Biological Modeling of Neural Networkslcn · 2019-01-04 · Biological Modeling of Neural Networks:...
Transcript of Biological Modeling of Neural Networkslcn · 2019-01-04 · Biological Modeling of Neural Networks:...
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Biological Modeling
of Neural Networks:
Week 12 – Decision models:
Competitive dynamics
Wulfram Gerstner
EPFL, Lausanne, Switzerland
12.1 Review: Population dynamics
- competition
12.2 Perceptual decision making - V5/MT
- Decision dynamics: Area LIP
12.3 Theory of decision dynamics - shared inhibition
- effective 2-dim model
12.4. Decisions in connected pops.
- unbiased case
- biased input
12.5. Decisions, actions, volition - the problem of free will
Week 12 – Decision models
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Week 12-part 1: How do YOU decide?
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Week 12-part 1: Decision making
turn
Left? Right?
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noise model A
I(t) h(t)
(escape noise/fast noise)
high noise
slow transient
( ) ( ( ))A t F h t
( ) ( ( ))A t F h t
)()()( tIRththdtd
Population activity
Membrane potential caused by input
( ) ( ) ( ) ( ( ))extdeedt
h t h t R I t w F h t
Attention:
- valid for high noise only, else
transients might be wrong
- valid for high noise only, else
spontaneous oscillations may arise
eew
Week 12-part 1: Review: High-noise activity equation
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I(t)
)(tAn
Week 12-part 1: Review: microscopic vs. macroscopic
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)(2, tAe)(1, tAe
)(tAinh
Input indicating
‘left’
Input indicating
‘right’
eew eew
iew
eiw
iew
Week 12-part 1: Competition between two populations
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Week 12-part 1: How do YOU decide?
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Biological Modeling
of Neural Networks:
Week 12 – Decision models:
Competitive dynamics
Wulfram Gerstner
EPFL, Lausanne, Switzerland
12.1 Review: Population dynamics
- competition
12.2 Perceptual decision making - V5/MT
- Decision dynamics: Area LIP
12.3 Theory of decision dynamics - shared inhibition
- effective 2-dim model
12.4. Decisions in connected pops.
- unbiased case
- biased input
12.5. Decisions, actions, volition - the problem of free will
Week 12 – Decision models
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‘Is the middle bar shifted to the left or to the right?’
Week 12-part 2: Perceptual decision making?
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2) Neighboring cells in visual cortex MT/V5
respond to motion in similar direction
cortical columns
visual
cortex
1) Cells in visual cortex MT/V5 respond
to motion stimuli
Week 12-part 2: Detour: receptive fields in V5/MT
Albright, Desimone,Gross,
J. Neurophysiol, 1985
IMAGE
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Recordings from a single neuron in V5/MT
Receptive Fields depend
on direction of motion
Week 12-part 2: Detour: receptive fields in V5/MT
Random moving dot stimuli: e.g.Salzman, Britten, Newsome, 1990
Roitman and Shadlen, 2002
Gold and Shadlen 2007
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Receptive Fields depend
on direction of motion: = preferred direction = P
Week 12-part 2: Detour: receptive fields in V5/MT
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coherence 0.8=80%
coherence 0.5 = 50%
coherence 0.0
Image: Salzman, Britten, Newsome, 1990
Eye movement coherence -1.0
opposite
direction
Week 12-part 2: Experiment of Salzman et al. 1990
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Monkey behavior w. or w/o Stimulation
of neurons in V5/MT
X = coherent motion
to bottom right -1.0 0.5
No bias, each point
moves in random direction
0.5 1.0
Monkey
chooses right
fixation Visual stim.
