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.
The Perceptron
( )K tD
0 T
Affe
ren
ts
Vthr
V rest
tmax 0 tD
What does a neuron do?
spike
no spike
Affe
ren
ts
0 Ttmax-
VthrNull
We consider a simplified case: input is synchronous
Affe
ren
ts
Alternatively, input is constant
The perceptron
j jj
h W X 11 sgn
2 Y h
1X 2X 3X 4X
Y1W 4W
11 sgn
2
Y W X
Geometrical interpretation
11 sgn
21
sgn cos2
Y W X
1X 2X
Y
1W 2W
W
1W
2W
X
1X
2X
The perceptron
The Perceptron categorizes the space of inputs into inputs that should evoke a response and inputs that should not evoke a response
Constraints on possible categorizations
1 11 sgn 1 sgn
2 2
i i
i
Y W X W X
1X
2X
Constraints on possible categorizations
1X
2X
1 11 sgn 1 sgn
2 2
i i
i
Y W X W X
Constraints on possible categorizations
1X
2X
1 11 sgn 1 sgn
2 2
i i
i
Y W X W X
Constraints on possible categorizations
1X
2X
22 1 0 X X
Solution: change of coordination
21X
2X
22 1 0 X X
Solution: change of coordination
More complicated rules can be realized if an additional non-linear layer is added
Deerinck 2002
Llinas 1975
Ramon Y Cajal
Llinas 1975
Increasing network capacity?
The perceptron Learning algorithm
1 11 sgn 1 sgn
2 2
i i
i
Y W X W X
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:
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
Perceptron.m
Hebbian plasticity and unsupervised learning
1X 2X 3X 4X
Y1W 4W
Unsupervised learning in linear neurons
Y W X
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
Geometrical interpretation
1X 2X
Y
1W 2W
W
1W
2W
X
1X
2X