NON-ALGORITHMICALLY IMPLEMENTED ARTIFICIAL NEURAL NETWORKS AND COMPONENTS THEREOF

Abstract: Constructing and simulating artificial neural networks and components thereof within a spreadsheet environment results in user friendly neural networks which do not require algorithmic based software in order to train or operate. Such neural networks can be easily cascaded to form complex neural networks and neural network systems, including neural networks capable of self-organizing so as to self-train within a spreadsheet, neural networks which train simultaneously within a spreadsheet, and neural networks capable of autonomously moving, monitoring, analyzing, and altering data within a spreadsheet. Neural networks can also be cascaded together in self-training neural network form to achieve a device prototyping system.

Description: NON-ALGORITHMICALLY IMPLEMENTED ARTIFICIAL NEURAL NETWORKS AND COMPONENTS THEREOF Field of the Invention This invention relates generally to artificial neural networks and more particularly, to artificial neural networks implemented in a non-algorithmic fashion in a data space, such as a spreadsheet, so as to facilitate cascading of such artificial neural networks and so as to facilitate artificial neural networks capable of operating within the data space, including networks which move through the data space and self- train on data therewithin. Background ofthe Invention This application is related to applicant's co-pending application Serial No. 08/323,238 filed October 13, 1994, entitled Device For The Autonomous Generation Of Useful Information, in which the "creativity machine" paradigm was introduced. The creativity machine paradigm involves progressively purturbing a first neural network having a predetermined knowledge domain such that the perturbed network continuously outputs a stream of concepts, and monitoring the outputs or stream of concepts with a second neural network which is trained to identify only useful concepts. The perturbations may be achieved by different means, including the introduction of noise to the network, or degradation ofthe network. Importantly, the present application provides an excellent system for constructing such creativity machines, and further builds upon the creativity machine invention to achieve self training neural networks. The current explosion of information has made it necessary to develop new techniques for handling and analyzing such information. In this regard, it would be helpful to be able to effectively discover regularities and trends within data and to be able to effectively sort and/or organize data. Currently, various algorithmic techniques and systems may be utilized to analyze data, however, such techniques and systems generally fail to display the creativity needed to enable them to organize the data and exhaust sets of data of all potential discoveries The use of neural networks for such tasks would be advantageous Further, the advantages of new artificial neural networks (ANNs) are ever increasing Currently, such artificial neural networks are often trained and implemented algorithmically These techniques require the skills of a neural network specialist who may spend many hours developing the training and/or implementation software for such algorithms. Further, when using algorithms to train artificial neural networks, once new training data is obtained, the new training data must be manually appended to the preexisting set of training data and network training must be reinitiated, requiring additional man hours Disadvantageously, if the newly acquired training data does not fit the pattern of preexisting training data, the generalization capacity ofthe network may be lowered An additional drawback to traditional algorithm implemented training and operation of artificial neural networks is that within such schemes, individual activation levels are only momentarily visible and accessible, as when the governing algorithm evaluates the sigmoidal excitation of any given node or neuron. Except for this fleeting appearance during program execution, a neuron's excitation, or activation level, is quickly obscured by redistribution among downstream processing elements. Accordingly, it is desirable and advantageous to provide a simpler method of training, implementing, and simulating artificial neural networks It is further desirable to provide artificial neural networks which can be easily cascaded together to facilitate the construction of more complex artificial neural network systems It also is desirable and advantageous to provide neural networks which can be configured to perform a variety of tasks, including self training artificial neural networks, as well as networks capable of analyzing, sorting, and organizing data A principal object ofthe present invention is to provide a user friendly system of implementing or simulating neural networks in which movement of such networks and cascading of such networks is facilitated Another object ofthe present invention is to provide self training artificial neural networks. A further object ofthe present invention is to provide artificial neural networks capable of analyzing data within a data space Yet another object ofthe present invention is to provide artificial neural networks which are mobile within a data space. Still another object ofthe present invention is to provide artificial neural networks which can be easily duplicated within a data space and which can be easily interconnected to facilitate the construction of more complex artificial neural network systems. Summary ofthe Invention These and other objects ofthe invention are attained by artificial neural networks which are implemented in a data space, such as a spreadsheet within some spreadsheet application such as Microsof Excel which is operable with most IBM compatible personal computers having a model 386 or higher level microprocessor and sufficient memory associated therewith, such computers typically including a monitor or other display device. Of course, the faster the computer speed, the better the results obtained. As used herein the term neural network object (NNO) includes artificial neural networks or combinations of artificial neural networks implemented within such a data space and having an associated set of properties and methods. These properties and methods may be incoφorated within a knowledge domain of each artificial neural network and may also be incoφorated in programs associated with the artificial neural networks. The data space or spreadsheet includes a plurality of cells and the spreadsheet application allows for association or interrelating of such cells through relative cell referencing. While use ofthe spreadsheet application Microsoft Excel is suggested herein, it is understood that other spreadsheet applications could be utilized, and it if further understood that new applications could be engineered for the puφose of creating a data space suitable for construction and operation of neural network objects as described herein. Moreover, while the various neural network objects described below may refer to programs