{"title": "Cycles: A Simulation Tool for Studying Cyclic Neural Networks", "book": "Neural Information Processing Systems", "page_first": 290, "page_last": 296, "abstract": null, "full_text": "290 \n\nCYCLES: A Simulation Tool for Studying \n\nCyclic Neural Networks \n\nTexas Instruments Incorporated, Dallas, TX 75265 \n\nMichael T. Gately \n\nABSTRACT \n\nA computer program has been designed and implemented to allow a researcher \n\nto analyze the oscillatory behavior of simulated neural networks with cyclic con(cid:173)\nnectivity. The computer program, implemented on the Texas Instruments Ex(cid:173)\nplorer / Odyssey system, and the results of numerous experiments are discussed. \n\nThe program, CYCLES, allows a user to construct, operate, and inspect neural \n\nnetworks containing cyclic connection paths with the aid of a powerful graphics(cid:173)\nbased interface. Numerous cycles have been studied, including cycles with one or \nmore activation points, non-interruptible cycles, cycles with variable path lengths, \nand interacting cycles. The final class, interacting cycles, is important due to its \nability to implement time-dependent goal processing in neural networks. \n\nINTRODUCTION \n\nNeural networks are capable of many types of computation. However, the \nmajority of researchers are currently limiting their studies to various forms of \nmapping systems; such as content addressable memories, expert system engines, \nand artificial retinas. Typically, these systems have one layer of fully connected \nneurons or several layers of neurons with limited (forward direction only) connec(cid:173)\ntivity. I have defined a new neural network topology; a two-dimensional lattice of \nneurons connected in such a way that circular paths are possible. \n\nThe neural networks defined can be viewed as a grid of neurons with one \nedge containing input neurons and the opposite edge containing output neurons \n[Figure 1]. Within the grid, any neuron can be connected to any other. Thus \nfrom one point of view, this is a multi-layered system with full connectivity. I \nview the weights of the connections as being the long term memory (LTM) of the \nsystem and the propagation of information through the grid as being it's short \nterm memory (STM). \n\nThe topology of connectivity between neurons can take on any number of \npatterns. Using the mammalian brain as a guide, I have limit~d the amount of \nconnectivity to something much less then total. In addition to making analysis \nof such systems less complex, limiting the connectivity to some small percentage \nof the total number of neurons reduces the amount of memory used in computer \nsimulations. In general, the connectivity can be purely random, or can form any \nof a number of patterns that are repeated across the grid of neurons. \n\nThe program CYCLES allows the user to quickly describe the shape of the \nneural network grid, the source of input data, the destination of the output data, \nthe pattern of connectivity. Once constructed, the network can be \"run.\" during \nwhich time the STM may be viewed graphically. \n\n\u00a9 American Institute of Physics 1988 \n\n\finput column \n\noutput column \n\n~ \n\n~ \n\n-000000 00 000 - -\n-00000000000 - -\n-00000000000 - -\n~OOOOOOOOOOo--\n\n~OOOOOOOOOOo--\n\n~OOOOOOOOOOo--\n\n~O \n\n~OOOOOOOOOOo--\no 0 0 000--\n~O 000 \n00000 - -\n~O \n00000 - -\n0 000 0--\no 0 000 0--\n-0 00 o 0 0 0 000 - -\n\n~O \n\n~O \n\nsample connectivity \npattern -- replicated \nacross all neurons \n\nt \n\noutput column \n\n..... vJI ...... '_,.lIr _\". .... ;\"r \u2022\u2022 ,Ii \n\n- 11.,61 ... \" ~ \n\n.\u2022\u2022...... \n...... ,. , \n\u00b7 . ......... \n' .... \" . , , \nI'\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7 . \n\u00b7 .. ' \u2022..... \n.. ' \n\u00b7 '., ... , .. \n\u00b7 .. , ...... \n\u00b7 .......... \n' \u2022..... \n\nGRAPHICAL DISPLAY WINDOW \n\nw_I' \n\nNYlI\" \n\n''''' \" \n\n\"'~ r .... \" '_ 0' fI'.\" .... 11 ... 8' ,,,,,,\" 1 \n\"\" ... t_ ~ of .... t ' .. ,t .... ,,' \"J \u2022\u2022\u2022\u2022 ~ , .. \n,.._ IN,.,.... .. 0Jf '.Itt,,,,. ,,,_ .. rt.,..