neuron-request@HPLMS2.HPL.HP.COM ("Neuron-Digest Moderator Peter Marvit") (06/05/90)
Neuron Digest Monday, 4 Jun 1990 Volume 6 : Issue 38 Today's Topics: Summary: References on "Training issues for Bp...." Send submissions, questions, address maintenance and requests for old issues to "neuron-request@hplabs.hp.com" or "{any backbone,uunet}!hplabs!neuron-request" Use "ftp" to get old issues from hplpm.hpl.hp.com (15.255.176.205). ------------------------------------------------------------ Subject: Summary: References on "Training issues for Bp...." From: rcoahk@koel.co.rmit.oz (Alvaro Hui Kau) Date: 14 May 90 01:38:41 +0000 [[ Editor's Note: You'll find troff and refer style citations below. Fair warning, but good information... -PM ]] To all good people out there! I post a request two weeks ago asking for a guide to the available references on the topic : "Training issues for back-bone propagation alg. with neural nets" And HERE all the response I get!!!!!!! Thank you ,thank you , thank you...... to all those who response!!!!! Now it is the problem on finding the time to read the references... Thanks again........ rcoahk@koel.co.rmit.oz.au. akkh@mullian.ee.mu.oz.au. --------------------------------------------------------------------- Hi, there, I read your message seeking reference on Bp networks. I am not sure whether you want to write a survey on "Training Issues for Bp ..." or you want to do some innovative research on Bp for your thesis. So far as a know, training issues for Bp have been very well studied in the past five years. Lots of reference can be found from IEEE first International Conf. on NN, 1987; 1988; and Proceedings of International Joint Conf on NN, 1989; 1990. I think most engineering libraries at least have some copies on Proceedings of 87',88', and 89'. If your library doesn't have them, try interlibrary loan. Good luck on your thesis work! xiping wu 3150 Newmark CE Lab, MC-250 205 N Mathews Ave Urbana, IL 61801 email: xwu@civilgate.ce.uiuc.edu Suggest that the training issues you might like to consider are: a) scaling of speed of training with size of network: an exponential relationship would be bad news but is probably the case. b) classification in the presence of noise: additional noise channels degrade techniques like k nearest neighbours more than error propagation networks. c) an analysis of the many speed up hacks which exist. If this is the sort of thing you are after, somerefs follow. Tony Robinson. @techreport{TesauroJanssens88, author= "Gerald Tesauro and Robert Janssens", title= "Scaling Relationships in Back-Propagation Learning: {D}ependence on Predicate Order", year= 1988, institution= "Center for Complex Systems Research, University of Illinois at Urbana Champagne", number= "CCSR-88-1"} @article{Jacobs88, author= "Robert A. Jacobs", title= "Increased Rates of Convergence Through Learning Rate Adaptation", journal= "Neural Networks", year= 1988, volume= 1, pages= "295-307"} @article{ChanFallside87-csl, author= "L. W. Chan and F. Fallside", year= 1987, journal= "Computer Speech and Language", pages= "205-218", title= "An Adaptive Training Algorithm for Back Propagation Networks", volume= "2", number= "3/4"} consider these: %A Y. Le Cun %D 1985 %J Proceedings of Cognitiva %T Une Procedure d'Apprentissage pour Reseau a Seuil Assymetrique %P 599--604 %V 85 %A D. B. Parker %C Cambridge, MA %D 1985 %I Massachusetts Institute of Technology, Center for Computational Research in Economics and Management Science %R TR-47 %T Learning-Logic %A D. E. Rumelhart %A G. E. Hinton %A R. J. Williams %D 1986 %J Nature %P 533--536 %T Learning Representations by Back-Propagating Errors %V 323 three papers which, simultaneously, introduced BP %D 1988 %I AFCEA International Press %T {DARPA} Neural Network Study %X A good overview of the state of the art in neural computing (in 1988). Is in fact a large annoted bibliography. Unfortunately, the choice of public makes than not all applications presented are evaluated upon equally much. %A S. E. Fahlman %A G. E. Hinton %D January 1987 %J Computer %P 100--109 %T Connectionist Architectures for Artificial Intelligence %V 20 %N 1 %A G. E. Hinton %C Pittsburgh, PA, USA %D 1987 %I Computer Science Department, Carnegie Mellon University %R CMU-CS-87-115 (version 2) %T Connectionist Learning Procedures %X One of the better neural networks overview papers, although the distinction between network topology and learning algorithm is not always very clear. Could very well be used as an introduction to neural networks. %A K. Hornik %A M. Stinchcombe %A H. White %T Multilayer Feedforward Networks are Universal Approximators %J Neural Networks %V 2 %N 5 %D 1989 %P 359--366 One of the papers proving that ... %A R. P. Lippmann %D April 1987 %J IEEE Transactions on Acoustics, Speech, and Signal Processing %V 2 %N 4 %P 4--22 %T An Introduction to Computing with Neural Nets %X Much acclaimed as an overview of neural networks, but rather inaccurate on several points. The categorization into binary