being associated therewith, it is understood that in a data space where self referencing is permissible, such programs could be eliminated. Exploiting the many analogies between biological neurons and cells within a spreadsheet, the state of any given neuron may be evaluated by relative cell referencing and resident spreadsheet functions. Unlike traditional algorithmic network simulation, all neuron activations are simultaneously visible and randomly accessible within the data space simulation. More like a network of virtual, analog devices, this simulation may be considered quasi-parallel, with all neurons updated with each wave of data space calculation or renewal, where spreadsheet renewal is asynchronous with the feed forward algorithm. Neural network objects are mobile within the data space as provided by the spreadsheet application which typically includes resident commands for cutting and pasting groups of cells. Accordingly, movement of neural network objects is achieved by simultaneously cutting the information within the cell group or cell array comprising the neural network object from one location within the data space and pasting the same information to another location within the data space. Such movement may be accomplished manually or through programs associated with the neural network objects. Alternatively, neural network objects can be replicated using a copy command and moved elsewhere within the data space. Such neural network objects are advantageously implemented without requiring any underlying software based algorithm and are therefore extremely versatile and user friendly. Moreover, neural network objects are easily portable such as by saving or storing, on a computer readable storage medium such as a floppy disk, information operable to effect such neural network objects.. Further, by relatively referencing the outputs of one neural network object to the inputs of another, neural network objects can be easily cascaded such that the outputs from one neural network object are applied as inputs to another neural network object. The compound or cascaded neural networks which result are transparent in operation and easily accessible for modification and repair. Accordingly, recurrences and all manner of neural network paradigms, including IAC, Boltzmann Machine, Harmonium, Hopfield nets, and self-organizing maps, may be readily implemented. Importantly, the ease with which neural network objects can be cascaded provides a system where multiple neural network objects may be combined so as to simulate interconnected processes or hardware devices, wherein each neural network object is trained within a knowledge domain of a particular process or hardware device. In addition, this specification provides several examples of other neural network objects in order to demonstrate both their versatility and utility. One advantageous neural network object provides for the training of an artificial neural network. This self training artificial neural network object (STANNO) is a simple alternative to Adaptive Resonance Technology, disclosed in Caφenter et al U.S. Patent No. 5,214,715, wherein complex algorithms are utilized to allow neural networks to flexibly adapt to new, emerging information. Advantageously, the STANNO requires no such complex algorithms. In general, training an artificial neural network requires a set of training data, including multiple input vectors and associated output vectors, and includes various techniques such as backpropagation, involving repetitive application of input vectors to an input layer ofthe artificial neural network. With each application of an input vector, the actual output ofthe artificial neural network, obtained at the output layer, can be evaluated in light ofthe desired output so that the connection weights and/or biases ofthe artificial neural network can be adjusted. The self training artificial neural network object or STANNO may include imaging cells which allow the STANNO to observe or input data located within the data space utilizing the aforementioned relative cell referencing scheme The artificial neural network which is to be trained is itself part ofthe STANNO, and at least some ofthe imaging cells may be representative ofthe input layer ofthe artificial neural network. The remaining imaging cells can be used by the STANNO to compare the actual output ofthe artificial neural network with the desired output associated with each particular input vector. In this regard, the STANNO also includes a training network which is configured to adjust the weights ofthe artificial neural network as determined by comparing the actual output ofthe artificial neural network with the desired output. In backpropagation, the training network may include four associated modules to implement the backpropagation training regime The first module is configured to determine what the activation level of each artificial neural network neuron would be if the inputs thereto are increased by some infinitesimal amount. The second module determines the derivatives of neuron activations with respect to net input thereto. The third module determines error terms and the fourth module determines correction values from which the weights and biases ofthe artificial neural network can be adjusted These four modules can be implemented distinctly within the data space or they can be integrated with each other and with the artificial neural network. The STANNO may be operable to move within the data space such that with each movement thereof the artificial neural network is trained on an input vector and corresponding output vector within the data space. Thus, the STANNO may continuously move through and thereby continuously train the artificial neural network within the data space. Advantageously, the STANNO may also remain stationary while training the artificial neural network on data which is fed directly into the data space, such as data from known systems which may include known devices or processes. Such a data feed may take the form of a dynamic data exchange Essentially, the STANNO is a network training a network with neither represented in algorithmic code. Advantageously, at any point during training, the artificial neural network may be copied from or moved from the STANNO and placed at another location within the data space or placed in an entirely different data space for operation. By taking advantage ofthe unique training ability ofthe STANNO and the ability to combine neural network objects to simulate interconnected devices, a device prototyping system is achievable. In this device prototyping system, a prototyping neural network is constructed, wherein at least some ofthe neurons of the prototyping neural network are represented by component neural networks, each trained within a knowledge domain of a component which will be used to construct the device being prototyped. By training the prototyping neural network on predetermined inputs and associated desired outputs, the finalized weighting values associated therewith can be used to determine how to interconnect the components in order