1. ‫הקורס‬ ‫מנחה‬
‫ד‬
"
‫ר‬
‫לרי‬
‫מנביץ‬
'
1

2. ‫נושאים‬

‫נוירון‬ ‫זה‬ ‫מה‬
?

3
‫הנוירון‬ ‫מודל‬ ‫של‬ ‫דורות‬

‫ביולוגי‬ ‫נוירון‬

‫לנוירון‬ ‫סימולציה‬

IPSP
/
EPSP

LSM

‫מאמרים‬ ‫סקירת‬
2

3. Man versus Machine
(hardware)
3
Numbers Human brain Von Neumann
computer
# elements 1010 - 1012 neurons 107 - 108 transistors
# connections / element 104 - 103 10
switching frequency 103 Hz 109 Hz
energy / operation 10-16 Joule 10-6 Joule
power consumption 10 Watt 100 - 500 Watt
reliability of elements low reasonable
reliability of system high reasonable

4. Man versus Machine
(information processing)
4
Features Human Brain Von Neumann computer
Data representation analog digital
Memory localization distributed localized
Control distributed localized
Processing parallel sequential
Skill acquisition learning programming
No memory management,
No hardware/software/data distinction

5. Biologically Inspired
 Electro-chemical signals
 Threshold output firing
5
Axon
Terminal Branches
of Axon
Dendrites

6. The Perceptron
 Binary classifier functions
 Threshold activation function
6
Axon
Terminal Branches
of Axon
Dendrites
S
x1
x2
w1
w2
wn
xn
x3 w3
Yj : output from unit j
Wij : weight on connection from j to i
Xi : weighted sum of input to unit i
xi = ∑j wij yj
yi = f(xi – qi)
Threshold

7. Type 1. Perceptron
 feedforward
 Structure: 1 input layer
1 output layer
 Supervised learning
 Hebb learning rule
 Able : AND or OR.
 Unable: XOR
x0 f
i1
w01
y0
i2
b=1
w02
w0b

8. Learning in a Simple Neuron
Perceptron Learning Algorithm:
1. Initialize weights
2. Present a pattern and target output
3. Compute output :
4. Update weights :
Repeat starting at 2 until acceptable
level of error
]
[
2
0
i
i
i
x
w
f
y 


i
i
i
w
t
w
t
w 


 )
(
)
1
(

9. Computing other functions: the OR
function
 Assume a binary threshold activation function.
 What should you set w01, w02 and w0b to be so that you
can get the right answers for y0?
9
i1 i2 y0
0 0 0
0 1 1
1 0 1
1 1 1
x0 f
i1
w01
y0
i2
b=1
w02
w0b

10. Many answers would work
y = f (w01i1 + w02i2 + w0bb)
recall the threshold function
the separation happens when
w01i1 + w02i2 + w0bb = 0
move things around and you get
i2 = - (w01/w02)i1 - (w0bb/w02)
10
i2
i1
n
N
n
n x
w
u
y 



1

11. The XOR Function
11
X1/X2 X2 = 0 X2 = 1
X1= 0 0 1
X1 = 1 1 0
i2
i1

12. 12

13. Type 2. Multi-Layer-Perceptron
 feed forward
 1 input layer,
1 or more hidden layers, 1
output layer
 supervised learning
 delta learning rule,
backpropagation (mostly
used)
 Able : every logical
operation

14. The Perceptron
14

15. Type 3. Backpropagation Net
 feedforward
 1 input layer,
1 or more hidden layers,
1 output layer
 supervised
 backpropagation
 sigmoid
 Used :complex logical
operations, pattern
classification, speech
analysis

16. The Back-propagation
Algorithm
On-Line algorithm:
1. Initialize weights
2. Present a pattern and target output
3. Compute output :
4. Update weights :
Repeat starting at 2 until acceptable level
of error
o f w o
j ij
i
n
i
 

[ ]
0
w t w t w
ij ij ij
( ) ( )
  
1 

17. Pattern Separation and NN
architecture
17

18. ‫נוירונים‬ ‫רשתות‬ ‫של‬ ‫סימולציות‬
‫דור‬
I
 McCulloch-Pitts threshold

‫בוליאניות‬ ‫משוואות‬ ‫לחשב‬ ‫מסוגל‬
‫דור‬
II
 feed-forward, recurrent neural networks and backward
propagation

‫משוואות‬ ‫לחשב‬ ‫מסוגלות‬
‫פולינומיאלית‬
‫גם‬ ‫ונקראים‬
universal approximation
‫כל‬ ‫לחקות‬ ‫שמסוגלים‬ ‫מכיוון‬
‫אנלוגית‬ ‫משוואה‬
.