and continuous-valued input neural networks is rather arbitrary, and may work confusing for the unexperienced reader. Not all networks discussed are of equal importance. %A J. L. McClelland %A D. E. Rumelhart %D 1986 %I The MIT Press %K PDP-2 %T Parallel Distributed Processing: Explorations in the Microstructure of Cognition (Volume 2) %A J. L. McClelland %A D. E. Rumelhart %D 1988 %I The MIT Press %T Explorations in Parallel Distributed Processing: Computational Models of Cognition and Perception %A D. E. Rumelhart %A J. L. McClelland %D 1986 %I The MIT Press %K PDP-1 %T Parallel Distributed Processing: Explorations in the Microstructure of Cognition (Volume 1) %X Excellent as a broad-spectrum survey in neural networks, but written from the viewpoint of cognitive psychology. The point of focus in most reports is the cognitive implication of distributed computing. %A A. I. Wasserman %D 1989 %I Van Nostrand Reinhold %T Neural Computing: Theory and Practice a text book on nn's %A B. Widrow %A M. E. Hoff %B 1960 IRE WESCON Convention Record %C New York %D 1960 %P 96--104 %T Adaptive Switching Circuits Check out Hecht-Nielsen's "Theory of the Backpropagation Network" in the 1989 Proc. IJCNN (Int'l Joint Conference on Neural Networks.) Also, the poster who complained that backprop is inefficient on serial machines is correct. Grobbins. grobbins@eniac.seas.upenn.edu Backpropagation is described well in _Parallel_Distributed_Processing_ (MIT PRESS). I personally feel that it is time for researchers to look beyond simple backpropagation of feedforward networks. Conjugate-gradient methods provide much faster means of training feedforward networks (or at least use Fallman's Quickprop). Backpropagation methods involving recurrent networks, however, needs to be investigated further. There are a large bunch of recurrent network training algorithms which should be studied in complex applications involving temporal behavior. Willams and Zisper published a nice paper on continuously running resurrent networks, Pineda published an interesting relaxation algorithm for recurrent nets, and Schmidhuber has published a truly wonderful group of papers concerning using two recurrent nets for interesting temporal behavior (one net is an environment model, the other uses that model to figure out how to perform tasks in the environment) that deserves to be used in complex behavioral applications. >Backpropagation is described well in _Parallel_Distributed_Processing_ >(MIT PRESS). D.E. Rumelhart and J.L. McClelland Eds >Willams and Zisper published >a nice paper on continuously running resurrent networks, R.J. Williams, D. Zisper. _A Learning Algorithm for Continually Running Fully Recurrent Neural Networks_. Institute for Cognitive Science, Report 8805, October 1988. >Pineda published >an interesting relaxation algorithm for recurrent nets, and Pineda, F.J. (1987). Generalization of bapropagation to recurrent and higher order neural networks. _Proceedings of IEEE Conference on Neural Information Processing Systems_. >Schmidhuber has published a truly wonderful group of papers >concerning using two recurrent nets for interesting temporal behavior J.H. Schmidhuber (1990). _Making the world differentiable: On supervised learning fully recurrent networks for dynamic reinforcement learning and planning in non-stationary environments_. FKI-126-90 report Technische Universitat Munchen (Institut fur Informatik). I have some interest in this problem. There are a number of books - try PDP Vol 1 (Rumelhart and McClelland) (standard - not very exciting - but gets you going - also Explorations in PDP by same authors has discs for IBM computers containing programs - not very good but gets you going! I have seen a good book by Khanna - publisher is Addison Wesley - there is also a book by Pao (?) published by AW. Igor Aleksander has just published a book - publisher is Chapman & Hall - I think it should be quite good. Issues in Back prop - 1) Topology - net topology makes a difference! Number of hidden units for application? A few problems have been solved - it IS possible to map any suitably continuous function [0,1] sup n -> [0,1] sup m for suitable n and m well enough (i.e. approximately) - based on a theorem by Kolmogorov, and recently proved for 3 layer nets by Halbert White - see recent issues of Neural Networks. 2) Unit type - most workers use semilinear units, BUT higher order units train much faster - see papers by Sejnowski and Hinton in "Neural Computation" - first issue - also papers by Giles, Lee etc in ICNN 87 etc. 3) Convergence - Most workers seem to assume that BP converges - it doesn't! it can get stuck in local minima and does! To speed up BP you could use momentum (described in PDP 1), or the delta-bar-delta method (described in a paper by Jacobs, Neural Networks ?), or Quickprop, (described by Fahlman in Proc Connectionist Summer School, 1988). As a useful alternative to back propagation - see Baba's paper in Neural Networks (vol 2 - ???) (recent) on Random Optimisation methods. One other method is to apply Genetic Algorithms - there is some evidence that they can work well (see papers by Whitley in 3rd Proc on GAs, 1989) 4) Applications - good applications - see Sejnowski & Gorman's paper in Neural Networks - issue 1 (on sonar) - also Sejnowski & Lehky's short article on shape from shading (Nature, 1988?) Also articles on spirals etc in Procs of 1988 Connectionist Summer School, published by Morgan Kauffman. 