to construct the prototyped device. A second neural network object acts as a data filtering artificial neural network object (DFANNO) whereby data within a data space can be monitored, analyzed, and manipulated in order to either locate novel data or to locate suspect data within the data space. The underlying theory is based on the use of an autoassociative neural network which is a network having a knowledge domain wherein input data vectors within the knowledge domain are mapped to themselves. Thus, if an input vector to the autoassociative neural network falls within the knowledge domain thereof, the result is an output vector therefrom which closely matches the input vector. When associated with the STANNO the DFANNO is operable to determine whether or not the STANNO has already trained the artificial neural network on a given set of data, or data similar thereto. If the STANNO has already trained the artificial neural network on the set of data, the artificial neural network is not trained on the given set of data, thereby reducing time wasted by retraining on redundant data. Conversely, if the DFANNO determines that the STANNO has not trained the artificial neural network on the data, the STANNO is permitted to train the artificial neural network on such data. The DFANNO may also operate as a separate entity within a data space. As such, the DFANNO is operable to analyze data within the data space to determine if any ofthe data does not follow an overall pattem associated with the data, such as data which has been affected by noise or some other disturbance which may have occurred in the data gathering process. When the DFANNO finds such data it is operable to either remove, delete, or relocate the data from the data space or to in some way tag the data as being suspect. Accordingly, the DFANNO is also an effective device for eliminating or calling attention to suspect data within a given data space. A third neural network object acts as a data scanning artificial neural network object (DSANNO) whereby various groupings of data within the data space are examined in attempt to find a set of data values having a predetermined relationship. The DSANNO may be stationary within the data space yet able to focus its attention to various groups of cells within the data space by taking advantage of relative cell referencing. The DSANNO includes a field positioning neural network which is operable to determine the position ofthe group of cells within the data space which will be analyzed by the DSANNO Through relative cell referencing, a set of imaging cells associated with the DSANNO is used to develop a working image ofthe group of cells which will be analyzed. A searching network is then utilized to view the working image from some perspective which is in turn analyzed by a detection network which determines if the set of data values making up the perspective meets the predetermined or desired relationship. Any set meeting the relationship can be tagged or possibly copied to another part ofthe data space. The DSANNO is thus useful as a tool for examining large databases for data strings having some desired relationship. The herein described techniques and neural network objects, or components thereof, may advantageously be combined in a variety of ways to develop more complex and advanced neural network systems. Brief Description ofthe Drawings Fig. 1 is an illustration of a traditional neural network neuron and the corresponding data space simulation thereof; Fig 1 A is a partial block diagram of a computer; Fig. 2 illustrates a plurality of neural network objects in a system for simulating interconnected processes or hardware devices; Fig. 3 is a block diagram illustration of a neural network object operable within a data space; Fig. 4 is a high level flow chart for movement ofthe neural network object illustrated in Fig. 3; Fig. 5 is a high level flow chart providing the neural network object of Fig. 3 with the ability to act upon the data space; Fig. 6 is a block diagram illustration of a self training artificial neural network object which includes an artificial neural network and a training network; Fig. 7 is a flow chart illustration of traditional backpropagation neural network training; Fig. 8 is a continuation ofthe flow chart of Fig. 7; Fig. 9 is a nodal illustration of an exemplary artificial neural network which forms part ofthe self training artificial neural network object of Fig. 6; Fig. 10 is a data space simulation or implementation ofthe artificial neural network illustrated in Fig. 8; Fig. 11 illustrates a first module ofthe training network associated with Fig. 6, the first module operable to determine activation levels when inputs are increased by some small amount; Fig. 12 illustrates a second module ofthe training network associated with Fig. 6, the second module operable to determine the derivative of neuron activations with respect to net inputs thereto; Fig. 13 illustrates a third module ofthe training network associated with Fig. 6, the third module operable to determine error terms; Fig. 14 illustrates a fourth module ofthe training network associated with Fig. 6, the fourth module operable to determine weight update terms for the artificial neural network illustrated in Fig. 10; Fig. 15 illustrates the self training artificial neural network of Fig. 6 as it moves through and trains within the data space; Fig. 16 is a Visual Basic program associated with the self training artificial neural network illustrated in Figs. 10-15; Fig. 17 illustrates a plurality of sets of training data; Figs. 18-21 illustrate various portions of an integrated self training artificial neural network object, wherein the training network is integrated with the artificial neural network being trained; Fig. 22 illustrates a subroutine associated with the integrated self training artificial neural network of Figs. 18-21; Fig, 23 illustrates a plurality of self training artificial neural network objects training simultaneously within a data space, Fig 24 illustrates a subroutine flow chart for implementing dynamic pruning in association with self training artificial neural network objects, Fig 25 illustrates a subroutine flow chart for implementing dynamic addition of neurons in association with self training artificial neural network objects, Fig 26 illustrates an exemplary untrained device prototyping neural network, Fig 27 illustrates the device prototyping neural network of Fig 26 after training, including finalized weight values, Fig 28 illustrates a data filtering artificial neural network object, Fig 29 is a Visual Basic program associated with the data filtering artificial neural network object of Fig. 28, Fig 30 is a block diagram illustration of a data filtering artificial neural network object associated with a self training artificial neural network object, both objects moving together through a data space, Fig 31 is a block diagram illustration of a data scanning artificial neural network object, including a search network, a detection network, and a field positioning network, Fig 32 is a nodal illustration of an