# Neural Networks Model

## A single neuron model: logistic unit • Takes 3+1 inputs(the extra input called bias is just like $θ_0$ in logistic regression, not shown in picture).
• Both input and output could be represented as vectors, in which each unit has its own parameters $θ$
• All the units in the same layer take the same input $x$, as the pic shows.
• Each unit has only one output: $sigmoid(θ^Tx)$. Of course there’re other choices for sigmoid function.

## Neural Networks # Calculation from one layer to the next In the picture above, we have the networks from layer j to layer j+1, in which layer j has 3(+1) units while layer j+1 has 3 layers. Let $s_j=3$, $s_j+1=3$

• $α^{(j)}$ : Output of the $j_{th}$ layer. $s_j+1$ dimension vector.
• i^{(j)}$: Parameters in the$i{th}$unit of$(j+1)_{th}$layer.$s_j+1$dimension vector. •${\theta^{(j)} } = \begin{bmatrix} \theta1^{(j)} & \theta_2^{(j)} & \cdots & \theta{s(j + 1)}^{(j)} \end{bmatrix}^T$: All the network parameters from$j{th}$layer to${(j+1)}_{th}$layer. • We have:$\alpha^{(j+1)} = sigmoid(\mathbf{\theta^{(j)} }\alpha^{(j)})$add$\alpha_0^{(j+1)}$# Multiclass Classification Each$y^{(i)}$represents a different image corresponding to either a car, pedestrian, truck, or motorcycle. The inner layers, each provide us with some new information which leads to our final hypothesis function. The setup looks like: # Summary Example: layer 1 has 2 input nodes and layer 2 has 4 activation nodes. Dimension of$\Theta^{(1)}$is going to be 4×3 where$sj = 2$and$s{j+1} = 4$, so$s_{j+1} \times (s_j + 1) = 4 \times 3

Coursera ML(6)-Neural Networks Representation

https://iii.run/archives/b78e03f5e241.html

mmmwhy

2017-04-15

2022-10-30