5) Generalisation - this is a BIG issue - getting a network to classify training vectors is difficult, but no big deal - the problem everyone wants to solve is to get good performance on unseen inputs. This (as I am just realising!) is VERY hard. Lots of workers have claimed generalisation - but basis is not sound. A paper to read is by Solla, Levin and Tishny, IJCNN89 (Washington DC). An earlier paper by Solla is in nEuro88 Procs, Paris 6) Classification - alternative methods - Ron Chrisley and Kohonen have compared PDP with other methods - see the proceedings of nEuro88 - (also published elsewhere, but not sure of exact details) - compare with Learning Vector Quantisation, and Hopfield nets .... 7) Fault-tolerance - reliability - changing weight values or killing units altogether may make little difference in a network with trained redundant units. However, Sejnowski claims that additional hidden units are unassigned, whereas Hinton claims that the additional HUs perform redundant processsing. Hinton uses a weight decay process in training - Sejnowski doesn't! Neural networks (of BP type) require a LOT of processing power, if you want to study anything even of moderate size. I hope this helps - in my next message I will include the text of a Study Guide which I prepared for a course I gave earlier this year. dave martland dept of cs Brunel University UK .ft H .fo 'CS434 Guide'- % -'DM October 1989 .nh .de HI .ft HB \\$1 .ft H .. .de IN .in +3m .. .de EX .in -3m .. .de TI .ti -3m .. .de BD .ft HI \\$1 .ft H .. .ft HB .ce 2 NEURAL NETWORK SYSTEMS - STUDY GUIDE (CS 434) David Martland, October 1989 .ft H .HI "Introduction" This guide is intended to help you get to grips with the study of neural networks. It gives a brief outline of the background to neural network research, and then describes some book and papers which you are likely to find useful. You will not need to buy all of the books, nor will you need to photo-copy all of the papers, although it may help you to copy some. The books which will be most useful to buy are the books by Rumelhart and McClelland, all three of them. The first two books describe a significant number of the current network types, whilst the third book, Explorations in PDP, contains a disc with software which can run on IBM computers. If you prefer, there is now also a version of the software which runs on Macintoshes, although it is no more sophisticated. Later sections of this guide gives some ideas as to how you can discover more about neural networks for yourself, both by reading, and also by exploring the subject using packages included in "Explorations". Finally there is a section on the assesment by course work. .HI Background During the last few years, the study of neural network systems has become increasingly more popular. Partly this has been because of an awareness that intelligent animals can solve problems which are impossible for even the most powerful modern computers, and partly because of the desire by engineers and computer scientists to explore and exploit parallel hardware systems, and apply them to practical problems. Additionally, there are a number of problem types which now look appropriate for solution using various types of artificial neural network, and these may lead to successful applications being developed in areas such as military systems, medical diagnosis, and plant control. The course introduces biological models of neural networks, and then moves away to deal with aspects of artificial systems of current interest. .HI Objectives There are a number of objectives for this course. .br You should become familiar with major network types, including perceptrons, adaline, mult-layer perceptrons, Hopfield networks, Boltzmann machines, Kohonen networks, boolean network models, and Grossberg's ART model. You should expect to gain a deeper understanding of some of the networks and their adaptation and operating processes. Some mathematical expertise, including knowledge of differential calculus, and matrix and vector algebra will be desirable. These will be used in the description of heuristic optimisation processes, and for the stability proofs for Hopfield networks. You will gain practical experience, mostly based on software packages, and designed to demonstrate that the presented theory works. You should also expect to gain an understanding of the types of application that can be handled by current artificial neural network technology. Since these applications are typically very costly both in terms of hardware and execution time, it