파이콘 한국 2020) 파이썬으로 구현하는 신경세포 기반의 인공 뇌 시뮬레이터

파 썬으로 구현하는
신경세포 기반의
인공 뇌 시뮬레이터
김성현

저는 인간의 학습 원리와 최신 딥러닝 기술을 융합하여
AGI (Artificial general intelligence) 를 개발하는
꿈을 가지고 있습니다.
✉ bananaband657@gmail.com
🏠 https://banana-media-lab.tistory.com
https://github.com/MrBananaHuman

Introduction01
- Introduction to neuroscience
Spiking Neural Network (SNN)02
- SNN as a neuromorphic neural network model
Modeling of SNN03
- Python Nengo library for SNN modeling
Applications of SNN04
- Deep SNN models
Future of SNN05
- Neuromorphic chip

Introduction
Introduction to neuroscience
01

Introduction
The brain is the most complex 1.5 kg organ that controls all functions of the body, interprets information from the outside
world, and embodies the essence of the mind and soul.
Thoughts
Perceptions
Language
Sensations
Memories
Actions
Emotions
Learning

History of Neuroscience - Neuron
Neuroscience is the study of how the nervous system develops, its structure, and what it does.
The first drawing of a neuron as the nerve cell (1865) [1] The first illustrated a synapse (1893, 1897) [2-3]
[1] Otto Friedrich Karl Deiters, Deiters, 1865
[2] Sherrington CS, 1897, A textbook of physiology, London:Macmillian, p.1024-70
[3] Cajal R, 1893, Arch Anat Physiol Anat Abth., V & VI:310-428

History of Neuroscience - Neuron
A typical neuron consists of a cell body (soma), dendrites, and a single axon.
[1] https://ib.bioninja.com.au/standard-level/topic-6-human-physiology/65-neurons-and-synapses/neurons.html
Synapse
Dendrite
Nucleus Soma
(Cell body)
Axon terminal
Myelin
sheath
Axon
Synapse
[1]

History of Neuroscience – Action Potential
An action potential is a rapid rise and subsequent fall in voltage or membrane potential across a cellular membrane with a
characteristic pattern.
[3]
[1] [2]
[1] How big is the GIANT Squid Giant Axon?, @TheCellularScale
[2] Hodgkin AL & Huxley AF, 1945, J Physiol
[3] https://www.moleculardevices.com/applications/patch-clamp-electrophysiology/what-action-potential#gref

History of Neuroscience - Synapse
Synapses are biological junctions through which neurons' signals can be sent to each other.
[2]
[1] https://synapseweb.clm.utexas.edu/type-1-synapse
[2] Besson, P., 2017, Doctoral dissetation
Presynaptic
neuron
Postsynaptic
neuron
Synpase
[1]
Excitatory postsynaptic potential
(EPSP)
Inhibitory postsynaptic potential
(IPSP)

History of Neuroscience - Synaptic Plasticity in Synapse
Synaptic plasticity refers to the phenomenon whereby strength of synaptic connections between neurons changes over time.
[1] M G LARRABEE, D W BRONK, 1947, J Neurophysiol.
Presynaptic neuron
Postsynaptic neuron
Before
stimulating
After
stimulating
Action potentials recorded from the
postganglionic nerve (1947) [1]

History of Neuroscience - The Brain
Neuron
Synapse
Plasticity
Dendrite
Nucleus Soma
(cell body)
Axon terminal
Myelin
sheath
Axon
• 86 Billion
• 10–25 μm
• > 1,000 types
• 7,000 syn/neuron
• 100-500 trillion
• Potentiation
• Depression
[1] https://ib.bioninja.com.au/standard-level/topic-6-human-physiology/65-neurons-and-synapses/neurons.html
[2] https://commons.wikimedia.org/w/index.php?curid=41349083
[3] https://sites.google.com/site/mcauliffeneur493/home/synaptic-plasticity
[1]
[2]
[3]

