Given weights, inputs, and bias for a single neuron layer, compute its output using matrix multiplication and the sigmoid activation function. Consider a layer with 3 inputs and 2 neurons, taking a single batch containing just one sample.

1. Determining Shapes:

   • The shape of the input matrix I should have its first dimension representing the number of samples in the batch. Given one sample with 3 inputs, its size will be 1x3.
   • The weight matrix W should have its columns representing input weights for each neuron. So for 2 neurons with 3 inputs, the expected shape is 3x2. This isn't the case, so you need to transpose the weight matrix to achieve the required shape.

2. Matrix Multiplication:

   • With the matrices in the correct shape, perform the matrix multiplication.
   • Recall that in matrix multiplication, the output is derived from the dot product of each row of the first matrix with each column of the second matrix. Ensure you multiply in the right order.

3. Bias Addition:

   • Simply perform an element-wise addition of the result from the matrix multiplication with the bias.

4. Applying Activation:

   • Use the sigmoid activation function on the outcome from the bias addition to get the output of the neuron.
   • TensorFlow provides the sigmoid function as tf.sigmoid().

Note

In the end of the course we'll delve into implementing a complete feed-forward network using TensorFlow. This exercise is setting the foundation for that.