\u00b7,., \n\nII,\\IIM \"\"_1 W .... \", .. ,,.. tVf'\u00ab\"ltJ w,~,,_ \n\n,..,_t,.,,,,,_01 r ... \"\"'tU.raf' ....... \\ \n\nUSER INTERACTION WINDOW \n\nCOMMAND WINDOW \n\n.,~~,~~ \n\nAlt., GlobM VaN., . . \n\n'nllI./n \n\nI .,,_ fI/II~\",*- ,~. \n\nIIlIIZIII \n\nu.rou.F_tII'Y \n\nHM. \n\nIt_,~ \n\n...... \n\ny ... ,.. \n\nSTI rus WINDOW \n\nFigure 1. COMPONENTS OF A CYCLES NEURAL NETWORK \n\nFigure 2. NEURAL NETWORK WORKSTATION INTERFACE \n\ntv \nto \nI-' \n\n\f292 \n\nIMPLEMENTATION \n\nCYCLES was implemented on a TI Explorer/Odyssey computer system with \n\n8MB of RAM and 128MB of Virtual Memory. The program was written in Com(cid:173)\nmon LISP. The program was started in July of 1986, put aside for a while, and \nfinished in March of 1987. Since that time, numerous small enhancements have \nbeen made - and the system has been used to test various theories of cyclic neural \nnetworks. \n\nThe code was integrated into the Neural Network Workstation (NNW), an \ninterface to various neural network algorithms. The NNW utilizes the window \ninterface of the Explorer LISP machine to present a consistent command input \nand graphical output to a variety of neural network algorithms [Figure 2]. \n\nThe backpropagation-like neurons are collected together into a large three(cid:173)\ndimensional array. The implementation actually allows the use of multiple two(cid:173)\ndimensional grids; to date, however, I have studied only single-grid systems. \n\nEach neuron in a CYCLES simulation consists of a list of information; the \nvalue of the neuron, the time that the neuron last fired, a temporary value used \nduring the computation of the new value, and a list of the neurons connectivity. \nThe connectivity list stores the location of a related neuron and the strength of \nthe connection between the two neurons. Because the system is implemented in \narrays and lists, large systems tend to be very slow. However, most of my analysis \nhas taken place on very small systems \u00ab 80 neurons) and for this size the speed \nis acceptable. \n\nTo help gauge the speed of CYCLES, a single grid system containing 100 \nneurons takes 0.8 seconds and 1235 cons cells (memory cells) to complete one \nupdate within the LISP machine. If the graphics interface is disabled, a test \nrequiring 100 updates takes a total of 10.56 seconds. \n\nTYPES OF CYCLES \n\nAs mentioned above, several types of cycles have been observed. Each of these \n\ncan be used for different applications. Figure 3 shows some of these cycles. \n1. SIMPLE cycles are those that have one or more points of activation traveling \nacross a set number of neurons in a particular order. The path length can be \nany SIze. \n\n2. NON-INTERRUPTABLE cycles are those that have sufficiently strong con(cid:173)\n\nnectivity strengths that random flows of activation which interact with the \ncycle will not upset or vary the original cycle. \n\n3. VARIABLE PATH LENGTH cycles can, based upon external information, \nchange their path length. There must be one or more neurons that are always \na part of the path. \n\n4. INTERACTING cycles typically have one neuron in common. Each cycle \nmust have at least one other neuron involved at the junction point in order to \nkeep the cycles separate. This type of cycle has been shown to implement a \ncomplex form of a clock where the product of the two (or more) path lengths \nare the fundamental frequency. \n\n\f293 \n\nFigure 3. Types of Cycles [Simple and Interacting] \n\n\u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \n\u2022 \u2022 \n\u2022 \u2022 \u2022 \n\u2022 \u2022 \u2022 \n\u2022 \u2022 \n\u2022 \u2022 \n\u2022 \u2022 \u2022 \n\u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \n\n* \n\n\u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \n\u2022 \u2022 \u2022 \n\u2022 \u2022 \n\u2022 \u2022 \n\u2022 \u2022 \u2022 \n\u2022 \u2022 \n\u2022 \u2022 \u2022 \n\u2022 \u2022 \n\u2022 \u2022 \u2022 \u2022 \n\u2022 \u2022 \u2022 \n\u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \u2022 \n\nFigure 4. Types of Connectivity [Nearest Neighbor and Gaussian] \n\nINPUT \n\nOUTPUT \n\nIntent \n\nJoint 3 Extended \n\nJoint 2 Centered \n\nJoint 1 Extended \n\nChuck Opened \n\nChuck Closed \n\nCompleted \n\nMove Joint 3 \n\nMove Joint 2 \n\nMove Joint 1 \n\nOpen Chuck \n\nClose Chuck \n\nFigure 5. Robot Arm used in Example \n\n\f294 \n\nCONNECTIVITY \n\nSeveral types of connectivity have been investigated. These are shown in \n\nFigure 4. \n1. In TOTAL connectivity, every neuron is connected to every other neuron. \nThis particular pattern produces very complex interactions with no apparent \nstability. \n\n2. With RANDOM connectivity, each neuron is connected to a random number \n\nof other neurons. These other neurons can be anywhere in the grid. \n\n3. A very useful type of connectivity is to have a PATTERN. The patterns can \n\nbe of any shape, typically having one neuron feed its nearest neighbors. \n\n4. Finally, the GAUSSIAN pattern has been used with the most success. In this \npattern, each neuron is connected to a set number of nodes - but the selection \nis random. Further, the distribution of nodes is in a Gaussian shape, centered \naround a point \"forward\" of itself. Thus the flow of information, in general, \nmoves forward, but the connectivity allows cycles to be formed. \n\n\\ \n\nALGORITHM \n\nThe algorithm currently being used in the system is a standard inner product \nequation with a sigmoidal threshold