\[y = b + \sum_i x_i w_i\]
Here \(y =\) output, and \(x_i = i\)-th input. The sum is over the input connections.
\[z = b + \sum_i x_i w_i\] \[y = \text{ if } z >= 0 \text{ then } 1 \text{ else } 0\]
Can rewrite the bias to be a threshold in the if statement (threshold should be -b).
\[z = b + \sum_i x_i w_i\] \[y = \text{ if } z >= 0 \text{ then } z \text{ else } 0\]
\[z = b + \sum_i x_i w_i\] \[y = 1 / (1 + \exp(-z)) = S(z)\]
where S is the sigmoid function.
Learning handwritten digits by learning templates; winner is the template that has the most overlap (weighted) with the written digit.