autoassociative neural network which forms the field positioning network of Fig 31 , Fig 33 illustrates an exemplary viewing field ofthe data scanning artificial neural network object of Fig 31, Fig 34 is a nodal illustration of an autoassociative neural network which forms the search network of Fig 31, and Fig 35 is a nodal illustration of an exemplary detection network for the data scanning artificial neural network object of Fig 31 Detailed Description ofthe Drawings Referring to the drawings more particularly by reference numbers, number 10 in Fig 1 refers to a classical representation of a neural network neuron and number 12 refers to the implementation ofthe neuron 10 in a data space 14 The illustrated data space 14 includes a plurality of columns 16 and a plurality of rows 18, each column 16 being identifiable by a letter at the top thereof and each row 18 being identifiable by a number located at the left hand side thereof The column and row combination results in a plurality of cells 20, each of which may be identified by a corresponding letter and number designation This data space 14 configuration is typical of spreadsheets within a spreadsheet application The data space implementation 12 of neuron 10 is the building block of neural network objects described herein, but deviations may be used which do not deviate from the spirit ofthe present invention The data space implementation 12 includes a first plurality of cells 22, in this case five (5) cells, each having an associated predetermined numeric value, w„ w 2 , w 3 , w 4 , and θ respectively The number of cells 22 will vary depending on the number of inputs to the neural network neuron 10 In this case, a second plurality of cells 24 contain input values x,, x^ x 3 , and x 4 Accordingly, the plurality of cells 22 include four (4) corresponding weight values w,, w 2 , w 3 , and w 4 , and one bias value θ As used herein, the terms weight or weighting value include bias values which are presumed to be associated with constant neuron inputs of one (1) In an untrained neural network the numeric value associated with each cell 22 may be randomly assigned while in a trained neural network the numeric values are determined by training the neural network of which the neuron is a part An activation cell 26 contains a transfer function 28 which references each of the cells 22 and each ofthe cells 24, the transfer function 28 acting to apply the appropriate weights to the appropriate input values in determining an activation level associated with the neuron 10 Accordingly, the numeric value associated with the activation cell 26 is dependent upon the numeric values associated with each of cells 22 and 24 as well as the form ofthe transfer function 28, which in this case is a sigmoid function, although other known transfer functions could be utilized During normal operation of neural network objects the transfer function 28 is hidden and the numeric value associated with the activation cell 26 is displayed on a computer screen or other display device 27, see Fig 1 A Thus, the displayed numeric value represents the activation level ofthe activation cell 26 and accordingly the neural network neuron 10. As shown in Fig IA, a computer such as an IBM compatible personal computer including microprocessor 29, RAM 31 , and ROM 33 may be utilized in association with the present invention. A plurality of data space implemented neurons 12 may be used to construct artificial neural networks in accordance with the present invention. Such networks typically include both hidden layer and output layer neurons. Accordingly, in such networks, input values for a given neuron may be values associated with activation cells of another neuron within the neural network Utilizing such data space implemented neurons 12 advantageously facilitates construction of artificial neural networks without requiring any specialized algorithm implementing software Once a given artificial neural network is constructed or implemented in a spreadsheet or data space 14, advantage may be taken of resident spreadsheet capabilities such as the ability to copy and paste a group of cells or to cut and paste a group of cells. Accordingly, artificial neural networks constructed in accordance with the present invention may be easily interconnected to construct increasingly complex artificial neural networks. One advantageous use for such artificial neural networks is in providing a system for simulating interconnected processes or interconnected devices such as electronic or mechanical devices. Such a system is illustrated in Fig. 2 wherein two data spaces 30 and 32, which may be distinct but associated spreadsheets, such as spreadsheets associated in workbook form, are shown. Located in data space 30 are various neural network objects 34, 36, 38, and 40, in which the cross-hatched regions represent cells associated with the operation of each. By way of example, each neural network object 34, 36, 38, and 40 may be trained within the knowledge domain of some electrical component such as a resistor, capacitor, inductor, or transistor. Of course, the knowledge domain of any electrical component could be incoφorated into a neural network object within the data space 30. Such a system would be particularly useful when there is no existing mathematical model for the component's behavior. Having established a plurality of operable, neural network objects such as 34, 36, 38, and 40, various electronic circuit configurations can then be simulated by copying the neural network objects to the data space 32, as indicated by arrow 42 with respect to neural network object 40, so as to interconnect, through relative cell referencing, the neural network objects in the configuration ofthe electronic circuit to be simulated. Accordingly, providing a spreadsheet, or plurality of spreadsheets in workbook form, with multiple neural network objects, each trained to emulate a particular electronic device, results in a system for simulating electronic circuits of numerous configurations. Moreover, such a system is advantageously user friendly due to the graphical representation of each neural network object which allows a user to easily manipulate such objects as required for a particular application. In addition to providing a system for simulating known devices, neural network objects can be configured for numerous puφoses. Some important aspects of such neural network objects is their ability to autonomously move within the data space, to operate on or alter data or other objects within the data space, and to self organize. Fig. 3 illustrates the block diagram configuration of a neural network object 44 which may be operable to move within the data space 14, alter or otherwise operate on data or other objects within the data space 14, and/or self organize. The neural network object 44 includes a first data space implemented artificial neural network 46 and also includes one or more imaging cells 48 which, through relative cell referencing, form a working image of a portion 50 ofthe data space 14. Thus, the imaging cells 48 are tantamount to a visual or