Neural Networks (Geoffrey Hinton Course)

Some Simple Models or Neurons

$y$ output, $x_i$ input.

$y = b + \sum_{i} x_i w_i$

$w_i$ weights, $b$ bias

$z = \sum_{i} x_i w_i$

$y = 1$ if $z \geq \theta$, $0$ otherwise.

Or, equivalently,

$z = b + \sum_{i} x_i w_i$

$y = 1$ if $z \geq 0$, $0$ otherwise.

$z = b + \sum_{i} x_i w_i$

$y = z$ if $z > 0$, $0$ otherwise. (linear above zero, decision at zero.)

Give a real-valued output that is a smooth and bounded function of their total input.

$z = b + \sum_{i} x_i w_i$

$y = \frac{1}{1 + e^{-z}}$