Artificial Neural Network (ANN) Revolution
[1]
ANN is abstract model that mimics the complex structure and functioning of the brain, which is developing explosively in
recent years.
[1] A brief history of neural nets and deep learning by A. Kurenkov

Limitation of ANN
Despite the success of the ANN algorithm, it has clear limitations.
Computational limitations
[1] Whittington and Bogacz, 2019, Trends in Cognitive Sciences
[2] Grossberg, 1987, Cognitive Science
[3] Lillicrap et al., 2020, Nature Review Neuroscience
• Lack of local error representation → Vanishing gradient [1]
• Symmetry of forwards and backwards weights → Weight transport problem [2]
• Feedback in brains alters neural activity [3]
• Unrealistic models of neurons → Large computational cost [1]
• Error signals are singed and potentially extreme-valued → Over fitting [3]

How Does The Brain Learn?
[1]
[1] Brainbow Hippocampus, Greg Dunn and Brian Edwards, 2014
[2] https://blogs.cardiff.ac.uk/acerringtonlab/ca1-pyramidal-neuron-red-hot/
[2]

Spiking Neural Network (SNN)
SNN as a neuromorphic neural network model
02

Overview
SNNs operate using spikes, which are discrete events that take place at points in time, rather than continuous values.
[1] Anwani and Rajendran, 2015, IJCNN
[1]
Components
• Spiking neuron model
• Synapse
• Synaptic plasticity

Spiking Neuron Model - Leaky Integrate-and-Fire (LIF)Model
A spiking neuron model is a mathematical description of the properties of certain cells in the nervous system that generate
sharp electrical potentials across their cell membrane, roughly one millisecond in duration.
[1] Teka, W. et al., 2014, PLoS Comput Biol.
[Appendix 1] https://www.youtube.com/watch?v=2_MIjvwWsrg
[Appendix 2] https://www.youtube.com/watch?v=KXnHxZdn8NU
Characteristics
• Subthreshold leaky-
integrator dynamic
• A firing threshold
• Reset mechanism
Resistor-Capacitor (RC) circuit [1]

Spiking Neuron Model - Leaky Integrate-and-Fire (LIF)Model
A spiking neuron model is a mathematical description of the properties of certain cells in the nervous system that generate
sharp electrical potentials across their cell membrane, roughly one millisecond in duration.
Characteristics
• Subthreshold leaky-
integrator dynamic
• A firing threshold
• Reset mechanism
[1] Louis Lapicque, 1907, Journal de Physiologie et de Pathologie Générale.
[Appendix 1] https://www.youtube.com/watch?v=2_MIjvwWsrg
[Appendix 2] https://www.youtube.com/watch?v=KXnHxZdn8NU
Leaky Integrate-and-Fire model [1]

Synapse Model
The synapse model activates as an input current stimulation to the spiking neuron model.
[1] Dutta, S. et al., 2017, Scientific reports
[1]

Synaptic Plasticity - Learning in the Brain
To reduce
punishment
To improve
knowledge
(reward(?))
ANN
output target
Error function
Loss function
Learning rate Error signal
SNN
• Unsupervised
learning
• Fire together,
wire together
• STDP learning
• BCM learning
• Supervised
learning
• Local error
propagation
• TP learning
• PES learning
[1] Timothy P. Lillicrap et al., 2020, Nat Rev Neurosci.
[1]
[1] [1]

Unsupervised Learning - Spike Timing Dependent Plasticity (STDP)
The Spike Timing Dependent Plasticity (STDP) algorithm, which has been observed in the mammalian brain, modulates the
weight of a synapse based on the relative timing of presynaptic and postsynaptic spikes. [1-3]
[1] Wang, R. et al., 2016, ISCAS
[2] Gerstner et al., 1996, Nature
[3] Bi and Poo, 1998, Journal of Neuroscience
[2-3]
[1]
PostPre
Spike
Spike
Time (ms)
Δt

