Chapter 18 Connectionist Models 323-670 Artificial Intelligence ดร.วิภาดา เวทย์ประสิทธิ์ ภาควิชาวิทยาการคอมพิวเตอร์ คณะวิทยาศาสตร์ มหาวิทยาลัยสงขลานครินทร์

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 323-670 Artificial Intelligence Lecture41-43 Page 2

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. 323-670 Artificial Intelligence Lecture41-43 Page 3

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) 323-670 Artificial Intelligence Lecture41-43 Page 4

Figure 18.1 p. 490 A Hopfield network Hopfield Networks Figure 18.1 p. 490 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 323-670 Artificial Intelligence Lecture41-43 Page 5

Figure 18.3 p. 491 Model of content-addressable memory Hopfield Networks Figure 18.3 p. 491 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. 323-670 Artificial Intelligence Lecture41-43 Page 6

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. 323-670 Artificial Intelligence Lecture41-43 Page 7

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 18.5-18.7 p.493-394 Threshold function Figure 18.8 Intelligence System g(x) = summation i = 1 to n of wixi output(x) = 1 if g(x) > 0 0 if g(x) < 0 323-670 Artificial Intelligence Lecture41-43 Page 8

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. 496 323-670 Artificial Intelligence Lecture41-43 Page 9

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) 323-670 Artificial Intelligence Lecture41-43 Page 10

Multilayer perceptron Figure 18.10 p. 497 Adjusting the weights by Gradient Descent hill-climbing/down-hill See Algorithm Fixed-Increment Perceptron Learning Figure 18.11 p.499 A perceptron learning to solve a classification problem : K = 10, K = 100, K = 635 Figure 18.12 p.500 the XOR is not linearly separable We need multilayer perceptron to solve the XOR problem See Figure 18.3 p. 500 where x1 = 1 and x2 = 1 323-670 Artificial Intelligence Lecture41-43 Page 11

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.503 323-670 Artificial Intelligence Lecture41-43 Page 12

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 323-670 Artificial Intelligence Lecture41-43 Page 13

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. 323-670 Artificial Intelligence Lecture41-43 Page 14

Backpropagation Algorithm p. 504-506... 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 323-670 Artificial Intelligence Lecture41-43 Page 15

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... 323-670 Artificial Intelligence Lecture41-43 Page 16

Backpropagation Algorithm Generalization Figure 18.17 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. 323-670 Artificial Intelligence Lecture41-43 Page 17

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. 323-670 Artificial Intelligence Lecture41-43 Page 18

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 323-670 Artificial Intelligence Lecture41-43 Page 19

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 323-670 Artificial Intelligence Lecture41-43 Page 20

Unsupervised Learning we need to sure that only one of the three output units becomes active for any given input. see Figure 18.19 p. 512 A competitive learning network use winner-take-all behavior 323-670 Artificial Intelligence Lecture41-43 Page 21

Unsupervised Learning single competitive learning algorithm p. 512-513 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. 323-670 Artificial Intelligence Lecture41-43 Page 22

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 18.22 p. 518 A Jordan network Figure 18.23 p. 519 A recurrent network with a mental model 323-670 Artificial Intelligence Lecture41-43 Page 23

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 323-670 Artificial Intelligence Lecture41-43 Page 24

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. 323-670 Artificial Intelligence Lecture41-43 Page 25