#function-class

Question 1: Single choice

A one-hidden-layer network computes $o = \mathbf{v}^\top\tanh(\mathbf{W}\mathbf{x} + \mathbf{b}) + c$ , with $\tanh$ applied elementwise. Which sigmoid network computes exactly the same function for every $\mathbf{x}$ ? ( $\mathbf{1}$ is the all-ones vector.)

None: sigmoid units only output values in $(0, 1)$ , so the network can never produce negative outputs1
$o = (2\mathbf{v})^\top\sigma(2\mathbf{W}\mathbf{x} + 2\mathbf{b}) + c - \mathbf{1}^\top\mathbf{v}$ 2
$o = \mathbf{v}^\top\sigma(2\mathbf{W}\mathbf{x} + 2\mathbf{b}) + c$ 3
$o = (2\mathbf{v})^\top\sigma(\mathbf{W}\mathbf{x} + \mathbf{b}) + c - \mathbf{1}^\top\mathbf{v}$ 4

Timed test