What the Forward Pass Has to Leave Behind
Last timeThe Layer Where Everything Cancels
Every backward rule needs some forward value to work with, and those values have to be held from the moment they are produced until the backward pass reaches them. That is the real cost of training.
Every rule in this course has an ingredient list. The rule for a multiplication
needs the other input; the rule for a matrix product needs both. Those
ingredients come from the forward pass, and they have to still be there when the
backward pass arrives, which can be a long time later. That waiting is what
training costs.
Reading the appetite off the rule
You do not have to look anything up. Whatever appears in a rule that is not a
derivative is something the forward pass must leave behind.
| values kept per element | arithmetic to use them | relative memory cost | |
|---|---|---|---|
| an addition | 0 | 1 | 0 |
| a saturating function | 1 | 1 | 1 |
| a matrix product | 2 | 1 | 2 |
| a gate | 1 | 1 | 1 |
Additions are free, which is a small reason to prefer architectures full of them.
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