‫הדור‬ ‫הביולוגי‬ ‫לנוירון‬ ‫בהשוואה‬
2
‫ל‬ ‫מסוגל‬
"
‫דבר‬
"
‫ב‬
-
rate
coding
‫או‬
frequency coding
‫היריות‬ ‫תדירות‬ ‫שזה‬
(
‫לירייה‬ ‫ירייה‬ ‫בין‬ ‫המרחק‬
)
18

19. ‫נוירונים‬ ‫רשתות‬ ‫של‬ ‫סימולציות‬
‫דור‬
III

‫הביולוגי‬ ‫לנוירון‬ ‫הסימולציות‬ ‫בקירוב‬ ‫נוספת‬ ‫עליה‬
.

‫לרבב‬ ‫מסוגלים‬ ‫הנוירונים‬
multiplexing
‫יריות‬ ‫תדרים‬
‫ו‬
"
‫לדבר‬
"
‫ב‬
-
pulse coding
‫ב‬ ‫במקום‬
–
rate coding
‫כמה‬ ‫להעביר‬ ‫ובכך‬
"
‫מילים‬
"
‫זמן‬ ‫באותו‬

"
‫שעון‬
"
‫יחידה‬ ‫לכל‬ ‫עצמי‬
19

20. 20

21. 21

22. 22

23. 23

24. 24

25. 25

26. 26

27. 27

28. 28

29. 29

30. Hodgkin-Huxley Model
100
mV
0
)
(
)
(
)
(
)
( 4
3
t
I
E
u
g
E
u
n
g
E
u
h
m
g
dt
du
C l
l
K
K
Na
Na 






)
(
)
(
0
u
u
m
m
dt
dm
m




)
(
)
(
0
u
u
n
n
dt
dn
n




)
(
)
(
0
u
u
h
h
dt
dh
h




stimulus
Na
I K
I leak
I
inside
outside
Ka
Na
Ion channels Ion pump
C gl
gK gNa
I
K
=
‫אשלגן‬
Na
=
‫נתרן‬
30

31. Hodgkin-Huxley Model
)
(
)
(
)
(
)
( 4
3
t
I
E
u
g
E
u
n
g
E
u
h
m
g
dt
du
C l
l
K
K
Na
Na 






)
(
)
(
0
u
u
m
m
dt
dm
m




)
(
)
(
0
u
u
n
n
dt
dn
n




)
(
)
(
0
u
u
h
h
dt
dh
h




stimulus
Na
I K
I leak
I
inside
outside
Ka
Na
Ion channels Ion pump
u u
h0(u)
m0(u) )
(u
h

)
(u
m

pulse input
I(t)
31

32. ‫דוגמאות‬
 Integrate & Fire Neural Network.htm
 actionpotential.swf
32

33. ‫כללי‬ ‫נוירולוגי‬ ‫מבנה‬

‫מערכות‬ ‫סוגי‬ ‫שני‬ ‫יש‬ ‫בגופנו‬
,

‫ממריץ‬
(
‫אנדרנלין‬
)

‫מרגיע‬
‫מאיט‬
(
‫אציטין‬
‫חולין‬
)

‫סוגי‬ ‫שני‬ ‫לפחות‬ ‫יש‬
‫סינפציות‬
:

‫מעקבות‬
:
‫התא‬ ‫לגוף‬ ‫מתחברת‬ ‫לרוב‬

‫מעוררת‬
:
‫העצים‬ ‫בסופי‬ ‫מתחברות‬ ‫לרוב‬

‫בין‬ ‫מרווח‬
‫הסינפצות‬
‫הוא‬
20
‫ננומטר‬
.

‫הזמן‬ ‫מימד‬
-
‫הלמידה‬ ‫את‬ ‫ליראות‬ ‫ניתן‬
‫הזמן‬ ‫במימד‬ ‫שימוש‬ ‫היא‬ ‫אסוציאטיבית‬
,
-
‫שני‬
‫כלל‬ ‫בדרך‬ ‫הן‬ ‫זמנית‬ ‫בו‬ ‫שקורים‬ ‫מאורעות‬
‫לשני‬ ‫אחד‬ ‫קשורים‬
.
‫טעם‬ ‫פאבלוב‬ ‫ניסוי‬ ‫לדוגמא‬
‫וזמן‬ ‫גירוי‬
.
33

34. 34

35. 35

36. 36

37. 37

38. 38

39. 39

40. 40
‫נובע‬ ‫תאים‬ ‫בין‬ ‫הקשר‬ ‫בחיזוק‬ ‫השני‬ ‫השלב‬
‫חדשות‬ ‫סינפסות‬ ‫מיצירת‬
,
‫לטווח‬ ‫מתמשך‬
‫גנים‬ ‫שפעול‬ ‫ומצריך‬ ‫ארוך‬
.

