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I was following andrew-ng coursera course on deep learning and there's a question that has been asked there which I couldn't figure out the answer for?

Suppose your input is a 300 by 300 color (RGB) image, and you use a convolutional layer with 100 filters that are each 5x5. How many parameters does this hidden layer have (including the bias parameters)?

  1. 2501

  2. 2600

  3. 7500

  4. 7600

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The right answer is the fourth.

From this, the formula to calculate the number of parameters in a convolutional layer is (nml+1)*k with n = m = 5, k = 100, l = 3 and +1 for the bias.

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As we have a RGB Image so our filter changes from 2D to 3D, whose dimension will be 5 * 5 * (no of channels from previous layer) = 5 * 5 * 3 = 75

Now we have 100 such filters, so total parameters increases to = 75 * 100 = 7500

Each filter has a constant bias associated with it, hence this introduces 100 biases for each filter or l00 more features

Total feature required = 5 * 5 * 3 * 100 + 100 = 7600

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