The document provides an introduction to spiking neural networks (SNNs) and neuromorphic computing. It discusses the characteristics and advantages of SNNs, including their spatio-temporal nature, asynchronous processing, sparsity, and energy efficiency. It also covers basic neuroscience concepts like neurons, action potentials, synaptic plasticity, and learning rules like STDP. Common SNN models and neural encoding schemes are described. Examples of SNN applications in visual processing and pattern generation are presented. Finally, neuromorphic hardware platforms like Intel's Loihi chip are introduced.

1. Jason Tsai (蔡志順)
Oct. 11, 2018 @台灣人工智慧學校 新竹分校
INTRODUCTION TO SPIKING NEURAL
NETWORKS
*Picture adopted from
https://bit.ly/2Rh7cYy

2. *Copyright Notice:
All figures in this presentation are taken from
the quoted sources as mentioned in the
respective slides and their copyright belongs
to the owners. This presentation itself adopts
Creative Commons license.

3. Neural Networks 3D Simulation
(Video demo)
*Video from https://youtu.be/3JQ3hYko51Y

4. Questions
 What are the advantages of spiking
neural networks and neuromorphic
computing?
 What are current challenges of spiking
neural networks (SNNs)?

5. Characteristics of SNNs
 Spatio-temporal
 Asynchronous
 Sparsity
 Additive weight operation
 Energy-efficient
 Stochastic
 Robust to noise

6. Outlines
• Basic neuroscience
• Learning algorithms
• Neuron models
• Neural encoding schemes
• SNN examples (papers)
• Neuromorphic platforms

7. Prerequisite
Neuroscience

8. Nerve Cell
(Neuron)
*Picture taken from https://en.wikipedia.org/wiki/Neuron

9. Neuron’s Spike: Action Potential
*Figure adopted from https://en.wikipedia.org/wiki/Action_potential & The front cover of
“Spikes: Exploring the Neural Code (1999)”

10. The Effect of Presynaptic Spikes on
Postsynaptic Neuron
*Figure adopted from Wulfram Gerstner & Werner M. Kistler. Spiking Neuron Models:
Single Neurons, Populations, Plasticity. Cambridge University Press. 2002. Page 5.

11. The Firing of a Leaky Integrate-and-
Fire Model Neuron
*Figure adopted from https://doi.org/10.1371/journal.pone.0001377

12. Hebb’s Learning Postulate
 "When an axon of cell A is near enough to excite a cell B and
repeatedly or persistently takes part in firing it, some growth
process or metabolic change takes place in one or both cells such
that A's efficiency, as one of the cells firing B, is increased.“*
* Refer to Donald O. Hebb, The Organization of Behavior: A Neuropsychological Theory. 1949 & 2002. Page 62.
 Causality
 Repetition

13. Long-Term Potentiation (LTP) / Long-
Term Depression (LTD)
 LTP is a long-lasting, activity-dependent increase in synaptic
strength that is a leading candidate as a cellular mechanism
contributing to memory formation in mammals in a very
broadly applicable sense.*
* Refer to J. David Sweatt. Mechanisms of Memory, Second Edition. Academic Press. 2010. Page 112.

14. Synaptic Plasticity
*Figure adopted from Wulfram Gerstner & Werner M. Kistler. Spiking Neuron Models:
Single Neurons, Populations, Plasticity. Cambridge University Press. 2002. Page 353.

15. Back-propagating Action Potential (bAP)
*Further reading: https://en.wikipedia.org/wiki/Neural_backpropagation
Induction of tLTP requires activation of the presynaptic
input milliseconds before the bAP in the postsynaptic
dendrite.

16. *Figure adopted from https://doi.org/10.3389/fnsyn.2011.00004
Spike-Timing-Dependent Plasticity
(STDP)

17. Experiment Evidence of STDP
 From Wikipedia:
“Henry Markram, when he was in Bert Sakmann's lab and published their
work in 1997, used dual patch clamping techniques to repetitively
activate pre-synaptic neurons 10 milliseconds before activating the post-
synaptic target neurons, and found the strength of the synapse
increased. When the activation order was reversed so that the pre-
synaptic neuron was activated 10 milliseconds after its post-synaptic
target neuron, the strength of the pre-to-post synaptic connection
decreased.
Further work, by Guoqiang Bi, Li Zhang, and Huizhong Tao in Mu-Ming
Poo's lab in 1998, continued the mapping of the entire time course
relating pre- and post-synaptic activity and synaptic change, to show that
in their preparation synapses that are activated within 5-20 ms before a
postsynaptic spike are strengthened, and those that are activated within a
similar time window after the spike are weakened.”
*Further reading: https://en.wikipedia.org/wiki/Spike-timing-dependent_plasticity

