Transcript lecture 1 () - Stanford University

Lecture 1
MATHEMATICS OF THE BRAIN
with an emphasis on the problem
of a universal learning computer (ULC)
and a universal learning robot (ULR)
Victor Eliashberg
Consulting professor, Stanford University,
Department of Electrical Engineering
Slide 0
WHAT DOES IT MEAN TO UNDERSTAND THE BRAIN?
1. User understanding.
2. Repairman understanding.
3. Programmer (educator) understanding.
4. Systems developer understanding.
5. Salesman understanding.
Slide 1
TWO MAIN APPROACHES
1. BIOLOGICALLY-INSPIRED ENGINEERING (bionics)
Formulate biologically-inspired engineering / mathematical problems. Try to
solve these problems in the most efficient engineering way.
This approach had big success in engineering: universal programmable
computer vs. human computer , a car vs. a horse, an airplane vs. a bird.
It hasn’t met with similar success in simulating human cognitive functions.
2. SCIENTIFIC / ENGINEERING (reverse engineering = hacking)
Formulate biologically-inspired engineering or mathematical hypotheses.
Study the implications of these hypotheses and try to falsify the
hypotheses. That is, try to eliminate biologically impossible ideas!
We believe this approach has a better chance to succeed in the area of
brain-like computers and intelligent robots than the first one. Why?
So far the attempts to define the concepts of learning and intelligence per
se as engineering/mathematical concepts have led to less interesting
problems than the original biological problems.
Slide 2
HUMAN ROBOT
Slide 3
CONTROL SYSTEM
Slide 4
OUR MOST IMPORTANT PERSONAL COMPUTER
Parietal Lobe
12 cranial nerves ; ~1010 neurons in each hemisphere
Frontal Lobe
Occipital Lobe
~1011 neurons
Temporal Lobe
Cerebellum
31 pairs of nerves;
~ 107 neurons
Cervical Spinal Cord
8 pairs
Thoracic Spinal Cord
Dura mater
Our brain still
lives in a sea!
12 pairs
Lumbar Spinal Cord
5 pairs
Cauda Equina
6 pairs
Slide 5
The brain has a very large but topologically simple circuitry
The shown cerebellar network has ~1011 granule (Gr) cells and ~2.5 107 Purkinje (Pr) cells. There
are around 105 synapses between T-shaped axons of Gr cells and the dendrites of a single Pr cell.
Pr
Memory is stored in
such matrices
Slide 6
LTM size:
Cerebelum: N=2,5 107 * 105= 2.51012 B= 2.5 TB.
Neocortex: N=1010 * 104= 1014 B= 100 TB.
Big picture: Cognitive system (Robot,World)
External system (W,D)
Sensorimotor devices, D
W
External world, W
Computing system, B, simulating
the work of human nervous system
D
B
Human-like robot (D,B)
B(t) is a formal representation of B at time t, where t=0 is the
beginning of learning. B(0) is an untrained brain.
B(0)=(H(0),g(0)), where
H(0) = H is the representation of the brain hardware,
g(0) is the representation of initial knowledge (state of LTM)
Slide 7
CONCEPT OF FORCED MOTOR TRAINING
External system (W,D)
Brain (NS,NM,AM)
NS
W
S
D
AM
M
Motor control:
M
SM
associations
NM
Teacher
.
During training, motor signals (M) can be controlled byTeacher or by learner (AM) .
Sensory signals (S) are received from external system (W,D).
Slide 8
Turing’s machine as a system (Robot, World)
Slide9
TWO TYPES OF LEARNING
Working memory and
mental imagery
M
S
NS
W
AS
S
S
MS
associations
Motor control
D
S
M
NM
AM
M
SM
associations
M
Teacher
Slide 10
Mental computations (thinking) as an interaction between
motor control and working memory (EROBOT.EXE)
Slide 11
Motor and sensory areas of the neocortex
Motor control
AM
Working memory, episodic
memory, and mental imagery
AS
Slide 12
Primary sensory and motor areas, association areas
Slide 13
Association fibers (neural busses)
Slide 14
SYSTEM-THEORETICAL BACKGROUND
Slide 15
Fundamental constraint associated with the general levels of
computing power
Type 0
Type 0: Turing machines
(the highest computing power)
Type 1
Type 2
Type 1: Context-sensitive grammars
Type 3
Type 2: Context-free grammars
(push-down automata)
Type 4
Type 3: Finite-state machines
Type 4: Combinatorial machines
(the lowest computing power)
Traditional ANN models are below the red line. Symbolic systems go above the red
line but they require a read/write memory buffer. The brain doesn’t have such buffer.
Fundamental problem: How can the human brain achieve the highest level of
computing power without a memory buffer?
Slide 16
General structure of universal programmable
systems of different types
Type 4: Combinatorial machines
X={a,b,c}
PROM
G
x
a
b
c
b
a
c
0
1
0
0
1
1
f
Y={0,1}
f: X×G→Y
y
PROM stands for Programmable Read-Only Memory.
In psychological terms PROM can be thought of as a Long-Term
Memory (LTM). Letter G implies the notion of synaptic Gain.
Slide 17
Type 3: Finite-state machines
PROM
x
s
G
snext
y
a
b
c
b
a
c
X={a,b,c}
0
a0
0
1
0
1
1
1
1
S=Y={0,1}
1
1
0
0
1
0
0
1
1
f: X×S×G→S×Y
y
x
f
s
snext
register
Slide 18
Type 0: Turing machines (state machines coupled with a
read/write external memory)
PROM
f: X×S×G×M→S×M×Y
G
y
x
f
s
snext
M
Memory buffer,
e.g, a tape
register
Slide 19
Basic arcitecture of a primitive E-machine
Association
inputs
Data inputs to ILTM
INPUT LONG-TERM MEMORY (ILTM)
DECODING, INPUT LEARNING
Similarity function
Control inputs
E-STATES (dynamic STM and ITM)
MODULATION, NEXT E-STATE PROCEDURE
Modulated (biased) similarity function
CHOICE
Data inputs to
OLTM
Selected subset of active locations of OLTM
Control outputs
OUTPUT LONG-TERM MEMORY (OLTM)
ENCODING, OUTPUT LEARNING
Data outputs from OLTM
Association
outputs
Slide 20
The brain as a complex E-machine
D
SUBCORTICAL SYSTEMS
S1
SENSORY CORTEX
AS1
ASk
W
D
M1
MOTOR CORTEX
SUBCORTICAL SYSTEMS
AM1
AMm
Slide 21
A GLANCE AT THE SENSORIMOTOR DEVICES
Slide 21
VISION
Slide 22
EYE
Slide 23
EYE MOVEMENT CONTOL
Slide 24
AUDITORY AND VESTIBULAR SENSORS
Slide 25
AUDITORY PREPROCESSING
~100,000,000 cells
~580,000 cells
~4,000 inner hair cells
~12,000 outer hair cells
~390,000 cells
~90,000 cells
~30,000 fibers
Slide 26
OTHER STUFF
Slide 27
EMOTIONS (1)
Slide 28
EMOTIONS (2)
Slide 29
SPINAL MOTOR CONTROL
SENSORY FIBERS
MOTOR FIBERS
Slide 30