Why the Last Two Steps Are One Step
Last timeThe Matrix That Is Never Built
The scores become probabilities and the probabilities become a loss. Doing the backward step through both at once gives an answer so simple that implementations refuse to separate them.
Most of a network has awkward derivatives that are merely awkward. The last two
operations are different: taken separately they are worse than awkward, and taken
together they collapse into the simplest expression in the whole subject. This
lesson does that collapse slowly, because the answer is worth recognising on
sight.
The two operations
The network's final layer produces one score per option, unbounded and
uninterpretable. Two things happen to them.
The collapse
Take the simplest case that shows it: two options, scores and , with the
first one correct. The loss is the negative logarithm of the first probability,
which written out is the negative of plus the logarithm of the total.
The lesson stops here
5 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