18. Lateral Inhibition
Lateral inhibition is a Central Nervous System process whereby
application of a stimulus to the center of the receptive field excites a
neuron, but a stimulus applied near the edge inhibits it.
*Figure adopted from https://bit.ly/2yaat37

19. Lateral Inhibition
(Cont’d)
*Figure adopted from http://wei-space.blogspot.tw/2007/11/lateral-inhibition.html
& https://en.wikipedia.org/wiki/Lateral_inhibition

20. Hierarchical Sparse Distributed
Representations in Visual Cortex
*Figure adopted from https://bit.ly/2Ov5qV2 & https://bit.ly/2xTS1fw

21. Dopamine: Essential for Reward
Processing in Mammalian Brain
*Figure adopted from http://www.jneurosci.org/content/29/2/444
Dopamine neurons form huge synaptic contacts to target!

22. Learning Rule

23. Two Hot Approaches
 Supervised: Stochastic Gradient Descent
based Backpropagation learning rule
(Treat the membrane potentials of spiking neurons as
differentiable signals, where discontinuities at spike
times are considered as noise.*)
Unsupervised: STDP (Spike-Timing-
Dependent Plasticity) based learning rule
*Refer to Jun Haeng Lee, et al., Training Deep Spiking Neural Networks Using Backpropagation.
Frontiers in Neuroscience, 08 November 2016. https://doi.org/10.3389/fnins.2016.00508

24. *Refer to Yu, Q., Tang, H., Hu, J., Tan, K.C., Neuromorphic Cognitive Systems: A Learning and Memory
Centered Approach. Springer International Publishing. 2017. Page 9.
STDP Learning Rule

25. STDP Learning Rule (1-to-1)
*Figure adopted from http://dx.doi.org/10.7551/978-0-262-33027-5-ch037

26. STDP Learning Rule (2-to-1)
N0 is stimulated until N1 fires, then e0 is stopped for 30 ms.
N2 is stimulated by e2 during those 30 ms.
*Figure adopted from http://dx.doi.org/10.7551/978-0-262-33027-5-ch037

27. STDP Finds Spike Patterns
*Figure adopted from https://doi.org/10.1371/journal.pone.0001377

28. Reward-modulated STDP
*Figure adopted from https://doi.org/10.1371/journal.pcbi.1000180

29. Neural Modeling

30. 1st Generation of Neuron Models
(McCulloch–Pitts Neuron Model)
*Figure adopted from http://wwwold.ece.utep.edu/research/webfuzzy/docs/kk-thesis/kk-thesis-html/node12.html

31. 2nd Generation of Neuron Models
*Figure adopted from http://cs231n.github.io/neural-networks-1/

32. 3rd Generation of Neuron Models
(Spiking Neuron Models)
*Figure adopted from http://kzyjc.cnjournals.com/html/2018/5/20180512.htm

33. Spiking Neuron Models
Miscellaneous models:
 Hodgkin-Huxley model
 Izhikevish model
 Leaky Integrate-and-Fire (LIF) model
 Spike Response model (SRM)
……
*Further reading: https://en.wikipedia.org/wiki/Biological_neuron_model
& http://www.scholarpedia.org/article/Spike-response_model

34. Hodgkin-Huxley Model
*Figure adopted from Wulfram Gerstner & Werner M. Kistler. Spiking Neuron Models: Single Neurons,
Populations, Plasticity. Cambridge University Press. 2002. Page 34.

35. Hodgkin-Huxley Model (Cont’d)
*Taken from: https://www.bonaccorso.eu/2017/08/19/hodgkin-huxley-spiking-neuron-model-python/amp/

36. Izhikevich Model
*Taken from: http://www.physics.usyd.edu.au/teach_res/mp/ns/doc/nsIzhikevich3.htm

37. Izhikevich Model (Cont’d)
*Refer to Simple Model of Spiking Neurons (2003) https://www.izhikevich.org/publications/spikes.htm

38. Leaky Integrate-and-Fire Model
*Figure adopted from Wulfram Gerstner, Werner M. Kistler, Richard Naud and Liam Paninski “Neuronal Dynamics:
From Single Neurons to Networks and Models of Cognition” Cambridge University Press. 2014. Page 11.

