rhythms, named synfire chains Gray & Singer (1989): stimulus-dependent synchronization of oscillations in monkey visual cortex O Keefe & Recce (1993): phase coding in rat hippocampus supporting spatial location information Bialek & Rieke (1996, 1997): in H1 neuron of fly, spike timing conveys information about time-dependent input etc., etc. 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 12
13 Synchronization in Spiking Neural Networks 1. Temporal Coding Neural networks The neural code Questions of representation The binding problem Feature binding in cell assemblies Grandmother cells Relational graph format Solving the binding problem with temporal coding A molecular metaphor 2. Coupled Oscillators 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 13
14 Questions of representation The binding problem complex feature cells input = = = = 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 14
15 Questions of representation Feature binding in cell assemblies unstructured lists of features lead to the superposition catastrophe soft big green corners + = hard small red 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 15
16 Questions of representation Grandmother cells = one way to solve the confusion: introduce overarching complex detector cells 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 16
17 Questions of representation Grandmother cells however, this soon leads to an unacceptable combinatorial explosion! 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 17
18 Questions of representation Relational graph format another way to solve the confusion: represent relational information + = 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 18
19 Questions of representation Solving the binding problem with temporal coding complex feature cells input = another way to solve the confusion: represent relational information = = = von der Malsburg, C. (1981) The correlation theory of brain function. 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 19
20 Questions of representation A molecular metaphor cognitive isomers made of the same atomic features C 3 H 8 O 1-propanol 2-propanol 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 20
21 Synchronization in Spiking Neural Networks 1. Temporal Coding Neural networks The neural code Questions of representation 2. Coupled Oscillators 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 21
22 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 22
23 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators Temporal tagging Group synchronization Traveling waves 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 23
24 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators Temporal tagging The binding problem in language A model of semantic binding: SHRUTI Using correlations to implement binding Group synchronization Traveling waves 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 24
25 Temporal tagging The binding problem in language lamp John see give Rex car Mary book talk (a) John gives a book to Mary. (b) Mary gives a book to John. (c)* Book John Mary give. 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 25
26 Temporal tagging A model of semantic binding: SHRUTI John gives a book to Mary.... therefore: Mary can sell the book. Shastri, L. & Ajjanagadde, V. (1993) From simple associations to systematic reasoning. Behavioral and Brain Sciences, 16(3): /28/2005 CS 790R - Synchronization in Spiking Neural Networks 26
27 Temporal tagging Using correlations to implement binding Binding by correlations, or phase-locking 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 27
28 Temporal tagging Using correlations to implement binding Inference by propagation of bindings 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 28
29 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators Temporal tagging Group synchronization The scene segmentation problem Excitatory-inhibitory relaxation oscillator Van der Pol relaxation oscillator Networks of coupled oscillators A model of segmentation by sync: LEGION Traveling waves 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 29
30 Group synchronization The scene segmentation problem Real scene Doursat, Rene ( scene analysis and segmentation is a fundamental aspect of perception ability to group elements of a perceived scene or sensory field into coherent clusters or objects can be addressed with temporal correlations, especially: dynamics of large networks of coupled neural oscillators how does it work?... Schematic scene Wang, DeLiang ( 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 30
31 Group synchronization Excitatory-inhibitory relaxation oscillator w EI w EE N excitatory neurons M inhibitory neurons relaxation oscillators exhibit discontinuous jumps different from sinusoidal or harmonic oscillations w IE Wang, DeLiang ( 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 31
32 Group synchronization Van der Pol relaxation oscillator limit cycle attractor Van der Pol relaxation oscillator Wang, DeLiang ( 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 32
33 Group synchronization Networks of coupled oscillators Wang, DeLiang ( 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 33
34 Group synchronization A model of segmentation by sync: LEGION indirectly coupled through central pacemaker globally coupled locally coupled global inhibitor Terman & D.L. Wang s (1995) LEGION network: Locally Excitatory Globally Inhibitory Oscillator Network ( 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 34
