Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Hebbian Learning Rules Meg Broderick December 12, 2002 Submitted in Partial Fulfillment of the Requirements for DCS860E, Artificial Intelligence Doctor of Professional Studies Pace University Hebbian Learning Rules Learning rules are algorithms which describe the relative weights of connections in a network. Some communications, psychological and biological associations may be governed by these relationships. In 1949, D.O. Hobbs, the Father of Cognitive Psychobiology [Harnad], published a description of a simple set of rules in The Organization of Behavior [Hobbs]. Simply put, he explained that the simultaneous excitation of two neurons results in the strengthening of the connection between them. [French] This finding provided new ways to observe, measure and improve the interaction of elements in a computer network, web-based search engines, as well as physiological learning in the brain. While there are many variations on learning rules, including delta rule and back propagation, this report will focus only on the Hebbian Learning Rules. I. Neural Learning: The Hebb Legacy Donald Olding Hebb (1904-1985) was a graduate of Dalhousie University in Alberta and McGill University in Quebec, Canada. By training a psychologist, he performed significant research in the area of neurology and the reaction of the brain to various stimuli. Despite the pervasive behavioral turn that psychology had taken at that time, he continued to pursue the physiological relationships of neurons and brain functioning [Klein]. Hebb postulated that the “connections between neurons increase in efficacy in proportion to the degree of correlation between pre- and post- synaptic activity.” [Klein] He also suggested that groups of neurons firing together create a cell-assembly which last after the firing event. Finally, he postulated that thinking is the sequential activation of cell-assemblies [Klein]. Another way of viewing these hypotheses is that the proximity and activity of neurons can create a type of persistent learning or memory. Page 2 of 9 II. Types of Learning The Hebbian learning laws described coincidence learning, in which the proximity of the events affected the relative weights of the learning. Using the example from Artificial Learning: Structures and Strategies for Complex Problem Solving [Luger]: Suppose neuron i and j are connected so the output of i (oi) is an input of j (oj). The weight adjustment between them, ΔW is the sign (+ or -) of c, the constant controlling the learning rate. Oi and Oj are the signs of the outputs oi and oj, respectively. A. Oi Oj Oi *Oj + + + + - - - + - - - + Unsupervised Learning Unsupervised learning describes the “natural” way in which the various neurons learn from each other. No artificial weights are added to move the inputs in one direction or another. Miller and McKay postulate that these correlation-based synaptic methods are basically unstable: either all synapses grow until each reaches the maximum allowable strength or all decay to zero strength [MacKay]. For this reason, supervised learning, forced or modified (hybrid) constraints in learning are often used in psychobiological training models. An example of hybrid Hebbian learning shown in Luger models the classic experiment of Pavlovian training for dogs: the dogs hear the bell and see the food. This fires the neurons to train them to respond to the auditory and visual stimuli. Ultimately, the brain “learns” that the sound of Page 3 of 9 the bell implies food and the physical response (salivation) occurs. The formula that demonstrates that relationship is: ΔW = c * f(X,W) * X Where: c = learning constant F(X,W) = oi, X is input to i Using the example in the text (pages 447-450), the reader learns that by applying the rules to the initial vectors {1, -1,1} and { -1, 1, -1}, and the weight factors {1, -1, 1} and {0, 0, 0}, after 13 interations the network continued to respond positively to the stimulus. Then, changing the stimulus, the network responded as it had been trained . More graphically, the dog started to salivate at the bell without the visual stimulus, even when the stimulus was degraded. B. Supervised Learning Supervised Hebbian Learning uses the same concepts as described earlier, with a small, but powerful change. The weight is adjusted to guide the learning to the desired action or solution. This method starts in the same way as the unsupervised training, but a variable D, or desired output vector, is introduced into the process: ΔW = c * f(X,W) * X becomes ΔW = c * D * X and ΔWjk = c * dk * xj then ΔW = c * Y * X, where Y*X is the other vector product (matrix multiplication) and training the network, Wt+1 = Wt +c*Yj * Xj which explodes to , W1 = W0 +c(Y1 * X1+ Y2 * X2+…Yt * Xt), where W0 is the initial weight configuration. Page 4 of 9 Managing the weights provide significant control over the behavior of the processes. While the mathematics is interesting, the application of these algorithms provides real insight into the brilliance of these discoveries. III. Application of Hebbian Learning Rules A. Unsupervised Learning and Zip Code Identification One variation of the use of the Hebbian Learning model is pattern identification including handwritten digit recognition. In this example, Sven Behnke of the University of Berlin generated a neural abstraction pyramid using the iterative techniques. This parallels the pattern