Four Rules That Cover Most of a Network
Last timeWhy the Sweep Runs Backwards
Addition copies the derivative to both inputs, multiplication swaps the two, a matrix product transposes, and an elementwise function scales. Almost every layer in use is built from these four.
There is one backward rule per kind of operation, and the list of operations
that matter is short. Four of them cover almost everything in a standard
network.
Addition: copy it
The derivative of a sum with respect to either of its inputs is one, so whatever
arrives at the output is handed to both inputs untouched.
- the derivative of the loss with respect to the output of this operation
- the derivative of the loss with respect to the first input
Addition also needs nothing from the forward pass. It does not matter what the
inputs were; the rule is the same either way.
The lesson stops here
6 more paragraphs to go
You have read the opening. The rest of the argument, the problems that check whether it landed, and the lines worth keeping at the end all come with a plan.
The first lesson of every course in the library reads the whole way through, free, so you can see exactly what the rest of them are.
See the planThe contentsThis is the reading half
Starting the course gives you your own copy of it. Every idea on every page has problems standing under it, marked with a reason rather than a tick, and any sentence you do not believe can be opened and argued with. None of that can happen on a page nobody owns.
The contents