35 Group synchronization A model of segmentation by sync: LEGION Wang, D. L. & Terman, D. (1995) Locally excitatory globally inhibitory oscillator networks. IEEE Trans. Neural Net., 6: /28/2005 CS 790R - Synchronization in Spiking Neural Networks 35
36 Group synchronization A model of segmentation by sync: LEGION Wang, D. L. & Terman, D. (1997) Image segmentation based on oscillatory correlation. Neural Computation, 9: ,1997 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 36
37 Group synchronization A model of segmentation by sync: LEGION Wang, D. L. & Terman, D. (1997) Image segmentation based on oscillatory correlation. Neural Computation, 9: ,1997 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 37
38 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators Temporal tagging Group synchronization Traveling waves Phase gradients, instead of plateaus Wave propagation and collision 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 38
39 Traveling waves Phase gradients, instead of plateaus ϕ π ϕ π -π x -π x 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 39
40 Traveling waves Wave propagation and collision t = 5 t = 18 t = x 64 lattice of locally coupled Bonhoeffer-van der Pol oscillators Doursat, R. & Petitot, J. (2005) Dynamical Systems and Cognitive Linguistics: Toward an Active Morphodynamical Semantics. IJCNN 05, to appear in Neural Networks. 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 40
41 Traveling waves Wave propagation and collision t = 5 t = 22 t = 34 Two cross-coupled, mutually inhibiting lattices of coupled oscillators Doursat, R. & Petitot, J. (2005) Dynamical Systems and Cognitive Linguistics: Toward an Active Morphodynamical Semantics. IJCNN 05, to appear in Neural Networks. 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 41 (a) (b)
42 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators Temporal tagging Group synchronization Traveling waves 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 42
43 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 43
44 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators 3. Synfire Chains The compositionality of cognition A model of synfire self-organization Simulations of synfire growth Synfire chain bibliography 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 44
45 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators 3. Synfire Chains The compositionality of cognition Compositionality in language Compositionality in vision Structural bonds A model of synfire self-organization Simulations of synfire growth Synfire chain bibliography 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 45
46 The compositionality of cognition Compositionality in language lamp John see give Rex car Mary book talk (a) John gives a book to Mary. (b) Mary gives a book to John. (c)* Book John Mary give. 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 46
47 The compositionality of cognition Compositionality in language John S give R O book Mary language is a building block construction game 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 47
48 The compositionality of cognition Compositionality in language John S give O S Rgive John O book book R Mary Mary language is a building block construction game 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 48
49 The compositionality of cognition Compositionality in vision ( 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 49
50 The compositionality of cognition Structural bonds protein structures provide a metaphor for the mental objects or building blocks of cognition ( 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 50
51 The compositionality of cognition Structural bonds 3-D interactions are replaced with n-d spatiotemporal patterns and long-term/fast connections 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 51
52 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators 3. Synfire Chains The compositionality of cognition A model of synfire self-organization Focusing of the innervation A simple binary model The growth of a synfire chain Crystallization from seed neurons Dynamic composition of two chains Simulations of synfire growth Synfire chain bibliography 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 52
53 A model of synfire self-organization Focusing of the innervation selective stabilization (Changeux & Danchin, 1976) retinotopic projection (Willshaw & von der Malsburg, 1976) 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 53
54 A model of synfire self-organization A simple binary model Neuronal dynamics: fast McCulloch & Pitts 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 54
55 A model of synfire self-organization A simple binary model Synaptic dynamics: fast Hebbian cooperation 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 55
56 A model of synfire self-organization A simple binary model Synaptic dynamics: competition 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 56
57 A model of synfire self-organization The growth of a synfire chain... 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 57
