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Ultimately, the goal is to get a predicted output that matches the actual output. Summing the product of the weights and the values helps achieve part of this process. Therefore, a random input of 0.5 and 0.5 would have a summation output of the following:

z = 0.5 * w1 + 0.5 * w2 + b 

Or it would have the following output with our current random values for our weights, w1 and w2:

z = 0.5 * (-0.2047) + 0.5 * (0.47894) + (-0.51943) = -7.557

The variable z is assigned as the product summation of the weights with the data points. Currently, the weights and biases are completely random. However, as mentioned earlier in the section, through a process called backpropagation, using gradient descent, the weights will be tweaked until a more desirable outcome is determined. Gradient descent is simply the process of identifying the optimal values for our weights that will give us the best prediction output with the least amount of error.  The process of identifying the optimal values involves identifying the local minimum of a function. Gradient descent will be discussed later on in this chapter.