is unlikely that you will be able to develop an interesting application of reasonable size. However, you should be aware of what is possible. You may wish to formulate other objectives for yourself, such as a study of architecture of systems which will support artificial neural networks. These will not be major objectives. .HI "Course books and papers" There are many books now available about neural network systems, but few that are comprehensive enough to support the course. During the year new books will become available, but of currently available books the following will be useful. .IN .TI Rumelhart, D.E. and McClelland, J.L. (Eds), "Parallel Distributed Processing, Vol 1",MIT Press, Cambridge, MA, 1986 This volume describes feed-forward systems, the interactive activation model, the harmony machine and the Boltzmann machine. This book is considered by many to be the best book available as an introduction at the present time. .TI Rumelhart, D.E. and McClelland, J.L. (Eds), "Parallel Distributed Processing, Vol 2", ,MIT Press, Cambridge, MA, 1986 This volume continues where Vol 1 leaves off, and concentrates on applying the techniques described in Vol 1 to several applications of interest to cognitive psychologists. .TI McClelland, J.L.& Rumelhart, D.E.,"Explorations in parallel distributed processing", Cambridge, MA, MIT Press, 1988 This book contains a floppy disc containing a number of programs which illustrate principles described in the other PDP books. The programs, written in C, are not very sophisticated, but they can help to demonstrate properties of the systems described if enough effort is put in by the reader. .TI Aleksander, I., (Ed), "Neural Computing Architectures",North Oxford Academic, 1989 This book concentrates on boolean models of artificial neural networks. .TI Hinton, G.E. & Anderson, J.A. (Eds),"Parallel Models of Associative Memory", Lawrence Erlbaum Ass., Hillsdale NJ, 1981 This book contains a number of articles by authors who have made contributions to neural network theory. The article by Sejnowski on accurate neural modelling is of interest. Also, the article by Willshaw, based on the earlier paper in Nature, about holographic storage is still of interest. .TI Kanerva, P, "Sparse Distributed Memory",MIT Press, 1988 This book describes an associative memory system based on the use of neural units, and in which the data representation for any stored pattern is spread out over several (possibly many) different units. This could render the system tolerant of failure, and also leads to very rapid recall using appropriate parallel hardware. .TI Kohonen, T :"Self organisation and Associative Memory", Springer-Verlag, 1984 This book is basically about a neural network model developed by Teuvo Kohonen. It introduces concepts such as lateral inhibition, and also shows how an unsupervised training procedure can lead to cluster formation appropriate to classification tasks. An additional feature of the model is that adaptive process results in a structured representation of the input data classes, in which similar classes are likely to be represented by physically nearby neural units. .TI Minsky, M and Papert, S ,"Perceptrons: An introduction to computational geometry", MIT Press, Cambridge, MA ,1969 This is the classic book by Minsky and Papert, in which they showed what perceptrons cannot do. However, they were perhaps too restrictive in their specification of a perceptron system, as the more recently adopted multi-layer perceptron models overcome many of the problems that they discussed. Despite this, it is still an important book, and the perceptron learning algorithm is an important process for dichotomising linearly separable pattern sets. Additionally, the concepts introduced within the book, and the (fairly) thorough treatment of the subject using mathematics, still make very interesting reading today. .TI Palm, G., "Neural Assemblies",Springer-Verlag, Berlin, 1982 This book contains a detailed description of an associative memory model based on the associative memory model of Willshaw et al. .TI Press, W.H, Flannery, B.R., Teukolsky, S.A., Vetterling, W.T., "Numerical Recipes in C" This very useful book contains programs in C for a large number of algorithms, and gives brief, readable, descriptions of minimisation procedures appropriate to neural network study. .EX .HI Papers There are many papers on neural networks, but some are of greater significance than others. Important papers include: .IN Grossberg, ART ... (decent readable reference to be supplied!) Hopfield, J.J., "Neural networks and physical systems with emergent collective computational abilities" Proceedings of the National Academy of Sciences,USA V 79, 2554-2558, 1982 Hopfield, J.J.," Neurons with graded response have collective computational properties like those of two-state neurons", Proceedings of the National Academy of Sciences, USA, V 81, 3088-3092, 1984 Hopfield, J.J. & Tank, D.W. "'Neural' computation of decisions in optimization