Unsupervised Learning - Bienenstock, Cooper & Munro (BCM)
The BCM model proposes a sliding threshold for long-term potentiation (LTP) or long-term depression (LTD) induction, and
states that synaptic plasticity is stabilized by a dynamic adaptation of the time-averaged postsynaptic activity.
[1] Bienenstock, Cooper & Munro 1982 J Neurosci
Bienenstock, Cooper & Munro (BCM) learning [1]
Learning in visual cortex BCM model

Supervised Learning - Target Propagation (TP)
output target
Local layer-wise errors
Hypothesis
• The essential idea behind using a
stack of auto-encoders for deep
learning
• This backward-propagated target
induces hidden-activity targets
that should have been realized by
the network
• Learning proceeds by updating
the forward weights to minimize
these local layer-wise activity
differences
Target propagation (TP) learning [1]

Supervised Learning - Prescribed Error Sensitivity (PES)
[1]
[2] Voelker, A. R., 2015, Centre for Theoretical Neuroscience
Prescribed Error Sensitivity (PES) learning [2]
A connection from x to y learns to output y ∗ by minimizing |y ∗ − y|.

Modeling of Spiking Neural Network (SNN)
Python Nengo library for SNN modeling
03

Nengo Library
The Nengo Brain Maker is a Python package for building, testing, and deploying neural networks as a Neural Engineering
Framework (NEF).
[1] https://www.nengo.ai/
[1]

Nengo Tutorial
Installation
Usage
Build a network
!pip install nengo
import nengo
import numpy as np
net = nengo.Network()
with net:
sin_input = nengo.Node(output=np.sin)
input_neuron = nengo.Ensemble(n_neurons=4, dimensions=1)
nengo.Connection(sin_input, input_neuron)
Node
(Sine)

Spiking Neuron Model
Characteristics
import matplotlib.pyplot as plt
%matplotlib inline
from nengo.dists import Choice
from nengo.utils.ensemble import tuning_curves
from nengo.utils.matplotlib import rasterplot
with nengo.Simulator(net) as sim:
plt.figure()
plt.plot(*tuning_curves(input_layer, sim))
plt.xlabel("input value")
plt.ylabel("firing rate")
plt.xlim(-1, 1)
plt.title(str(nengo.LIF()))
sim.run(5.0)

Neural Dynamics
intercepts=[-.5] intercepts=[0] intercepts=[.5]
Input value
Firingrate(Hz)
Characteristics
input_neuron = nengo.Ensemble(intercepts=[-.5])

Neural Dynamics
Characteristics
input_neuron = nengo.Ensemble(intercepts=[0], encoders=[[-1]])
Input value
Firingrate(Hz)
intercepts=[-.5], encoders=[[-1]] intercepts=[0], encoders=[[-1]] intercepts=[.5], encoders=[[-1]]

Neural Dynamics
Characteristics
input_neuron = nengo.Ensemble(intercepts=[0], encoders=[[-1]], max_rates=[100])
Input value
Firingrate(Hz)
max_rates=[10] max_rates=[100] max_rates=[200]

Neural Dynamics
Characteristics
input_neuron = nengo.Ensemble(intercepts=[0], encoders=[[-1]], max_rates=[100], radius=1)
Input value
Firingrate(Hz)
radius=1 radius=2 radius=10

Neural Decoding
Characteristics
with net:
sin_input = nengo.Node(np.sin)
input_layer = nengo.Ensemble(n_neurons=2,dimensions=1, intercepts=[-.5, -
.5], encoders=[[1], [-1]], max_rates = [100, 100])
nengo.Connection(sin_input, input_layer)
Input value
Firingrate(Hz)

Neural Decoding
Prober
with net:
sin_probe = nengo.Probe(sin_input)
spikes = nengo.Probe(input_layer.neurons)
filtered = nengo.Probe(input_layer, synapse=0.01)
t = sim.trange()
# Plot the spiking output of the ensemble
plt.figure(figsize=(10, 8))
plt.subplot(2, 2, 1)
rasterplot(t, sim.data[spikes], colors=[(1, 0, 0), (0, 0, 0)])
plt.yticks((1, 2), ("On neuron", "Off neuron"))
plt.ylim(2.5, 0.5)
# Plot the decoded output of the ensemble
plt.figure()
plt.plot(t, sim.data[filtered])
plt.plot(t, sim.data[sin_probe])
plt.xlim(0, 10)