41. 41

42. 42

43. ‫פלט‬
/
‫טיפוסי‬ ‫קלט‬
43

44. 44

45. Generation of multiple Action
Potentials
 Rate is dependent on depolarization
 Firing frequency
 1 per second is 1 Hz
 Maximum is about 1000Hz
 Absolute refractory period
 Relative refractory period
 I(ion)=g(ion)(Vm-Eion)
45

46. ‫אינסטינקטיבית‬ ‫תגובה‬
46

47. Mapping from biological neuron
Nervous System Computational Abstraction
Neuron Node
Dendrites Input link and propagation
Cell Body Combination function, threshold,
activation function
Axon Output link
Spike rate Output
Synaptic strength Connection strength/weight
47

48. EPSP
excitatory postsynaptic potential
IPSP
Inhibitory postsynaptic potential
48

49. ‫חוק‬
Hebb
:
‫יתחזק‬ ‫זמנית‬ ‫בו‬ ‫הפועלים‬ ‫תאים‬ ‫בין‬ ‫הקשר‬
49

50. Liquid State Machine (LSM)
50

51. Liquid State Machine (LSM)
• Maass’ LSM is a spiking recurrent neural
network which satisfies two properties
– Separation property (liquid)
– Approximation property (readout)
• LSM features
– Only attractor is rest
– Temporal integration
– Memoryless linear readout map
– Universal computational power: can
approximate any time invariant filter
with fading memory
– It also does not require any a-priori
decision regarding the ``neural code''
by which information is represented
within the circuit.
51

52. Maass’ Definition of the Separation Property
The current state x(t) of the microcircuit at time t has to hold all information
about preceding inputs.
Approximation Property
Readout can approximate any continuous
function f that maps current liquid states x(t)
to outputs v(t).
52

53. 2 motors, 1 minute footage of each case, 3400 frames
Readouts could utilize wave interference patterns
53

54. Zero One
54

55. ‫מאמרים‬ ‫סקירת‬
 Spiking neural networks, an introduction.pdf

‫דור‬ ‫של‬ ‫ומבנה‬ ‫נוירונים‬ ‫רשתות‬ ‫על‬ ‫וסיכום‬ ‫הקדמה‬
3
‫במודלים‬
 is the integrate-and-fire model good enough – a
review.pdf

‫מודל‬ ‫בין‬ ‫השוואה‬
I&F
‫מודל‬ ‫לבין‬
HH
‫מודל‬ ‫של‬ ‫הרחבה‬ ‫כולל‬
I&F
‫שניהם‬ ‫את‬ ‫שמשלב‬ ‫למודל‬
 LSM (Liquid State Machine)
 Liquid State Machines,a review.pdf
 Liquid State Machine Built of Hodgkin–Huxley Neurons.pdf
 The Echo State approach to analysing and training recurrent
neural networks.pdf
 LSM  Turing Maching
 On the Computational Power of Circuits of Spiking neurons.pdf
 The Echo State approach to analysing and training recurrent
neural networks.pdf
55

56. ‫מאמרים‬ ‫סקירת‬
 The Tempotron

‫לנוירון‬ ‫מודל‬
LIF
‫לימוד‬ ‫עם‬ ‫פולסים‬ ‫סדרות‬ ‫למיין‬ ‫המסוגל‬
 Spike Timing Dependent Plasticity Finds the Start of
Repeating Patterns in Continuous Spike
Trains2.PDF

‫מודל‬
LIF
‫לימוד‬ ‫ללא‬ ‫בפולסים‬ ‫חזרות‬ ‫של‬ ‫רצף‬ ‫לזהות‬ ‫המסוגל‬
,
‫ע‬ ‫רק‬
"
‫הקלטים‬ ‫משקלי‬ ‫שינוי‬ ‫י‬
 Hubb’s Rule
 Hebbian learning and spiking neurons.pdf
 Competitive Hebbian learning through spike-timing
dependent synaptic plasticity.pdf
 Spike-Timing-Dependent Hebbian Plasticity as Temporal
Difference Learning.pdf
 Pitch Perception Models.pdf

‫ע‬ ‫שמיעה‬ ‫ולהבין‬ ‫לחקות‬ ‫המנסה‬ ‫מודל‬
"
‫התדרים‬ ‫של‬ ‫קימוט‬ ‫י‬
56