A Three-Layer Example: Working on the Output Layer

Input to the output layer

Let’s calculate the combined moderated input into the final layer $X = W \cdot I$.

The inputs into this layer are the outputs from the second layer we just worked out, named $O_\text{hidden}$. The weights are those for the links between the second and third layers, named $W_\text{hidden\_output}$, not those we just used between the first and second. Therefore, we have:

$$X_{\text{output}} = W_{\text{hidden\_output}} \cdot O_{\text{hidden}}$$

So, working this out in the same way we did before gives the following result for the combined moderated inputs into the final output layer:

$$X_{\text{output}} =\begin{bmatrix} 0.3 & 0.7 & 0.5 \\ 0.6 & 0.5 & 0.2\\ 0.8 & 0.1 & 0.9 \end{bmatrix} \cdot \begin{bmatrix} 0.761 \\ 0.603 \\ 0.650 \end{bmatrix}$$

$$X_{\text{output}} = \begin{bmatrix} 0.975 \\ 0.888 \\ 1.254 \end{bmatrix}$$