Neural Networks

$$h_{w,b}(x) = f\left(\sum_{i=1}^{3} w_i x_i + b\right)$$

where $f$ is called the activation function.

Common choices for activation function

1. Linear

2. Binary threshold

3. Rectified Linear Unit (ReLU)

4. Sigmoid activation function

$$f(z) = \frac{1}{1 + \exp(-z)}$$
  • output range: $0$ to $1$

5. Hyperbolic tangent (tanh)

$$f(z) = \tanh(z) = \frac{e^z - e^{-z}}{e^z + e^{-z}}$$
  • output range: $-1$ to $1$