receptive field in neurobiology. The image developed by the imaging cells 48 is then input to the artificial neural network 46, again through relative cell referencing. This first artificial neural network 46 may be trained within a known knowledge domain so as to process the input data and result in some desired output. For example, the artificial neural network 46 could be trained to simulate the output of a known system, such as a materials manufacturing process or some hardware device, in response to a multi variable vector input thereto. Alternatively, the artificial neural network 46 may be an untrained network which is to be trained on the data referenced by the imaging cells 48. Of course, the neural network object 44 may also include other associated networks 51. The neural network object 44 may be operable, via a program associated therewith, to perform some task. Exemplary programming routines are illustrated in the high level flow charts of Figs. 4 and 5. The routine 52 of Fig. 4 could be utilized to cause the neural network object 44 to move, wherein the movement is dependent upon some information produced by the neural network object 44. Staring at 54, such infoπnation would be obtained therefrom at step 56 and the movement would then be carried out by step 58, with the routine ending at 60. Similarly, the routine 62 of Fig. 5 could be utilized to delete or otherwise alter the data located in the portion 50 ofthe data space 14, or to self organize such as by modifying the artificial neural network 46. The intended action ofthe neural network object 44 would be determined, starting at 64, from information obtained therefrom at step 66. The action would then be carried out at step 68, with the program ending at 70. Autonomy ofthe neural network object 44 is ensured by partitioning its internal function from any governing algorithm in a technique resembling encapsulation within object-oriented programming wherein class objects or different portions of a computer code conceal data and algorithms from each other, passing only restricted information between each other The encapsulation feature allows for the portability ofthe class objects. In the present invention, the concept of encapsulation is extended to artificial neural networks wherein the activity between an algorithm and a neural network is segregated. Therefore, the neural network object 44, such as shown in Fig. 3, autonomously makes decisions based upon the imaged portion 50 ofthe data space 14 and the algorithm, 52 or 62, then effects those decisions. SELF TRAINING Various neural network objects can be constructed in accordance with the present invention to perform various functions or simulate known systems. For example, the block diagram configuration of a self training artificial neural network object or STANNO 72 which is operable to train an artificial neural network 74 is illustrated in Fig. 6. The STANNO 72 includes a plurality of imaging cells 76, the artificial neural network 74 which is to be trained, and a training network 78. The training network 78 includes four modules, 80, 82, 84, and 86 which are configured to implement backpropagation training ofthe artificial neural network 74. The steps involved in traditional backpropagation training are illustrated in the flow chart 88 of Figs. 7 and 8, and are summarized below. In this regard, x is defined as a multi variable vector whose components represent the individual inputs to the artificial neural network being trained; p is used as an index to signify the pth data vector presented to the neural network being trained. Accordingly a given input vector is designated ^. Beginning at 90 in flow chart 88, backpropagation training includes generating a table of random numbers corresponding to a starting set of weights at step 92. An input vector, p , is then input to the randomly set neural network at step 94. The net input values to the hidden layer nodes or neurons are then calculated, wherein net pj h , the total input to the jth hidden (h) layer neuron is the sum ofthe products of all inputs, x^, and weights w^ plus the bias term θ j h as demonstrated by the equation of step 96. The outputs from the hidden layer are then calculated as demonstrated by the equation of step 98 where i pj represents the activation level of the jth hidden layer neuron as a function of its net input and f represents some functional relation such as a sigmoid, linear threshold function, or hyperbolic tangent. The net input values to each unit ofthe output layer are then calculated as demonstrated by the equation at step 100, wherein the superscript o refers to the output layer quantities. The outputs ofthe output layer nodes or neurons are then calculated as demonstrated by the equation at step 102. The flow chart 88 then continues at 104 in Fig. 8. The error terms for each ofthe output units and each ofthe hidden layer units are then calculated according to the equations of steps 106 and 108. Next, the weights on the output layer are updated according to the equation of step 110, and the weights on the hidden layer are then updated according to the equation of step 112, wherein η represents the learning parameter. An error term Ep is then calculated according to the equation at step 114. A new input vector is then selected and training returns to step 94, as indicated by 116, with training continuing until the error Ep reaches some minimal value, as determined at step 118. The flow chart 88 ends at 120. Rather than performing all ofthe steps of flow chart 88 in sequence, the STANNO 72 of Fig. 6 utilizes the training network 78 to perform these operations in parallel fashion. The training network 78 includes first module 80 which is identical to the artificial neural network 74 except that it determines what the activation levels are when each ofthe inputs is increased by some infinitesimal amount, which may be represented by a value Δ of 0.01. It is understood that other values of Δ could also be utilized without departing from the scope ofthe present invention The second module 82 determines the derivatives of cell activations with respect to net input to those cells. The third module 84 utilizes the derivatives to determine the error terms corresponding to steps 106 and 108 of flow chart 88. The fourth module 86 determines weight updates, and the weights ofthe artificial neural network 74 and the first module 80 are then adjusted, as indicated by arrow 122, using the updates produced by the training network 78. Thus, training ofthe artificial neural network 74 is not carried out with algorithmic code, but rather by a network training a network. Figs. 9 through 14 illustrate in greater detail the different portions ofthe STANNO 72 of Fig. 6. A traditional representation 124 ofthe artificial neural network 74 is illustrated in Fig. 9. A two input neuron, 126 and 128, one output neuron 130 feed forward neural network is depicted, including a hidden layer 132 having three neurons 134, 136, and 138. However, it is understood that numerous artificial neural network configurations, including more complex artificial neural