The Perceptron. 0T Afferents V thr V rest t max 0 What does a neuron do? spike no spike.
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Transcript of The Perceptron. 0T Afferents V thr V rest t max 0 What does a neuron do? spike no spike.
![Page 1: The Perceptron. 0T Afferents V thr V rest t max 0 What does a neuron do? spike no spike.](https://reader031.fdocuments.us/reader031/viewer/2022032521/56649d5e5503460f94a3d20a/html5/thumbnails/1.jpg)
The Perceptron
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( )K tD
0 T
Affe
ren
ts
Vthr
V rest
tmax 0 tD
What does a neuron do?
spike
no spike
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Affe
ren
ts
0 Ttmax-
VthrNull
We consider a simplified case: input is synchronous
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Affe
ren
ts
Alternatively, input is constant
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The perceptron
j jj
h W X 11 sgn
2 Y h
1X 2X 3X 4X
Y1W 4W
11 sgn
2
Y W X
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Geometrical interpretation
11 sgn
21
sgn cos2
Y W X
1X 2X
Y
1W 2W
W
1W
2W
X
1X
2X
![Page 7: The Perceptron. 0T Afferents V thr V rest t max 0 What does a neuron do? spike no spike.](https://reader031.fdocuments.us/reader031/viewer/2022032521/56649d5e5503460f94a3d20a/html5/thumbnails/7.jpg)
The perceptron
The Perceptron categorizes the space of inputs into inputs that should evoke a response and inputs that should not evoke a response
![Page 8: The Perceptron. 0T Afferents V thr V rest t max 0 What does a neuron do? spike no spike.](https://reader031.fdocuments.us/reader031/viewer/2022032521/56649d5e5503460f94a3d20a/html5/thumbnails/8.jpg)
Constraints on possible categorizations
1 11 sgn 1 sgn
2 2
i i
i
Y W X W X
1X
2X
![Page 9: The Perceptron. 0T Afferents V thr V rest t max 0 What does a neuron do? spike no spike.](https://reader031.fdocuments.us/reader031/viewer/2022032521/56649d5e5503460f94a3d20a/html5/thumbnails/9.jpg)
Constraints on possible categorizations
1X
2X
1 11 sgn 1 sgn
2 2
i i
i
Y W X W X
![Page 10: The Perceptron. 0T Afferents V thr V rest t max 0 What does a neuron do? spike no spike.](https://reader031.fdocuments.us/reader031/viewer/2022032521/56649d5e5503460f94a3d20a/html5/thumbnails/10.jpg)
Constraints on possible categorizations
1X
2X
1 11 sgn 1 sgn
2 2
i i
i
Y W X W X
![Page 11: The Perceptron. 0T Afferents V thr V rest t max 0 What does a neuron do? spike no spike.](https://reader031.fdocuments.us/reader031/viewer/2022032521/56649d5e5503460f94a3d20a/html5/thumbnails/11.jpg)
Constraints on possible categorizations
1X
2X
22 1 0 X X
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Solution: change of coordination
21X
2X
22 1 0 X X
![Page 13: The Perceptron. 0T Afferents V thr V rest t max 0 What does a neuron do? spike no spike.](https://reader031.fdocuments.us/reader031/viewer/2022032521/56649d5e5503460f94a3d20a/html5/thumbnails/13.jpg)
Solution: change of coordination
More complicated rules can be realized if an additional non-linear layer is added
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Deerinck 2002
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Llinas 1975
Ramon Y Cajal
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Llinas 1975
Increasing network capacity?
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The perceptron Learning algorithm
1 11 sgn 1 sgn
2 2
i i
i
Y W X W X
![Page 20: The Perceptron. 0T Afferents V thr V rest t max 0 What does a neuron do? spike no spike.](https://reader031.fdocuments.us/reader031/viewer/2022032521/56649d5e5503460f94a3d20a/html5/thumbnails/20.jpg)
The perceptron Learning algorithm
• Algorithm starts with an arbitrary set of weights
• Examples are presented one by one
• If the Perceptron correctly classifies the example no change in synaptic weights
• If the Perceptron does not correctly classify the example then make a Hebbian change in weights:
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The perceptron Learning algorithm
• If the example is to be classifies as ‘1’:
i i iW W X
• If the example is to be classifies as ‘0’:
i i iW W X
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Perceptron.m
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Hebbian plasticity and unsupervised learning
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1X 2X 3X 4X
Y1W 4W
Unsupervised learning in linear neurons
Y W X
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Hebbian plasticity
1 i i iW n W n X n Y n
Wi(n+1) = efficacy of synapse i after n updates
1X 2X 3X 4X
Y1W 4W
Y W X
is the plasticity rate
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Geometrical interpretation
1X 2X
Y
1W 2W
W
1W
2W
X
1X
2X