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Unformatted text preview: Left: The synaptic response
of a neuron in the
somatosensory cortex to
repeated presynaptic
stimulation varies from trial
to trial. (Steriade) Review: Simple Hebb rule for synaptic learning
Simultaneous presynaptic and postsynaptic
activities lead to strengthened synapse. j Xj i Xi Wij
ΔWij = k Xi Xj
where Xj and Xi are presynaptic and postsynaptic activities,
respectively, and k > 0 is learning rate. Hebbian learning a Hopfield network
The weight matrix is a correlation matrix of the inputs:
T
W = s1s1 + s 2s T + + s ms T
2
m where the memory patterns are orthogonal to one another:
⎧ N if i = j
⎪
s s =⎨
⎪ 0 if i ≠ j
⎩
where N is the number of units in the network. Then
Ws i = Ns i
T
ij Each memory pattern is an eigenvector of the weight matrix. Inner product and outer product between vectors
⎛a⎞
⎛b⎞
1
⎟
⎜
⎜ 1⎟
Let a = ⎜ ⎟ and b = ⎜ ⎟ be two column vectors.
⎜a ⎟
⎜b⎟
⎝ n⎠
⎝ n⎠
Their inner product a Tb = a1b1 + + an bn is a scalar.
Their outer product is a matrix:
⎛ ab
⎜ 11
⎜ a2 b1
T
ab = ⎜
⎜
⎜ an b1
⎝ a1b2 a1bn ⎞
⎟
a2 b2 a2 bn ⎟
⎟ ⎟
an b2 an bn ⎟
⎠ Hippocampus in Rat Brain A slice of
hippocampus Cortex is cut out to reveal
the left hippocampus LongTerm Potentiation (LTP)
The synapses from the
CA3 neurons to a CA1
neuron were enhanced,
as measured by...
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 Spring '14

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