networks, could be trained as described herein. Fig. 10 illustrates a corresponding data space implementation ofthe artificial neural network 74. Also shown in Fig. 10 are the imaging cells 76. In relation to Fig. 9, the imaging cells Dl and El of Fig. 10 correspond to the input neurons 126 and 128 respectively, and activation cells F3, F4, and F5 relate to hidden layer neurons 134, 136 and 138 respectively. Cells D3 and E3 contain the weighting values and cell D4 contains the bias value for neuron 134. Similarly, cells D5, E5, and D6 contain the weight and bias values for neuron 136, while cells D7, E7, and D8 contain the weight and bias values for neuron 138. The value associated with each activation cell F3, F4, and F5 represents the activation level of respective neuron 134, 136, and 138, and is determined by a transfer function which references, either directly or indirectly, the corresponding weight and bias value containing cells as well as the imaging cells Dl and El . Activation cell H3 of Fig. 10 corresponds to the output neuron 130 of Fig. 9 and cells G3, G4, G5, and G6 contain the weight and bias values for the neuron 130. The transfer function of activation cell H3 references, either directly or indirectly, each ofthe hidden layer activation cells F3, F4, and F5 as well as each ofthe weight and bias containing cells G3, G4, G5, and G6. Although shown in Fig. 10, cells F6, F7, F8, and H4 are not necessary for simulating operation ofthe artificial neural network 74. Rather, cells F6, F7, F8 and H4 are used to determine the net input to each ofthe neurons 134, 136, 138, and 130, respectively, in accordance with steps 96 and 100 of flow chart 88, see Fig. 7. These determined values are then utilized by the training network 78, see Fig. 6, as indicated below. Altematively, the SUMPRODUCT functions within cells F6, F7, F8, and H4 could be directly incoφorated in the respective transfer functions of cells F3, F4, F5, and H3. The first module 80 ofthe training network 78 is illustrated in Fig. 11. It is evident that, similar to Fig. 10, the first module 80 contains the data space implementation ofthe artificial neural network 74 illustrated in Fig. 9. However, during training, the inputs to the first module 80 are increased by some infinitesimal amount Δ, as indicated by cells D9 and E9, in order to determine the effect on the activation level of, as well as the net input to, each ofthe hidden layer neurons 134, 136, and 138 and the output neuron 130 ofthe artificial neural network 74. The values determined in the first module 80 are then utilized by the second module 82 which is illustrated in Fig. 12 and is operable to determine the derivative of cell activations, which represent neuron activations, with respect to net inputs thereto. The derivatives are approximated according to the equations in cells F18, F20, F22, and HI 8, which represent the difference in activation value over the difference in net input. For example, cell F18 approximates the derivative ofthe hidden layer neuron 134, Fig. 9, with respect to the net input thereto by dividing the difference between the numeric value associated with cell Fl 1 and the numeric value associated with cell F3 by the difference between the numeric value associated with cell F14 and the numeric value associated with cell F6. Similar derivatives for the remaining hidden layer neurons 136 and 138 as well as the output neuron 130 are determined at cells F20, F22, and HI 8 respectively. Fig. 13 illustrates the third module 84 ofthe training network 78 wherein the error terms corresponding to steps 106 and 108 of flow chart 88 are determined. In cell H26 the error term δ ≠ °, is determined by multiplying the value associated with cell II by the value associated with cell H18, the value associated with cell II being the difference between the actual output ofthe artificial neural network 74 and the desired output and the value associated with cell HI 8 being the derivative value determined in the second module 82. The δ pk ° term of cell H26 is then backpropagated to determine the error terms for the hidden layer neurons 134, 136, and 138 in each of cells F26, F28 and F30. For example, in cell F26 the value of cells F18, G3 and H26 are multiplied together, the value associated with cell F18 being the derivative value determined in the second module 82 and the value associated with cell G3 being the weight term from hidden layer neuron 134 to output neuron 130 Similarly, in cells F28 and F30, the error terms for respective hidden layer neurons 136 and 138 are determined. In the fourth module 86, shown in Fig. 14, weight update terms are determined. With respect to the output neuron 130, the weight update terms correspond to the (ηδ p ^ ) portion ofthe equation shown in step 110 of flow chart 88, where the learning parameter η has a value of one (1). For example, in cell G34 the weight update term for the weight value associated with cell G3 of Fig. 10 is determined by multiplying the numeric value associated with cell H26 by the numeric value associated with cell F3, the value associated with cell H26 being the δ pk ° term and the value associated with cell F3 representing the i pj term which is the mput to output neuron 130 coming from the hidden layer neuron 134 Similarly, the respective weight update terms for the weight values associated with cells G4 and G5 of Fig 10 are determined in cells G35 and G36 In cell G37, the weight update term for the bias value is determined, the i pj term being designated as one ( 1 ) as explicitly shown The weight update terms for the hidden layer weights and biases are also determined in the fourth module 86 These weight update terms correspond to the (ηδ pj ^ j ) portion ofthe equation shown in step 112 of flow chart 88, where η, the learning parameter, is again given a value of one (1). For example, cell D34 determines the weight update term for cell D3 of Fig 10 by multiplying the numeric value associated with cell F26 by the numeric value associated with cell Dl, the value associated with cell F26 being the δ pj h term determined in the third module 84 and the value associated with cell D 1 being the input value to the hidden layer neuron 134. Similarly, cells E34, D35, D36, E36, D37, D38, E38 and D39 determine the weight update terms for each ofthe values in respective cells E3, D4, D5, E5, D6, D7, E7, and D8, of Fig 10 Importantly, the training network 78 determines all weight updates from observed errors, utilizing a parallel computation scheme built upon the backpropagation paradigm There are no algorithmic sequences of steps constituting the partial derivatives, error terms, and updates. The weight update terms determined in the fourth module 86 must then be added to their corresponding weight terms in the artificial neural network 74 and the first module 80. After updating the weight terms, the STANNO 72 is operable to move to another location in order to train on another set of data within the data space 14 The operation ofthe STANNO 72 is best shown in Fig 15 where the STANNO 72 is shown in block diagram form Multiple sets of training data may