58 A model of synfire self-organization The growth of a synfire chain synchronous pools start creating new pools ahead of them before reaching maturity, making a beveled head (along propagation axis) Doursat (1991) An epigenetic development model of the nervous system. In: A contribution to the study of representations in the nervous system and in artificial neural networks, Ph.D. dissertation, Université Paris VI. (Supervised by Bienenstock, E.) 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 58
59 A model of synfire self-organization Crystallization from seed neurons Doursat (1991) 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 59
60 A model of synfire self-organization Dynamics composition of two chains zipper-matching Doursat (1991) 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 60
61 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators 3. Synfire Chains The compositionality of cognition A model of synfire self-organization Simulations of synfire growth Network activity Network self-organization Cross-correlograms Synaptic evolution Synfire braids Synfire chain bibliography 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 61
62 Simulations of synfire growth Network activity Doursat (1991) 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 62
63 Simulations of synfire growth Network self-organization Doursat (1991) 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 63
64 Simulations of synfire growth Network self-organization Doursat (1991) 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 64
65 Simulations of synfire growth Cross-correlograms Doursat (1991) 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 65
66 Simulations of synfire growth Synaptic evolution Doursat (1991) 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 66
67 Simulations of synfire growth Synfire braids Doursat (1991) 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 67
68 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators 3. Synfire Chains The compositionality of cognition A model of synfire self-organization Simulations of synfire growth Synfire chain bibliography Origins (Abeles) Growth & compositionality models (Bienenstock, Doursat) Other experiments and models 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 68
69 Synfire chain bibliography Origins (Abeles) M. Abeles, Hebrew University, Jerusalem Abeles (1982) Local cortical circuits: An Electrophysiological Study. Springer-Verlag. Abeles (1991) Corticonics: Neural Circuits of the Cerebral Cortex. Cambridge University Press. Abeles, Hayon & Lehmann (2004) Modeling compositionality by dynamic binding of synfire chains. Journal of Computational Neuroscience, 17: /28/2005 CS 790R - Synchronization in Spiking Neural Networks 69
70 Synfire chain bibliography Growth & compositionality models (Bienenstock, Doursat) E. Bienenstock, CNRS & Brown University Doursat (1991) An epigenetic development model of the nervous system. In: A contribution to the study of representations in the nervous system and in artificial neural networks, Ph.D. dissertation, Université Paris VI. (Supervised by Bienenstock, E.) Bienenstock (1995) A model of neocortex. Network, 6: Bienenstock & Geman (1995) Compositionality in neural systems. In: The Handbook of Brain Theory and Neural Networks, M. Arbib ed, Bradford Books/MIT Press, pp Bienenstock (1996) Composition. In: A. Aertsen & V. Braitenberg (Eds.), Brain Theory (pp ). Elsevier. Bienenstock and Doursat (2005) The Hebbian development of synfire chains. (Article in preparation.) 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 70
71 Synfire chain bibliography Other experiments and models A. Aertsen, Universität Freiburg Diesmann, Gewaltig & Aertsen (1999) Stable propagation of synchronous spiking in cortical neural networks. Nature, 402: The stable propagation of precisely synchronized APs happens despite noisy dynamics. C. Koch, Caltech Marsalek, Koch & Maunsell (1997) On the relationship between synaptic input and spike output jitter in individual neurons. Proc. Natl. Acad. Sci. USA, 94: Preservation of highly accurate spike timing in cortical networks (e.g., macaque MT area), explained by analysis of output/input jitter in I&F model. 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 71
72 Synfire chain bibliography Other experiments and models R. Yuste, Columbia University Mao, Hamzei-Sichani, Aronov, Froemke & Yuste (2001) Dynamics of spontaneous activity in neocortical slices. Neuron, 32: Recording of spontaneous activity with statistically significant delayed correlations in slices mouse visual cortex, using calcium imaging Ikegaya, Aaron, Cossart, Aronov, Lampl, Ferster & Yuste (2004) Synfire chains and cortical songs: temporal modules of cortical activity. Science, 304: Cortical songs in vitro and in vivo (mouse and cat visual cortex) E. Izhikevich, The Neurosciences Institute, San Diego Izhikevich, Gally & Edelman (2004) Spike-timing dynamics of neuronal groups. Cerebral Cortex, 14: Self-organization of spiking neurons in a biologically detailed smallworld model of the cortex 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 72
73 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators 3. Synfire Chains The compositionality of cognition A model of synfire self-organization Simulations of synfire growth Synfire chain bibliography 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 73
74 Synchronization in Spiking Neural Networks 1. Temporal Coding 2. Coupled Oscillators 3. Synfire Chains 4/28/2005 CS 790R - Synchronization in Spiking Neural Networks 74
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