Neural Decoding
Characteristics
with net:
sin_input = nengo.Node(np.sin)
input_layer = nengo.Ensemble(n_neurons=100,dimensions=1)
nengo.Connection(sin_input, input_layer)
Input value
Firingrate(Hz)
Time (s)Inputvalue

Image Processing
Input function custom
urlretrieve("http://deeplearning.net/data/mnist/mnist.pkl.gz", "mnist.pkl.gz")
with gzip.open("mnist.pkl.gz") as f:
train_data, _, test_data = pickle.load(f, encoding="latin1")
train_data = list(train_data)
def image_input(t): # MNIST image data to Model
img = train_data[0][int(t)]
return img
neuron_number = 28*28
with net:
input_node = nengo.Node(image_input)
pre_neuron = nengo.Ensemble(neuron_number, dimensions=neuron_number, max_rates
= [100] * neuron_number, intercepts=[0] * neuron_number)
nengo.Connection(input_node, pre_neuron)

Image Processing
urlretrieve("http://deeplearning.net/data/mnist/mnist.pkl.gz", "mnist.pkl.gz")
with gzip.open("mnist.pkl.gz") as f:
train_data, _, test_data = pickle.load(f, encoding="latin1")
train_data = list(train_data)
def image_input(t): # MNIST image data to Model
img = train_data[0][int(t)]
return img
neuron_number = 28*28
with net:
input_node = nengo.Node(image_input)
pre_neuron = nengo.Ensemble(neuron_number, dimensions=neuron_number, max_rates
= [100] * neuron_number, intercepts=[0] * neuron_number)
nengo.Connection(input_node, pre_neuron) Time (s)
Neuronnumber(28*28)

Voice Processing
def voice_input(t):
ms = int(t * 1000)
frame_num = int(ms / frame_size)
voice = transposed_norm_S[frame_num]
return voice
with nengo.Network() as net:
voice_input = nengo.Node(output=voice_input)
input_neuron = nengo.Ensemble(n_neurons=80, dimensions=1,
max_rates=([100] * neuron_number))
nengo.Connection(voice, input_neuron, synapse=0.01)
spike_probe = nengo.Probe(input_neuron)

Voice Processing
def voice_input(t):
ms = int(t * 1000)
frame_num = int(ms / frame_size)
voice = transposed_norm_S[frame_num]
return voice
with nengo.Network() as net:
voice_input = nengo.Node(output=voice_input)
input_neuron = nengo.Ensemble(n_neurons=80, dimensions=1,
max_rates=([100] * neuron_number))
nengo.Connection(voice, input_neuron, synapse=0.01)
spike_probe = nengo.Probe(input_neuron)
neurons

Unsupervised Learning
BCM learning
with net:
sin = nengo.Node(lambda t: np.sin(t * 4))
pre = nengo.Ensemble(100, dimensions=1)
post = nengo.Ensemble(100, dimensions=1)
nengo.Connection(sin, pre)
conn = nengo.Connection(pre, post)
conn.learning_rule_type = nengo.BCM(learning_rate=5e-10)

Supervised Learning
Without PES learning
with net:
noise_input = nengo.Node(WhiteSignal(60, high=5), size_out=1)
input_layer = nengo.Ensemble(60, dimensions=1)
output_layer = nengo.Ensemble(60, dimensions=1)
nengo.Connection(noise_input, input_layer)
conn = nengo.Connection(input_layer, output_layer)
with nengo.Simulator(model) as sim:
sim.run(10.0)
Node
(Noise)
Input Output