be located in columns A, B, and L ofthe data space, with columns A and B containing the inputs and column L containing the corresponding desired output After training on a set or row of data, the STANNO 72 is operable to move down one row and train on another set of data Thus, the STANNO 72 moves through and therefore trains on the training data, with the error or difference between actual output ofthe artificial neural network 74 and the desired output in column L decreasing accordingly, and displayed at cell 140 Movement ofthe STANNO 72 and updating ofthe weight values ofthe artificial neural network 74 are achieved via software such as the Visual Basic program 142 shown in Fig. 16 The program may be located in a separate spreadsheet, not shown, which is associated with the spreadsheet or data space 14 ofthe STANNO 72. In program portion 144, the last training data point, lasti, and the Epoch value are recovered from the spreadsheet The program portion 146 randomly assigns initial weights between -8 and 8 to the weight cells ofthe artificial neural network 74. In each ofthe terms "Cells(x, y)" the x value corresponds to a row within the data space and the y value corresponds to a column with the data space. Altematively, weights may be initialized by placing the spreadsheet function rand() within the appropriate cell and calling a calculate command. In program portion 148 artificial neural network training takes place, with the Epoch value representing the number of times the STANNO 72 will be permitted to train on the training data, and the i value representing the number of rows or sets of data the STANNO 72 will be permitted to train on. The calculate term 150 triggers all calculations within the data space 14 Then update lines 152 update the weight cells by adding to them the weight update values determined in the fourth module 86 ofthe training network 78. After the weight values have been updated, program portion 154 determines if the STANNO 72 has reached the end ofthe training data, as indicated by zero (0) values in the training input columns. Program portion 156 causes the STANNO 72 to move down one row within the data space 14 After moving to the bottom ofthe i sets of data program portion 158 operates to move the STANNO 72 back up to the top ofthe training data. The movement ofthe STANNO 72 is accomplished by the copy and paste commands, which leave behind a diagnostic trail of network inputs and outputs. Cutting and pasting would erase this trail Training will be completed when the STANNO 72 has moved through the training data a predetermined number of times, which in this case is the upper limit ofthe Epoch value, or 1000 Alternatively, training could continue until the RMS error associated with the artificial neural network falls below some predetermined value It should be understood that the STANNO 72, illustrated in Figs 6 and 10-15 along with associated program 142 is merely one configuration among many possibilities for self training neural network objects The important aspect ofthe invention being a network which trains a network In this regard, Figs. 17 through 21 illustrate an altemative configuration for an integrated self training artificial neural network where the artificial neural network being trained and the associated training network are integrated with each other in the data space Figs 17 through 21 all refer to different portions ofthe same data space 14, and Fig 17 particularly illustrates columns A through S ofthe data space 14 Columns B through S contain multiple sets of training data, one set per row, where the sets include nine (9) inputs 160, designated xpl through xp9, and nine (9) associated outputs 160, designated ypl through yp9 Although only nine rows or sets of training data are shown, the number of sets of training data is limited only by the maximum number of rows allowable in the data space 14 Further, in the case of a dynamic data exchange as described below, the number of sets of training data is unlimited With regard to the integrated self training artificial neural network, Figs 18 through 21 illustrate portions thereof It is assumed that the artificial neural network being trained is a 9-9-9 network, having nine inputs, nine hidden layer neurons, and nine output layer neurons Fig 18 illustrates columns AK through BB ofthe data space 14, which columns are utilized to determine the maximum and minimum numeric values contained within each column ofthe training data illustrated in Fig 17, as shown in rows one (1) and two (2) In row three (3), the difference between the maximum and minimum values is determined In Figs 19 through 21, the configuration for two levels of neurons is illustrated, rows three (3) through twelve (12) representing the first level 164 and rows thirteen (13) through twenty-two (22) representing the second level 166 Seven more levels of neurons are included in a complete configuration, but, for ease of understanding, are not shown. With reference to column U of Fig 19, it is seen that the values determined in Fig. 18 are utilized to normalize the training inputs. Within column U, cells U3 through Ul 1 determine the normalization of each input, thus the cell combination U3 through Ul 1 represents the input vector. Cells U13 through U21 similarly represent the same input vector for the second level In column V, the delta value, 0.01 or -0.01, is added to the normalized inputs of column U. In this regard, because the transfer function being utilized, a sigmoid, has a linear region around the value 0.5, it is desirous when adding the delta value to the normalized input to adjust the input towards the linear region. Thus, in cell V3, the function =IF(U3<0.5, U3+0.01, U3-0.01), causes the positive delta value to be added to normalized inputs which are less than 0.5 and causes the negative delta value to be added to normalized inputs which are greater than 0.5. Again, for the second neuron level 166, similar values are used as indicated by the relative references of cells VI 3 through V21. The cells of column W contain the hidden layer weight values wji, where j represents the neuron level and i represents the input associated therewith, with biases given the designation q as shown in cells W12 and W22. The training based updated hidden layer weight values are determined in the cells of column X. Referring to Fig. 20, in column Y the activation levels and derivatives of activation level with respect to net input thereto are determined for each hidden layer neuron level. With respect to the first level 164, the activation level and net input for the normalized inputs of column U are determined in cell Y3 and Y4, respectively, the activation level and net input for the delta adjusted inputs of column V are determined in cells Y5 and Y6, respectively, and the derivative value is determined in cell Y7. Corresponding values for the second level 166 are determined in cells Y13 through Y17. Following this pattem, each of cells Y3, Y13, Y23, Y33, Y43, Y53, Y63, Y73, Y83 will contain the activation level of a hidden layer neuron. Thus, in column Z, all activation levels, act