1. Chapter 18 Connectionist Models
Artificial Intelligence
ดร.วิภาดา เวทย์ประสิทธิ์ ภาควิชาวิทยาการคอมพิวเตอร์ คณะวิทยาศาสตร์ มหาวิทยาลัยสงขลานครินทร์

2. Hopfiled [1982] : theory of memory p.483
Hopfield Networks
Hopfiled [1982] : theory of memory p.483
Model of content addressable memory p. 491
distribute representative
distributed, asynchronous control
content-addressable memory
fault tolerance
Figure 18.1 p. 490
black unit = active
white unit = inactive
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3. units are connected to each other with weighted symmetric connection
Hopfield Networks
units are connected to each other with weighted
symmetric connection
a positive weighted connection  indicates that the two unit tend to activate each other.
a negative weighted connection  allows an active unit to deactivate a neighboring units.
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4. Parallel relaxation algorithm
The network operates as follows:
a random unit is chosen
if any of it neighbors are active, the unit computes the sum of the weights on the connections to those active neighbors.
if the sum is positive, the unit becomes active,
otherwise it becomes inactive.
Another random unit is chosen, and the process repeat until the network reach a stable state. (e.g. until no more unit can change state)
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5. Figure 18.1 p. 490 A Hopfield network
Hopfield Networks
Figure 18.1 p A Hopfield network
black and positive  will attempt to activate the unit connected to it
Figure 18.2 p. 491 Four stable states : storing the pattern
given any set of weights and any initial state, the parallel relaxation algorithm will be stale into one of these four states
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6. Figure 18.3 p. 491 Model of content-addressable memory
Hopfield Networks
Figure 18.3 p Model of content-addressable memory
Setting the activities of the units to correspond to a partial pattern
To retrieve a pattern, we need to apply the portion of it.
the network will then settle into the stable state that best matches the partial pattern.
shows the local minima = nearest stable state
Figure 18.4 p. 492 what a Hopfield network compute
from one state to another state.
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7. Hopfield Networks
Problem : sometimes the network can not find global solution because the network stick with the local minima because they settle into stable states via a completely distributed algorithm. For example in Figure 18.4, If a network reaches a stable state A then no single unit willing to change its state in order to move uphill, so the network will never reach global optimal state B.
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8. A perceptron (1962) Rosenblatt
models a neural by taking a weight sum of its inputs and sending the output 1 if the sum is grater than some adjustable threshold value (otherwise it send 0)
Figure p Threshold function
Figure 18.8 Intelligence System
g(x) = summation i = 1 to n of wixi
output(x) = if g(x) > 0
0 if g(x) < 0
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9. x2 = -(w1/w2)x1 - (w0/w2)  equation for a line
Perceptron
In case of zero with two inputs
g(x) = w0 + w1x1 + w2x2 = 0
x2 = -(w1/w2)x1 - (w0/w2)  equation for a line
the location of the line is determine by the weight w0 w1 and w2
if an input vector lies on one side of the line, the perceptron will output 1
if it lies on the other side, the perceptron will output 0
Decision surface : a line that correctly separates the training instances corresponds to a perfectly function perceptron.
See Figure 18.9 p. 496
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10. so we know how good a set of weights is.
Decision surface
the absolute value of g(x) tells how far a given input vector x lies from the decision surface.
so we know how good a set of weights is.
let w be the weight vector (w0, w1,.., wn)
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11. Multilayer perceptron
Figure p. 497 Adjusting the weights by Gradient Descent
hill-climbing/down-hill
See Algorithm Fixed-Increment Perceptron Learning
Figure p.499 A perceptron learning to solve a classification problem : K = 10, K = 100, K = 635
Figure p.500 the XOR is not linearly separable
We need multilayer perceptron to solve the XOR problem
See Figure 18.3 p where x1 = 1 and x2 = 1
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12. Backpropagation Algorithm
Parker 1985, Rumelhart et. al 1986
fully connected, feedforward network, multilayer network
Figure 18.14, p.502
fast, resistant to damage , learn efficiently
see Figure 18.15, p.503
use for classify problem
use sigmoid activation function (S-shaped) : it process a real value between 0 and 1 as output see Figure 18.16, p.503
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13. Backpropagation Algorithm
Figure 18.14, p.502
start with a random set of weights
the network adjusts its weights each time it sees an input-outout pair
each pair require two stages
1) a forward pass : involves presenting a sample input to the network and letting activations flow until they reach the output layer.
