HISTORY. In the 70 s vs today variants. (Multi-layer) Feed-forward (perceptron) Hebbian Recurrent
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1 NEURAL NETWORKS REFERENCES: ARTIFICIAL INTELLIGENCE FOR GAMES "ARTIFICIAL INTELLIGENCE: A NEW SYNTHESIS STEP- BY- STEP- BACKPROPAGATION- EXAMPLE/ "
2 HISTORY In the 70 s vs today variants (Multi-layer) Feed-forward (perceptron) Hebbian Recurrent
3 OVERVIEW Givens: Process: Using the Neural Network. Basically: a classifier.
4 EXAMPLE APPLICATION #1 Modeling a enemy AI. Supervised training Unsupervised training
5 EXAMPLE APPLICATION #2 (I.E. THE BORING LAB)
6 PERCEPTRONS Modeled after a single neuron. Components: Dendrites (Input) Axon (Output) Soma (Activation Function)
7 PERCEPTRON ACTIVATION FUNCTIONS Notation: II the vector of all input values. For us, input values are 0 or 1. WW the vector of weight values (same size as I) Positive, or negative, no limit. I usually initialize to -0.5 to = II WW the total (weighted) input to the perceptron.
8 PERCEPTRON ACTIVATION FUNCTIONS, CONT. Square function: ff Σ = 1 iiii Σ δ 0 iiii Σ < δ Sigmoid [logistic] function (the one we ll use): 1 ff Σ = 1 + ee kk(σ δ)
9 EXAMPLES Two inputs, one output, k=5.0 AND OR WW = δ=0.75 WW = δ=0.75 Input Σ f(σ) [0 0] [0 1] [1 0] [1 1] Input Σ f(σ) [0 0] [0 1] [1 0] [1 1] XOR Problem! Can t be done with a single perceptron O 0 Perceptron w 0 w 1 I 0 I 1
10 WHY NOT XOR? The first two examples are linearly separable WW 0 WW 1 W 2 =δ II = II 0 II 1 OUTPUT=1 OUTPUT=0 OOOOOOOOOOOO = 0 0 In higher dimensions, the dividing line is a hyper-plane, not a plane
11 AND AND OR δ=0.75 δ= AND OR
12 XOR You can t draw a line to separate the True s from the False s
13 MULTI-LAYER PERCEPTRON NETWORKS , WW 00 = δ= WW 11 = δ= , 0.6
14 XOR NNET O 0 Perceptron 1,0 <0.4> Perceptron 0,0 <0.2> Perceptron 0,1 <0.3> I 0 I 1
15 FEED FORWARD Feed Input to bottom of NNet Each Perceptron outputs its activation result to next layer as input I used a k=20 here Input Step# P(layer,#) Σ f(σ) [0,0] 1 P0, P0, P1, [0,1] 1 P0, P0, e-8 3 P1, [1, 0] 1 P0, e-8 2 P0, P1, [1, 1] 1 P0, P0, P1,
16 TRAINING INTRO Feed Forward is using a Nnet. Training is creating a NNet. Error-correction procedure (single perceptron) o WWnnnnnn = WW + cc II ff EEEEEE o δδ = δδ cc ff EEEEEE BTW (Keith): the derivation of this formula involves partialderivatives
17 TRAINING INTRO, CONT. f f(1-f) WWWWWWWW = WW + cc II ff EEEEEE Err = dd oo Observations
18 MY TRAINING RESULTS One perceptron, trying to learn ADD Initial weights and threshold = 0 total_error = sum of err 2 for all 4 cases (shuffled) Repeated for 1000 iterations
19 TRAINING (1 LAYER, M OUTPUTS) Similarities and differences EEEEEE = dddddddddddddd aaaaaaaaaaaa Correction update for i in range(num_perceptrons): WW ii += cc II ff ii EEEEEE ii δ = cc ff ii EEEEEE ii I found this useful: ttttttttll eeeeee = EEEEEE (i.e. vector-magnitude)
20 TRAINING (N LAYERS, M OUTPUTS) The most general case. For all perceptrons, calculate the following (in reverse (output to input)) BBBBBBBBBB ii,jj = nn kk=0 EEEEEE jj wwww jj kk BBBBBBBBBB ii+1,kk iiii llllllllll ii iiii aaaa oooooooooooo llllllllll eeeeeeee II SSSSSSSSSSSS ii = OOOOOOOOOOOO oooo llllllllll ii 1 Then to update a perceptron: WW ii,jj += cc SSSSSSSSSSSS ii ff ii,jj BBBBBBBBBB ii,jj iiii ii iiii ttttttt iiii ttttt bottommost llllllllll eeeeeeee δ = cc ff ii BBBBBBBBBB ii,jj Make sure you use the existing weights for blame calculations. Perhaps wait until the back-prop is done to update weights?
21 MY SUGGESTION Start with a Perceptron / NNet class Manually set up AND, OR, XOR, test feed-forward Learn AND Learn XOR Learn XOR w/ weird structure 2 input, 1 output hidden-size=[5, 3] Learn a challenging problem (i.e. the lab)
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