This article focus on the back propagate in CNN and its math foundation.

The following picture shows the last 3 layer of CNN. This CNN has n layers totally. And we will demonstrate the **back propagate** and **weight updating** process of on it.

**Important Notations:**

Then the Loss function is:

### Update the weights of **last** layer (layer n)

First, let’s update the weights of **last** layer. That is: update all parameters of the 2 filters of layer n.

So apply **chain rule** again:

### Update the weights of **inner** layer (eg: layer n-1)

Second, let’s update the weights of inner layers (eg: layer n-1). That is: update all parameters of the 3 filters of layer n-1.

Instead of stopping at equation ③, we have to continue:

### Convergence

The network reaches a convergence when the outcome of Loss function is stably less than a determined value

*Disclaimer:*

*This is only a study note. Correctness is not guaranteed*

*Original work. Error correction and Forwarding is welcomed*.