2) a backward pass : the network’s actual output (from the forward pass) is compared with the target output and error estimates a re computed for output units
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14. Backpropagation Algorithm
The weight connected to the output units can be adjusted in order to reduce the errors.
We can use the error estimates of the output units to derive error estimates for the units in the hidden layers.
Finally errors are propagated back to the connections stemming from the input units.
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15. Backpropagation Algorithm
p initial weight = -0.1 to 0.1, initial the activation function of the thresholding unit, learning rate = ,
choose an input-output pair
oj = network actual value (ค่าที่ network คำนวณได้)
yj = target output (ค่าจริงของข้อมูล ที่เราใช้ train)
adjust weights between the hidden layer and output layer (w2ij)
adjust weights between the input layer and hidden layer (w1ij)
input layer w1ij hidden layer w2i j output layer
Xi A
hj B
oj C
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16. Backpropagation Algorithm
Backpropagation updates its weights after seeing each input-output pair. After it has seen all the input-output pairs and adjusts its weight that many times, we call one epoch had been completed.
number of epochs make the network more efficiency
we can speed up the network by using the momentum term 
see equation p. 506
perceptron convergence theorem (Rosenblatt 1962) : guarantees that the perceptron will find a solution...
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17. Backpropagation Algorithm
Generalization
Figure p.508
Good network should capable of storing entire training sets and have a setting for weights that generally describe the mapping for all cases, not the individual input-output pairs.
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18. use Hopfield machine and simulated annealing (p. 30 Chapter 3)
Boltzman Machine
p. 509
use Hopfield machine and simulated annealing (p. 30 Chapter 3)
try to get global solution
if several units decided to change state simultaneously, the network might be able to scale the hill and slip into state B.
See Figure 18.4 p.492
more time consuming than backpropagation because the complex annealing process but it has the advantage to solve the constraint satisfaction problem.
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19. Reinforcement Learning
use punishment and reward system (same as animal)
1) the network is presented with a sample input form the training set
2) the network computes what it thinks should be the sample output
3) the network is supplied with a real-valued judgment by a teacher
receive positive value : indicates good performance
receive negative value : indicates bad performance
4) the network adjusts its weights, and process repeats
we try to receive positive value or to have good performance
supervised learning
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20. Unsupervised Learning
no feedback for its outputs
no teacher required
given a set of input data, the network is allowed to discover regularities and relations between the different parts of the input
feature discovery : Figure 18.8 p. 511 Data for unsupervised learning
3 types of animal... 1) mammals 2)reptiles 3) birds
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21. Unsupervised Learning
we need to sure that only one of the three output units becomes active for any given input.
see Figure p. 512 A competitive learning network
use winner-take-all behavior
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22. Unsupervised Learning
single competitive learning algorithm p
1) present an input vector
2) calculate the initial activation for each output unit
3) let the output units fight until only one is active
4) adjust the weights on the input lines that lead to the single active output unit, increase the weights on connections between the active output unit and active input units. (this makes it more likely that the output unit will be active next time the pattern is required)
5) repeat steps 1 to 4 for all input patterns for many epochs.
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23. use in temporal AI task, planning, natural language processing
Recurrent Networks
Jordan 1986
use in temporal AI task, planning, natural language processing
we need more than a single output vector
we need a series of output vectors
Figure p A Jordan network
Figure p A recurrent network with a mental model
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24. Connectionist AI and Symbolic AI
- Search : parallel relaxation
Knowledge Representation : very large number of real-valued connection strengths. Structure often stored as distributed patterns of activation.
Learning : Backpropagation, Boltzmann machines, reinforcement learning, unsupervised learning
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25. Connectionist AI and Symbolic AI
- Search : state space traversal
Knowledge Representation : Predicate logic, semantic networks, frames, scripts.
Learning : Macro-operators, version spaces, explanation-based learning, discovery.
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