function. Each time a neuron's weight is to \nbe calculated, the value of each contributing neuron on the connectivity list is \nmultiplied by the strength of the connection and summed. This sum is passed \nthrough a sigmoidal thresholding function. The value of the neuron is changed \nto be the result of this threshold function. As you can see, the system updates \nneurons in an ordered fashion, thus certain interactions will not be observed. Since \ntiming information is saved in the neurons, asynchron:' could be simulated. \n\nInitially, the weights of the connections are set randomly. A number of inter(cid:173)\n\nesting cycles have been observed as a result of this randomness. However, several \nexperiments have required specific weights. To accommodate this, an interface to \nthe weight matrix is used. The user can create any set of connection strengths \ndesired. \n\nI have experimented with several learning algorithms-that is, algorithms that \nchange the connection weights. The first mechanism was a simple Hebbian rule \nthat states that if two neurons both fire, and there is a connection between them, \nthen strengthen the strength of that connection. A second algorithm I experi(cid:173)\nmented with used a pain/pleasure indicator to strengthen or weaken weights. \n\nAn algorithm that is currently under development actually presets the weights \nfrom a grammar of activity required of the network. Thus, the user can describe \na process that must be controlled by a network using a simple grammar. This \ndescription is then \"compiled\" into a set of weights that contain cycles to indicate \ntime-independent components of the activity. \n\n\f295 \n\nUSAGE \n\nEven without a biological background, it is easy to see that the processing \npower of the human brain is far more than present associative memories. Our \nrepertoire of capabilities includes, among other things: memory of a time line, \ncreativity, numerous types of biological clocks, and the ability to create and ex(cid:173)\necute complex plans. The CYCLES algorithm has been shown to be capable of \nexecuting complex, time-variable plans. \n\nA plan can be defined as a sequence of actions that must be performed in \nsome preset order. Under this definition, the execution of a plan would be very \nstraightforward. However, when individual actions within the plan take an inde(cid:173)\nterminate length of time, it is necessary to construct an execution engine capable \nof dealing with unexpected time delays. Such a system must also be able to abort \nthe processing of a plan based on new data. \n\nWith careful programming of connection weights, I have been able to use \nCYCLES to execute time-variable plans. The particular example I have chosen \nis for a robot arm to change its tool. In this activity, once the controller receives \nthe signal that the motion required, a series of actions take place that result in \nthe tool being changed. \n\nAs input to this system I have used a number of sensors that may be found \nin a robot; extension sensors in 2-D joints and pressure sensors in articulators. \nThe outputs of this network are pulses that I have defined to activate motors on \nthe robot arm. Figure 5 shows how this system could be implemented. Figure \n6 indicates the steps required to perform the task. Simple time delays, such as \nfound with binding motors and misplaced objects are accommodated with the \nbuilt in time-independence. \n\nThe small cycles that occur within the neural network can be thought of as \nshort term memory. The cycle acts as a place holder - keeping track of the system's \ncurrent place in a series of tasks. This type of pausing is necessary in many \"real\" \nactivities such as simple process control or the analysis of time varying data. \n\nIMPLICATIONS \n\nThe success of CYCLES to simple process control activities such as robot arm \ncontrol implies that there is a whole new area of applications for neural networks \nbeyond present associative memories. The exploitation of the flow of activation as \na form of short term memory provides us with a technique for dealing with many \nof the \"other\" type of computations which humans perform. \n\nThe future of the CYCLES algorithm will take two directions. First, the \ncompletion of a grammar and compiler for encoding process control tasks into a \nnetwork. Second, other learning algorithms will be investigated which are capable \nof adding and removing connections and altering the strengths of connections \nbased upon an abstract pain/pleasure indicator. \n\n\f296 \n\nThe robot gets a signal \nto begin the tool change \nprocess. A cycle is started \nthat outputs a signal to \nthe chuck motor. \n\nWhen sensor indicates \nthat the chuck is open. \nthe first cycle is stopped \nand a second begins \nactiv