problems", Biological Cybernetics,V 52, 141-152, 1985 Kohonen, T. "Analysis of a simple self organizing process" ,Biological Cybernetics, V 44 , 135-140, 1982 Little, W.A & Shaw, G.L.,"A statistical theory of short and long term memory", J. Behav. Biol. V 14 115, 1974 Little, W.A.,"The existence of persistant states in the brain", Mathematical Bioscience, V 19, 101-120, 1974 Little, W.A. & Shaw, G.L. "Analytic study of the memory storage capacity of a neural network", Mathematical Biosciences, V 39, 281-290, 1978 Lehky, S.R. & Sejnowski, T.J., "Network model of shape-from shading:neural function arises from both receptive and projective fields", Nature, V 333, 452-454 , 1988 Gorman, R.P. & Sejnowski, T.J. "Analysis of hidden units in a layered network trained to classify sonar targets", Neural Networks,V 1,7 5-89, 1988 Jacobs, 1988, Neural Networks, V1-4, 1988 Widrow, IJCNN 89 Willshaw, D.J., Buneman, D.P., Longuet-Higgins,H.C. "Non-holographic associative memory" , Nature ,V 222 ,960-962, 1969 Willshaw, D.J.,"Holography, association and induction", in "Parallel models of associative memory" Hinton, G.E. and Anderson J.A.(Eds), Erlbaum ass., Hillsdale,NJ, 1982 .EX .HI "Introductory articles" There have been a number of useful "special issues", and introductory articles during the last few years. The following should be noted: Neural networks, number 1, vol 1, 1988 This contains introductory articles by Grossberg and Kohonen (An introduction to neural computing, pp 3-16), which are well worth re ading. IEEE Computer, March 1988. This issue is particularly worth getting hold of. The articles by Kohonen and Widrow are very good introductions to Kohonen networks, and adaptivc filtering systems respectively. The article by Linsker is particularly interesting. Byte, article by G.E.Hinton on Boltzmann machines (1985) is easy to read. The paper by Lippmann, R.P.,("An introduction to computing with neural nets", IEEE Acoustics Speech Signal Processing Magazine, 4, 1987,pp 4-22), is useful, although it contains a number of errors and incorrect statements. Read it, but don't believe everything it says! .HI "Journals and papers" There are several journals which deal with Neural Networks, and it is important to keep up to date with papers as they appear. Fruitful sources of inspiration can be found in: .IN Biological Cybernetics IEEE Trans on Systems, Man and Cybernetics Neural Networks .EX There have also been occasional articles worth reading in magazines/journals such as Byte, Scientific American, Science, and IEEE Computer. Other journals on neural networks are Neural Computation (edited by Terrence-Sejnowski - published by MIT), Journal of neural network computing (edited by Judith Dayhoff), International Journal of Neural Networks (edited by Kamal U.Karna) .HI "Computer Packages" Doing a study of neural network models is likely to require access to computer processing. Some network models can be analysed by mathematical models, but often true understanding only comes from running a model on a computer. Interesting problems are likely to be very costly in terms of computer power, and to require large running times on powerful machines. However, simple problems can be tackled to illustrate the principles. One of the simplest packages available is that included in the "Explorations" book. This has the merits of being fairly cheap, and it can run on IBM PCs. It is also possible to recompile the programs to run on more powerful machines. The user interface is quite poor, but at least you won't have to do much programming. Another package which we have available is the Rochester simulator package, which runs on the university UNIX based computers. This is slightly better as a general purpose tool, but is harder to program, since it requires some knowledge of C. Other commercially available packages have some advantages, but they cost more. Often commercially available packages come with demonstrations of major network types, so it is worth looking at demonstrations if you can. Packages such as NeuralWare, NeuralWorks come with many network types ready configured. .HI Societies There is now an International Neural Network Society (INNS). This publishes a journal called Neural Networks, which comes out several times a year. Membership of the society for students is moderately cheap, and also allows you reduced fees if you decide to go to any of the societies conferences! .HI "Conferences and workshops" There are now several conferences on neural networks each year. Ones to watch out for are: IEEE/INNS joint conference on neural networks (Now twice a year!). Locations currently Washington and San Diego. Previous conference proceedings were ICNN87 (IEEE San Diego), ICNN88 (IEEE San Diego), INNS 88(Boston), IJCNN89 (Washington) IEEE Natural Information Procesing Systems (NIPS) (usually Denver, in November) US summer schools on neural networks - for example Carnegie Mellon, Woods Hole. nEuro conference - supposed to be a nEuro90 somewhere in Europe. Previous conference