Part 3: Autonomous Agents
11/3/04
Reorganization of Cortex
Orientation Columns
• Median nerve
sectioned to show
fluidity of cortical
organization
• (C) before
• (D) immediately
after
• (E) several months
later
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(fig. < McClelland & al, Par. Distr. Proc. II)
1
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(fig. < Nicholls & al., Neur. to Brain)
2
Slow Potential Neuron
Orientation Columns
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(fig. < Nicholls & al., Neur. to Brain)
3
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(fig. < Anderson, Intr. Neur. Nets)
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Part 3: Autonomous Agents
11/3/04
Variations in Spiking Behavior
Frequency
Coding
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(fig. from Anderson, Intr. Neur. Nets)
5
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6
Chemical Synapse
Synapses
1.
2.
3.
4.
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video by Hybrid Medical Animation
7
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(fig. from Anderson, Intr. Neur. Nets)
Action potential
arrives at synapse
Ca ions enter cell
Vesicles move to
membrane, release
neurotransmitter
Transmitter
crosses cleft,
causes
postsynaptic
voltage change
8
2
Part 3: Autonomous Agents
11/3/04
Typical Receptor
Axon Hillock
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(fig. from Anderson, Intr. Neur. Nets)
9
11/3/04
(fig. from Peters, Palay & Webster)
Dendrite &
Dendritic
Branches
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(fig. from Peters, Palay & Webster)
10
Dendrite &
Dendritic Spine
11
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(fig. from Peters, Palay & Webster)
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3
Part 3: Autonomous Agents
11/3/04
Neuropil
axon
terminal
dend
Myelinated
Axon Making
Synapse on
Dendrite
rite
11/3/04
(fig. from Peters, Palay & Webster)
13
Excitatory
Synapse
Between
Axon
Terminal and
Dendritic
Thorn
Various
Synapses
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(fig. from Peters, Palay & Webster)
15
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axon
(fig. from Peters, Palay & Webster)
14
axon
terminal
dendritic
thorn
synapse
(fig. from Peters, Palay & Webster)
16
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Part 3: Autonomous Agents
11/3/04
Dendro-dendritic Synapses
Electrotonic Synapse
Type II
(symmetric)
Type I
(asymmetric)
11/3/04
(fig. from Peters, Palay & Webster)
17
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18
(fig. from Peters, Palay & Webster)
5B
Typical Artificial Neuron
connection
weights
Artificial Neural Networks
inputs
output
(in particular, the Hopfield Network)
threshold
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20
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Part 3: Autonomous Agents
11/3/04
Typical Artificial Neuron
linear
combination
Equations
activation
function
Net input:
net input
(local field)
New neural state:
n
hi = w ij s j j=1
h = Ws si = ( hi )
s = (h)
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21
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What to do about h = 0?
Hopfield Network
•
•
•
•
•
• There are several options:
Symmetric weights: wij = wji
No self-action: wii = 0
Zero threshold: = 0
Bipolar states: si {–1, +1}
Discontinuous bipolar activation function:
1,
( h ) = sgn( h ) = +1,
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22
(0) = +1
(0) = –1
(0) = –1 or +1 with equal probability
hi = 0 no state change (si = si)
• Not much difference, but be consistent
• Last option is slightly preferable, since
symmetric
h<0
h>0
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6