LED
Blackboard: Motion detection/stimulation
Salzman, Britten,
Newsome, 1990
P N
Week 12-part 2: Experiment of Salzman et al. 1990
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excites this
group of
neurons
coherence 0.8=80%
coherence 0.5 = 50%
coherence 0.0
coherence -1.0
Week 12-part 2: Experiment of Salzman et al. 1990
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Behavior: psychophysics
With stimulation
Week 12-part 2: Experiment of Salzman et al. 1990
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Biological Modeling
of Neural Networks:
Week 12 – Decision models:
Competitive dynamics
Wulfram Gerstner
EPFL, Lausanne, Switzerland
12.1 Review: Population dynamics
- competition
12.2 Perceptual decision making - V5/MT
- Decision dynamics: Area LIP
12.3 Theory of decision dynamics - shared inhibition
- effective 2-dim model
12.4. Decisions in connected pops.
- unbiased case
- biased input
12.5. Decisions, actions, volition - the problem of free will
Week 12 – Decision models
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coherence 85%
coherence 50%
coherence 0% RF of Neuron in LIP:
-selective to target of
saccade
-increases faster if
signal is stronger
- activity is noisy
LIP is somewhere between
MT (movement detection) and
Frontal Eye Field (saccade
control) Roitman and Shadlen 2002
Week 12-part 2: Experiment of Roitman and Shadlen in LIP (2002)
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Neurons in LIP: -selective to target
of saccade
-increases faster if
signal is stronger
- activity is noisy LIP is somewhere
between MT (movement
detection) and Frontal
Eye Field
(saccade control)
Week 12-part 2: Experiment of Roitman and Shadlen in LIP (2002)
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Quiz 1, now
Receptive field in LIP
[ ] related to the target of a saccade
[ ] depends on movement of random dots
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Biological Modeling
of Neural Networks:
Week 12 – Decision models:
Competitive dynamics
Wulfram Gerstner
EPFL, Lausanne, Switzerland
12.1 Review: Population dynamics
- competition
12.2 Perceptual decision making - V5/MT
- Decision dynamics: Area LIP
12.3 Theory of decision dynamics - shared inhibition
- effective 2-dim model
12.4. Decisions in connected pops.
- unbiased case
- biased input
12.5. Decisions, actions, volition - the problem of free will
Week 12– Decision models, part 3
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activity equations ( ) ( ( ))n nA t F h t
population activity
Membrane potential caused by input
1 1 1 1( ) ( ) ( ) ( ( )) ( ( ))extdee ei inhdt
h t h t R I t w F h t w F h t
2 2 2 2( ) ( ) ( ) ( ( )) ( ( ))extdee ei inhdt
h t h t R I t w F h t w F h t
Input indicating
left movement Input indicating
right movement
)(2, tAe)(1, tAe
)(tAinh
eew eew
eiweiw
iew
Week 12-part 3: Theory of decision dynamics
Blackboard: reduction from
3 to 2 equations
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activity equations ( ) ( ( ))n nA t F h tPopulation activity
( ) 0.2 0.8
(0) 0.1
(1) 0.9
F h h for h
F
F
,1 ,2( ) ( ( )) ( ) ( ( ) ( ))inh inh inh ie e eA t F h t h t w A t A t
Inhibitory Population
Blackboard: Linearized inhibition
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activity equations ( ) ( ( ))n nA t F h t
Membrane potential caused by input
1 1 1 1 2( ) ( ) ( ) ( ) ( ( )) ( ( ))extdeedt
h t h t h t w F h t F h t
2 2 2 2 1( ) ( ) ( ) ( ) ( ( )) ( ( ))extdeedt
h t h t h t w F h t F h t
population activity
Input indicating
left movement Input indicating
right movement
)(2, tAe)(1, tAe
)(tAinh
eew eew
eiweiw
iew
Week 12-part 3: Effective 2-dim. model
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Exercise 1 now: draw nullclines and flow arrows
)(hg ( ) 0.2 0.8
(0) 0.1
(0.9) 0.85
(1) 0.9
g h h for h
g
g
g
221 )( hhgh01hdtd
1.0
0.8
0.2
0.0
02hdtd
112 )( hhgh
1.0
0.8
0.2
0.0
1.0 h
))(())(()()()()( 21111 thgthgwththth eeext
dtd
1;5.1;8.021 eeextext
whh
Next Lecture at 10:36
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Phase plane, strong external input
01hdtd
9.0)1(
1.0)0(
8.02.0)(
g
g
hforhhg
02hdtd
1 20.8ext exth h
Week 12-part 3: Theory of decision dynamics
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Phase plane – biased input:
Population activity
01hdtd
02hdtd
01hdtd 01h
dtd 01h
dtd
2.02exth
2.01exth
2 1
ext exth h
2.02exth
Week 12-part 3: Theory of decision dynamics: biased input
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Phase plane – symmetric but small input
01hdtd
Weak external input:
Stable fixed point
02hdtd
extext hh 21 2.0
Week 12-part 3: Theory of decision dynamics: unbiased weak
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Phase plane 01h
dtd
02hdtd
02hdtd
02hdtd
Symmetric, but strong input
Week 12-part 3: decision dynamics: unbiased strong to biased
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Phase plane
01hdtd
Population activity
02hdtd
2.0
;8.0
2
1
ext
ext
h
h
Biased input = stable fixed point
decision reflects bias
Week 12-part 3: Theory of decision dynamics: biased strong
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Phase plane 01h
dtd
02hdtd
extext hh 21 8.0
Homogeneous solution
= saddle point
decision must be taken
Week 12-part 3: Theory of decision dynamics: unbiased strong
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Biological Modeling
of Neural Networks:
Week 12 – Decision models:
Competitive dynamics
Wulfram Gerstner
EPFL, Lausanne, Switzerland
12.1 Review: Population dynamics
- competition
12.2 Perceptual decision making - V5/MT
- Decision dynamics: Area LIP
12.3 Theory of decision dynamics - shared inhibition
- effective 2-dim model
12.4. Decisions in connected pops.
- unbiased case
- biased input
12.5. Decisions, actions, volition - the problem of free will
Week 12– Decision models, part 3
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Phase plane 01h
dtd
02hdtd
extext hh 21 8.0
Homogeneous solution
= saddle point
decision must be taken
Week 12-part 4: Review: unbiased strong
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Phase plane – symmetric but small input
01hdtd
Weak external input:
Stable fixed point
no decision
02hdtd
extext hh 21 2.0
Week 12-4: Review: unbiased weak
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Simulation of 3 populations of spiking neurons, unbiased strong input
X.J. Wang, 2002
NEURON
iew
eiw
iew
Popul.1
Popul. 2
stimulus
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Roitman and Shadlen 2002
Stimulus
onset
saccade onset
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Biological Modeling
of Neural Networks:
Week 12 – Decision models:
Competitive dynamics
Wulfram Gerstner
EPFL, Lausanne, Switzerland
12.1 Review: Population dynamics
- competition
12.2 Perceptual decision making - V5/MT
- Decision dynamics: Area LIP
12.3 Theory of decision dynamics - shared inhibition
- effective 2-dim model
12.4. Decisions in connected pops.
- unbiased case
- biased input
12.5. Decisions, actions, volition - the problem of free will
Week 12– Decision models, part 3
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goal
How would you decide?
Week 12-5: Decision: risky vs. safe
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goal
Start
How would you decide?
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fMRI variant of Libet experiment
Decision
and
Movement Preparation
-Subject decides spontaneously
to move left or right hand
- report when they made their decision
Libet, Behav. Brain Sci., 1985
Soon et al., Nat. Neurosci., 2008
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goal
What decides? Who decides?
goal
Start
-Your experiences are memorized in your brain
-Your values are memorized in your brain
-Your decisions are reflected in brain activities
‘Your brain decides what you want or what you prefer … ’ ‘ … but your brain – this is you!!!’
‘We don’t do what we want, but we want what we do’ (W. Prinz)
The problem of
Free Will (see e.g. Wikipedia
article)
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Wulfram Gerstner
EPFL
Suggested Reading: - Salzman et al. Nature 1990
- Roitman and Shadlen, J. Neurosci. 2002
- Abbott, Fusi, Miller:
Theoretical Approaches to Neurosci.
- X.-J. Wang, Neuron 2002
- Libet, Behav. Brain Sci., 1985
- Soon et al., Nat. Neurosci., 2008
- free will, Wikipedia
Chapter 16, Neuronal Dynamics, Gerstner et al. Cambridge 2014
Decision, Perception
and Competition in Connected Populations