was nEuro88. .HI "Other sources of information" Another very useful source of information about neural networks is available to users of computers connected to the Usenet system. Using a news reader program (ours is called .BD rn on the local machine Terra), it is possible to find out about a large number of different subjects, from Society Women to Ozone Depletion. In the present context, you will want to look out for the section .BD "comp.ai.neural-nets" and perhaps also .BD "comp.ai." You should note that it is possible to waste an enormous amount of time reading the news, and you should resist the temptation to do so. Using our mail reader, it is possible to scan read through a large number of articles looking for keywords, and knowing that the '=' command will give a list of all the articles in a newsgroup is also very helpful. For tracking down papers you should learn to use the CD ROM based system which is kept in the library. Currently this is very popular, but you should be able to book it in advance. Unfortunately the load period is 2 hours, which is too long, since useful work can be done in much less time, and the long period leads to queues. You could also use the Science Citation Index and the Abstracts, as well as using the other library services. .HI Strategy The course will introduce biological concepts of neurons, and neural networks. .BD Perceptrons will be introduced, and the concepts of .BD "linear separability" and the .BD "perceptron training algorithm" and .BD "convergence theorem" and .BD "cycling theorems" discussed. Widrow's adaline model will be mentioned, and a procedure based on the use of a .BD "least mean squares" minimisation algorithm introduced. The .BD "multi-layer perceptron" model will be dealt with in several lectures. The course will then move on to describe networks with feed-back, based on .BD "Hopfield networks," both discrete and continuous, and applications of such networks will be discussed. Later work will deal with other network types, including .BD "Kohonen's self organising topological feature maps," and .BD "Grossberg's ART models." .HI "Helping yourself" Things you can do to help you study - you do not have to follow the suggestions in the order stated, and you may find it helpful to read two or three books or papers during the same period. A very good introduction is the March 1988 issue of Computer (IEEE). This gives easy to understand presentations of several network types, and also deals with hardware implementation. You should read as much of the book by Minsky and Papert as possible. This book is moderately mathematical, although it is not really very difficult, and may seem strange at first. You should note in particular the Perceptron Convergence Theorem, and the Perceptron Cycling Theorem. Additionally, you should note the concepts of linear separability, and diameter limited, and order limited predicates. Later, you should examine the proofs of the theorems, but at first you should simply note the adaptive procedure. Next you should find the early paper by WIdrow, which describes an adaptation procedure based on Least Mean Squares. See how this procedure differs from the perceptron adaptation procedure. Then you should read the section of the PDP book which deals with back propagation - only there it's called the .BD "generalized delta rule." If you find the maths hard, then look at the examples and have faith that the method works. To give more credence to the back-propagation method, you could also run the BP program which is supplied with "Explorations". Try to devise your own networks using the network description language once you have tried out the example demonstrations. For example, you could make up a network for solving the symmetry problem, and see if the solutions described in the book are plausible. There are few books that deal well with Hopfield networks, so it is perhaps simplest to examine the original papers. (Hopfield 1982, 1984). Then you should read the book by Kohonen, which describes another type of network, which uses an unsupervised learning algorithm. Grossberg has written many articles and several books, most of them unreadable. However, his recent articles have proved to be more approachable, perhaps because of the influence of Gail Carpenter. Try to find out what Grossberg's ART models are, but leave this till later on. .HI "Course work assessment" You will be expected to do course work during the course, but much of the work will centre around laboratory exploration, and short presentations. A significant proportion of the available marks for the coursework will be for keeping a log book up to date during the course. Additional marks will be obtained for tackling specific problems, and for presentations later on. Currently the course work accounts for 25% of the marks available for the course. Further guidance will be given during the year. ------------------------------ End of Neuron Digest [Volume 6 Issue 38] ****************************************