Left the synaptic response of a neuron in the

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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 pre-synaptic and post-synaptic 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 Long-Term Potentiation (LTP) The synapses from the CA3 neurons to a CA1 neuron were enhanced, as measured by...
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