recognition done by the visual cortex. Each layer is 2-dimensional representation of the image. The columns of the pyramid are formed by the overlapping fields from the arrays. Using this technique, the system is able to learn the components that make up each of the digits from 0 – 9 that might appear in a German zip code. After the initial learning has taken place, the similar numbers, in different order, are passed through the processor, to test the error rate. In this study, the construction of the weights for the Neural Abstraction Pyramid led to very high recognition of digits in the test case. Behnke suggests that further work can be performed using this technique on more complex images. [Behnke] B. Neural Networks and Optical Character Recognition In his paper, P. Patrick van der Smagt applied different neural network techniques to optical character recognition. Using nearest neighbor (Hebbian), feed forward, Hopfield network and competitive (Kohonen) learning, he examines the characteristics of the images and the quality of the results. While the nearest neighbor technique seemed to perform the best, all methods Page 5 of 9 had the following advantages: automatic training and retraining, graceful degradation and robust performance and good resource use (parallel processing and reduced storage). [van der Smagt] C. Hebbian Learning and VLSI In this example, Hafliger and Mahowald describe the effect of spike-based normalizing hebbian learning on CMOS chips. As in the case of the neurons in the brain acting upon each other, the proximity of the circuits within the VLSI chip affect its behavior and performance and how it can be programmed. [Hafliger] NASA’s Jet Propulsion Laboratory described similar experience[Assad]. IV. Conclusion Imitating the Hebbian principles of learning as they apply to the brain, the computer scientist has the opportunity to build models to evaluate patterns or affect behavior of electronics in a very effective and efficient manner. As recent research indicates, the opportunities for these techniques are still evolving. Modifications to the methodology as well as the combination of multiple approaches can lead to much higher recognition rates in the area of pattern evaluation and computer chip creation. Page 6 of 9 References Assad, Christopher and Kewley, Davic, “Analog VLSI Circuits for Hebbian Learning in Neural Networks,” NPO-20965, August, 2001. http://www.nasatech.com/Briefs/Aug01/NPO20965.html Becker, Suzanna, Lecture 3: Learning and Memory, Fall 2002, McMaster University, Ontario, Canada. http://www.psychology.mcmaster.ca/3BN3/GazCh4PIModels.PDF Behnke, Sven, “Hebbian Learning and Competition in the Neural Abstraction Pyramid,” Free University of Berlin, Institute of Computer Science, October 10, 1999. http://page.inf.fuberlin.de/~behnke/papers/ijcnn99/ijcnn99.html Bollen, J. and Heylighen, F. (2001) “Learning Webs,” November 16, 2001, http://pespmc1.vub.ac.be/LEARNWEB.html http://pespmc1.vub.ac.be/ADHYPEXP.html French, Bonnie M., “Learning Rule,” University of Alberta Cognitive Science Dictionary, February, 1997. http://www.psych.ualberta.ca/~mike/Pearl_Street/Dictionary/contents/L/learning_rule.html Harnad, Steven, “D. O. Hebb: Father of Cognitive Psychobiology,” Behavioral and Brain Sciences, 1985. http://cogsci.soton.ac.uk/~harnad/Archive/hebb.html , http://www.princeton.edu/~harnad/hebb.html Halfiger, Philipp and Mahowald, Misha (1999). “Spike based normalizing hebbian learning in an analog VLSI artificial neuron,” Learning in Silicon, ed. Gert Cauwenberghs. Also, in Page 7 of 9 Kluwer Academics Journal on Analog integrated circuits and signal processing (18/2): Special issue on Learning in Silicon. http://www.ifi.uio.no/~halfiger/aicsp99_abstract.html Hebb, D. O. (1949). The Organization of Behavior. New York: Wiley. Howe, Michael and Miikkulainen, Risto (2000), “Hebbian Learning and Temporary Storage in the Convergence-Zone Model of Episodic Memory,” Neurocomputing 32-33: 817-821. http://www.cs.utexas.edu/users/nn/pages/publications/memory.html Klein, Raymond, “The Hebb Legacy,” Dalhousie University, Canada. http://web.psych.ualberta.ca/~bbcs99/hebb%20legacy.html http://www_mitpress.edu/MITECS/work/klein1_r.html Luger, George F. (2002) Artificial Intelligence: Structures and Strategies for Complex Problem Solving, 4th Edition. “Hebbian Coincidence Learning,” pp. 446-456. Addison-Wesley, Essex, England. McCarthy, J. and others, “A Proposal for the Dartmouth Summer Research Project on Artificial Intelligence,” August 31, 1955. http://wwwformal.stanford.edu/jmc/history/dartmouth/dartmouth.html Miller, Kenneth D. and MacKay, David J. C., “The Role of Constraints in Hebbian Learning,” Neural Computation, 1994.. http://www.inference.phy.cam.ac.uk/mackay/abstracts/constraints.html Orr, Genevieve, “Lecture Notes: CS-449 Neural Networks,” Willamette University, Fall 1999. http://www.willamette.edu/~gorr/classes/cs449/intro.html Page 8 of 9 Raicevic, Peter and Johansson, Christopher. “Biological Learning in Neural Networks,” Fran beteende till cognition, December, 2001. (Paper Submitted in partial fulfillment of course requirements.) Van der Smagt, P. Patrick, “A Comparative Study of Neural Network Algorithms Applied to Optical Character Recognition,” ACM, 089791-32-8/90/007/1037, 1990, pp. 1037-1044. Other Sources: http://140.113.216.56/course/NN2002_BS/slides/07hebbian.pdf http://web.bryant.edu/~bblais/slides/job_talk/tsld023.html Page 9 of 9