Supervised Learning
With PES learning
with net:
error_neuron = nengo.Ensemble(60, dimensions=1)
nengo.Connection(output_layer, error_neuron)
nengo.Connection(input_layer, error_neuron, transform=-1)
conn.learning_rule_type = nengo.PES()
nengo.Connection(error_neuron, conn.learning_rule)
sim.run(10.0)
Node
(Noise)
Input
Error
Output
-1

Supervised Learning
With PES learning
with net:
error_neuron = nengo.Ensemble(60, dimensions=1)
nengo.Connection(output_layer, error_neuron)
nengo.Connection(input_layer, error_neuron, transform=-1)
conn.learning_rule_type = nengo.PES()
nengo.Connection(error_neuron, conn.learning_rule)
sim.run(10.0)

Keras Model Converting
[1]
[1] https://towardsdatascience.com/mnist-handwritten-digits-classification-using-a-convolutional-neural-network-cnn-af5fafbc35e9

Keras Model Converting
MNIST model converting
converter = nengo_dl.Converter(model, epochs=2,
swap_activations={tf.nn.relu: nengo.RectifiedLinear())
with nengo_dl.Simulator(converter.net, seed=0, minibatch_size=200) as sim:
sim.compile(
optimizer=tf.optimizers.RMSprop(0.001),
loss={
converter.outputs[dense1]: tf.losses.SparseCategoricalCrossentropy(
from_logits=True
)
},
metrics={converter.outputs[dense1]: tf.metrics.sparse_categorical_accuracy},
)
sim.fit(
{converter.inputs[inp]: train_images},
{converter.outputs[dense1]: train_labels},
epochs=epochs,
)
sim.save_params("./mnist_model")

Applications of SNN
Deep SNN models
04

Solving XOR Problem
It is known that the XOR problem cannot be solved with the traditional perceptron model but Nengo based SNN can solve the
problem with only a single layer. [1]
[2]
[1] Gidon et al., 2020, Science
[2] https://github.com/sunggukcha/xor
[3] https://www.nengo.ai/examples/
[3]

Permuted Sequential MNIST
In the Permuted Sequential MNIST data containing the order information for writing numbers, the Nengo SNN-based
(Legendre Memory Units) LMU showed SOTA performance.
[2]
[1] https://github.com/edwin-de-jong/mnist-digits-stroke-sequence-data/wiki/MNIST-digits-stroke-sequence-data
[2] Coelker, A. et al., 2019, NIPS
[3] https://www.nengo.ai/examples/
[2]
[1]
[3]

Large Scale Virtual Brain Simulation
Methods
• Semantic Pointer Architecture
Unified Network (SPAUN)
• Using Nengo
• 2.5 million LIF neurons
• Success on 8 diverse tasks
• Copy drawing style
• Image recognition
• Reinforcement learning
• Serial working memory
• Counting
• Question Answering
• Rapid variable creation
• Fluid reasoning
[1] Eliasmith et al., 2012, Science
[1]

Future of SNN
Neuromorphic chip
05

Neuromorphic Advantages
Advantages
• Sparsification over time
→ Less communication
• Less communication
→ Fewer memory lookups
• Cheaper computation
→ Sum instead of multiply
[1] Jeehyun Kwak and Hyun Jae Jang, Neural Computation Lab (NCL), Korea Univ.
[1]

Neuromorphic Processing Unit
[1] Eliasmith and Suma, The Neuromorphic Advantage, Applied Brain Research (ABR)
[1]
Intel Loihi Chip

[1] Eliasmith and Suma, The Neuromorphic Advantage, Applied Brain Research (ABR)
[1]

[1] Eliasmith et al., 2016, arXiv
[2] Jang, H. J. et al., 2020, Science Advances
[1]
[2]
3D neuron model

Computational Neuroscience
[1] Trappenberg, T. P., 2009, Fundamentals of computational neuroscience, OUP Oxford
[1]

감사합니다 :-)
SNN와 관련된 대화는 언제나 환영합니다.
bananaband657@gmail.com

파이콘 한국 2020) 파이썬으로 구현하는 신경세포 기반의 인공 뇌 시뮬레이터

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