The hidden unit has no answer

The last slide followed the incoming weights for all four hidden units. For this bottle, they produced these four positive totals:

.50, .20, .15, .10

ReLU leaves them unchanged. These numbers are the hidden signals. They are not weights.

The four output weights on the right have also returned to the starting value 25. The network now has untrained weights on both sides of the hidden units.

Together they make this guess:

(.50 x 25) + (.20 x 25) + (.15 x 25) + (.10 x 25) = $23.75

The bottle's real price is $40, so the machine's $23.75 guess is $16.25 too low.

Now look at target ? beside each hidden signal. The signal itself is known. The question mark asks what the correct signal should have been.

The bottle tells us price = $40. It does not tell us whether hidden 1 should have sent .30, .50, or .80.

In Chapter 1, every weight connected an input directly to the price. Here, an incoming weight first changes a hidden signal. That signal then passes through another weight before reaching the price.

The bottle gives us one error, but it does not give each weight its own correction. Training must answer four questions:

Which weights affected the wrong price?
How strongly did each one affect it?
Should each weight move up or down?
How large should each nudge be?

That is the new problem. We must answer those questions using the price error we do have.

The hidden unit has no answer

The last slide followed the incoming weights for all four hidden units. For this bottle, they produced these four positive totals:

.50, .20, .15, .10

ReLU leaves them unchanged. These numbers are the hidden signals. They are not weights.

The four output weights on the right have also returned to the starting value 25. The network now has untrained weights on both sides of the hidden units.

Together they make this guess:

(.50 x 25) + (.20 x 25) + (.15 x 25) + (.10 x 25) = $23.75

The bottle's real price is $40, so the machine's $23.75 guess is $16.25 too low.

Now look at target ? beside each hidden signal. The signal itself is known. The question mark asks what the correct signal should have been.

The bottle tells us price = $40. It does not tell us whether hidden 1 should have sent .30, .50, or .80.

In Chapter 1, every weight connected an input directly to the price. Here, an incoming weight first changes a hidden signal. That signal then passes through another weight before reaching the price.

The bottle gives us one error, but it does not give each weight its own correction. Training must answer four questions:

Which weights affected the wrong price?
How strongly did each one affect it?
Should each weight move up or down?
How large should each nudge be?

That is the new problem. We must answer those questions using the price error we do have.