For Wednesday. Finish chapter 22 No homework. Program 4. Any questions?. MultiLayer Neural Networks. Multilayer networks can represent arbitrary functions, but building an effective learning method for such networks was thought to be difficult.
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oj = 1/(1 + e-(netj - Tj) )
E(W) = 1/2 *( S S(tkd - okd)2)
where D is the set of training examples, K is the set of output units, tkd is the target output for the kth unit given input d, and okd is network output for the kth unit given input d.
¶oj/ ¶netj = oj(1 - oj)
wji = -(E / wji)
wji = djoi
dj = oj (1 - oj) (tj - oj) if j is an output unit
dj = oj (1 - oj) Sdk wkj otherwise
where h is a constant called the learning rate,
tj is the correct output for unit j,
dj is an error measure for unit j.
Until all examples produce the correct output within e or the meansquared error ceases to decrease (or other termination criteria):
For each example in training set do:
Compute the network output for this example.
Compute the error between this output and the correct output.
Backpropagate this error and adjust weights to decrease this error.
Multilayer sigmoidal networks are very expressive.
Hidden unit A represents ¬(X Ù Y)
Hidden unit B represents ¬(X Ú Y)
Output O represents: A Ù ¬B
¬(X Ù Y) Ù (X Ú Y)
X Å Y
I saw the man on the hill with the telescope.
I saw the Grand Canyon flying to LA.
I saw a jet flying to LA.
Time flies like an arrow.
Horse flies like a sugar cube.
Time runners like a coach.
Time cars like a Porsche.
The dog bit the boy.
The boy bit the dog.
* Bit boy the dog the
Colorless green ideas sleep furiously.
Passerby: (pets dog) Chomp!
I thought you said your dog didn't bite!!
Clouseau:That, sir, is not my dog!
“grey twine” vs. “great wine”
“youth in Asia” vs. “euthanasia”
“yawanna” > “do you want to”
I ate spaghetti with a fork.
I ate spaghetti with meatballs.
I put the plant in the window.
Ford put the plant in Mexico.
The dog is in the pen.
The ink is in the pen.
The ham sandwich wants another beer.
John thinks vanilla.