39. Neural Coding

40. Hypothesized Neural Coding Schemes
 Rate Coding
 Temporal Coding
 Population Coding
 Sparse Coding
*Further reading: https://en.wikipedia.org/wiki/Neural_coding

41. Rate Coding
*Further reading: http://lcn.epfl.ch/~gerstner/SPNM/node7.html
Rate as a Spike Density
Rate as a Population Activity

42. Temporal Coding
*Further reading: http://lcn.epfl.ch/~gerstner/SPNM/node8.html
Time-to-First-Spike
(Latency Code)
Firing at Phases respecting
to Oscillation
Interspike synchrony

43. Population Coding
*Figure adopted from https://doi.org/10.1038/35039062

44. Sparse Coding
*Figure adopted from http://brainworkshow.sparsey.com/measuring-similarity-in-localist-vs-distributed-representations/

45. Sparse Coding with Inhibitory Neurons
 Population sparseness: Few neurons are
active at any given time
 Lifetime sparseness: Individual neurons
are responsive to few specific stimuli
*Figure adopted from https://doi.org/10.1523/JNEUROSCI.4188-12.2013

46. Sparse Coding Example based on
Linear Generative Model
*Slide credit: Andrew Ng

47. SNN Examples

48. Refer to “Milad Mozafari, et al., First-spike-based
visual categorization using reward-modulated STDP
(2018)” https://doi.org/10.1109/TNNLS.2018.2826721

49. Gabor Filter
*Further reading: https://en.wikipedia.org/wiki/Gabor_filter

50. Model Architecture

51. Formulae
S2 neuron fires if its Vi(t) reaches the threshold

52. R-STDP-based Learning Rule

53. Temporal Discrimination

54. Refer to “Luziwei Leng, et al., Spiking neurons with
short-term synaptic plasticity form superior
generative networks (2018)”
https://doi.org/10.1038/s41598-018-28999-2

55. Spiking Network Sampling

56. Generating Oriented Bars

57. tSNE Plots

58. Modeling Imbalanced Dataset

59. Neuromorphic
Computing

60. Categories of AI Chips
 AI Accelerator
 GPU
 FPGA
 ASIC
 Neuromorphic chip
 Network-on-Chip
 Memory-based
 Memristor-based
 Many-core CPU
 DSP
 Spintronics-based
 Photonics-based

61. Intel’s Loihi Chip
*Figure adopted from https://doi.org/10.1109/MM.2018.112130359
*Video demo https://youtu.be/cDKnt9ldXv0

62. ANN-to-SNN Conversion
 Train ANNs using standard supervised training
techniques like backpropagation to leverage
the superior performance of trained ANNs and
subsequently convert to event-driven SNNs for
inference operation on neuromorphic platform.
 Rate-encoded spikes are approximately
proportional to the magnitude of the original
ANN inputs.

63. ANN-to-SNN Conversion
(Cont’d)
*Figure adopted from https://arxiv.org/abs/1802.02627
A Poisson event-generation process is used to produce the input spike
train to the network.

64. Neuromorphic Chip Market Forecast
*Figure adopted from https://bit.ly/2xUfxZV

65. Software Simulation
 MATLAB
 PyNN http://neuralensemble.org/PyNN/
 BindsNET https://github.com/Hananel-
Hazan/bindsnet
 Brian http://briansimulator.org/
 Nengo https://www.nengo.ai/
 NEST http://www.nest-simulator.org/

66. Further Reading
 Wulfram Gerstner & Werner M. Kistler, “Spiking Neuron Models:
Single Neurons, Populations, Plasticity”. Cambridge University
Press (2002)
 Wulfram Gerstner, Werner M. Kistler, Richard Naud and Liam
Paninski, “Neuronal Dynamics: From Single Neurons to Networks
and Models of Cognition”. Cambridge University Press (2014)
 Eugene M. Izhikevich, “The Dynamical Systems in Neuroscience:
Geometry of Excitability and Bursting”. The MIT Press (2007)
 Nikola K. Kasabov, “Time-Space, Spiking Neural Networks and
Brain-Inspired Artificial Intelligence”. Springer International
Publishing (2018)
 Amirhossein Tavanaei, et al., “Deep Learning in Spiking Neural
Networks”. arXiv:1804.08150 (2018)