Updating cycles for postsynaptic neuron outputs and connection weights in a Hebbian Learning Network.Step 1: Initialization: Set initial synaptic weights to small random values in the interval [0, 1].Step 2: Activation: Compute the postsynaptic neuron output Y j from the presynaptic inputs element X i j in the data-item X j : Y j = if ( i=1..n Sum Xi j*Wi j –T)>=0 then 1 else 0. T is the threshold value of neuronStep 3: Update the weights in the network. Wi j+1 = Wi j +a * Y j*Xi j where a is the learning rate parameterStep 4: Iteration: go back to Step 2Task: Consider a Neuron with inputs from 4 neighbouring neurons. The learning rate a = 1 and the threshold T = 1The weights are initiated as W1 = 1 1 1 1. The training data vectors are: X1= 1 0 0 1, X2 = 0 1 1 0 and X3 = 1 1 0 0.X1 1 0 0 1 W1 1 1 1 1 Y1 = 1 W2 = W1 + Y1 * (1 0 0 1) = 2 1 1 2…...................................................................................................... ?How will the final weight vector look like when the training data has been processed? 3 2 2 3 2 2 3 3 3 3 2 2 3 2 3 2 None of the above
Question
Updating cycles for postsynaptic neuron outputs and connection weights in a Hebbian Learning Network.Step 1: Initialization: Set initial synaptic weights to small random values in the interval [0, 1].Step 2: Activation: Compute the postsynaptic neuron output Y j from the presynaptic inputs element X i j in the data-item X j : Y j = if ( i=1..n Sum Xi jWi j –T)>=0 then 1 else 0. T is the threshold value of neuronStep 3: Update the weights in the network. Wi j+1 = Wi j +a * Y jXi j where a is the learning rate parameterStep 4: Iteration: go back to Step 2Task: Consider a Neuron with inputs from 4 neighbouring neurons. The learning rate a = 1 and the threshold T = 1The weights are initiated as W1 = 1 1 1 1. The training data vectors are: X1= 1 0 0 1, X2 = 0 1 1 0 and X3 = 1 1 0 0.X1 1 0 0 1 W1 1 1 1 1 Y1 = 1 W2 = W1 + Y1 * (1 0 0 1) = 2 1 1 2…...................................................................................................... ?How will the final weight vector look like when the training data has been processed? 3 2 2 3 2 2 3 3 3 3 2 2 3 2 3 2 None of the above
Solution
The question is asking for the final weight vector after processing the training data in a Hebbian Learning Network. The initial weight vector is W1 = 1 1 1 1. The training data vectors are X1= 1 0 0 1, X2 = 0 1 1 0 and X3 = 1 1 0 0.
After processing X1, the weight vector becomes W2 = 2 1 1 2.
Next, we process X2. The output Y2 is calculated as follows: Y2 = if (Sum Xi jWi j –T)>=0 then 1 else 0. In this case, Y2 = if (02 + 11 + 11 + 0*2 - 1) >= 0 then 1 else 0. So, Y2 = 1.
Then, we update the weights: W3 = W2 + Y2 * X2 = 2 1 1 2 + 1 * (0 1 1 0) = 2 2 2 2.
Finally, we process X3. The output Y3 is calculated as follows: Y3 = if (Sum Xi jWi j –T)>=0 then 1 else 0. In this case, Y3 = if (12 + 12 + 02 + 0*2 - 1) >= 0 then 1 else 0. So, Y3 = 1.
Then, we update the weights: W4 = W3 + Y3 * X3 = 2 2 2 2 + 1 * (1 1 0 0) = 3 3 2 2.
So, the final weight vector after processing the training data is 3 3 2 2. Therefore, the correct answer is "None of the above".
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