j(xp), are relatively referenced such that, for example, the values associated with cells Z3 through Zl 1 represent an input vector to be applied to the output layer neurons Accordingly, in column AA, the delta value is added to the activation levels of column Z Column AB contains the output layer weight values wkj and the training based updated output layer weight values are determined in column AC Referring to Fig. 21, the activation levels and derivatives of activation level with respect to net input thereto are determined in column AD for each output layer neuron The actual activation levels, which represent output values, are then relatively referenced in column AE, cells AE3 through AE 11 In column AG, these actual output values are compared with the desired output values which are associated with column AF and which, although not shown, are normalized as were the inputs Accordingly, in cell AG12 an rms error value is determined In column AH the δ pk ° terms are determined and in column AI a δ pk ° vector term is developed, as represented by cells AI3 through AH 1 With reference to column AC of Fig 20, it is seen that the δ pk ° terms determined in column AI are utilized to determine the output layer weight update terms, wkj Similarly, with reference to column X Fig 19, it is seen that δ pk ° terms are also backpropagated to determine the hidden layer weight update terms, wji Thus, with each calculate command initiated within the data space, all necessary calculations for backpropagation training take place After each calculation, the weight values in columns W and AB must be replaced with their corresponding updated weight values associated with columns X and AC, respectively. Fig 22 illustrates a subroutine 168 which accomplishes this task In the subroutine 168, with regard to the hidden layer weights, the first line selects the cells of column X associated with the integrated self training artificial neural network and the second line copies those cells The third line selects the destination column for the copied material and the fourth and fifth lines operate to paste only the numeric values associated with the copied cells into the destination column. Similarly, the sixth through eleventh lines of subroutine 168 operate to replace the output layer weight values of column AB with the updated weight values of column AC As compared to the update method illustrated in portion 152 of Fig. 16, the subroutine 168 is able to complete the weight updating much more quickly, advantageously increasing training speed. Utilizing a dynamic data exchange provided by a product such as National Instruments Measure for Windows, which is operable with Microsoft Excel, the integrated self training artificial neural network illustrated in Figs. 18 through 21, is capable of training in real time as training data flows through the data space 14. In such a case, the data would flow through predetermined rows or columns and the integrated self training artificial neural network would remain stationary in the data space 14 while the training data moves relative thereto. Of course, the STANNO 72 illustrated in Figs 10 through 14 could also be utilized with such a dynamic data exchange. Another advantage of self training artificial neural networks is that multiple networks may be trained simultaneously, in parallel fashion, on the same, or different, sets of training data. Referring to Fig. 23, for example, in the case of a dynamic data exchange, multiple self training artificial neural network objects such as 170, 172, and 174, may be positioned within the data space 14 so as to train on the data flowing through the columns as indicated at 176. Each self trainer 170, 172, and 174, may also be configured to train on only some ofthe columns of data in order to result in trained networks having different knowledge domains. Further, each self trainer could train on completely different sets of data, such as where STANNO 170 trains on the data flowing through the columns to the left and STANNO 172 trains on the data flowing through the columns to the right, or where multiple self training neural network objects train on distinct data within separate spreadsheets altogether. Such a parallel training scheme would be extremely difficult to implement using traditional algorithm based training. Further, training multiple networks simultaneously results in substantial savings in training time. Still other advanced features can be incoφorated into the training schemes of self training artificial neural network objects. Two such features are dynamic pruning of networks during training and dynamic addition of neurons during training. With regard to dynamic pruning, for each neuron ofthe artificial neural network associated with the self training artificial neural network object, a subroutine 178 such as illustrated in Fig 24 may be provided, such as by embedding the subroutine 178 within the spreadsheet or data space Within this subroutine 178, the variable N may be a count of the number of sets of training data which have been operated upon and which is set to zero (0) at the beginning of training, Tl may be a predetermined value which is chosen to represent a change in magnitude associated with the activation level ofthe neuron, and T2 may be a predetermined number which is chosen to represent a number of activation level changes of magnitude greater than Tl The subroutine 178 is run in association with each wave of spreadsheet calculation The subroutine starts at 180 and at step 182 the change in activation level, Δ. ct , ofthe neuron is determined At step 184, if the change in activation is greater than Tl, the variable TRANSITIONS is increased by one. Moving to step 186, the N count, or count of number of sets of training data, is increased by one and at step 188 the N count is evaluated to see if it has reached a PREDETERMINED NUMBER. If N has not reached the PREDETERMINED NUMBER, the subroutine ends at 190 However, if the N count has reached the PREDETERMINED NUMBER, step 192 is reached and the N count is again set to zero At step 192 the TRANSITIONS variable is evaluated to see if it is less than the number T2, if not, the subroutine 178 ends at 190 However, if TRANSITIONS is less than T2, the activation function ofthe neuron is set to zero (0) at step 196, effectively eliminating the neuron from having any further effect Thus, Tl and T2 can be chosen to reflect the fact that the neuron is not significantly involved in the training regime and can therefore be pruned out of the artificial neural network, while the PREDETERMINED NUMBER of step 188 can be chosen to reflect how often the neuron should be evaluated to see if it should be eliminated With regard to dynamic addition of a neuron or neurons, a subroutine 198, illustrated in Fig. 25, may be associated with the operation of a self training neural network object The subroutine 198 begins at 200 and at step 202, the RMS ERROR between actual outputs and desired or training outputs, determined after each set of training data is operated upon, is evaluated to determine if it exceeds a desired THRESHOLD ERROR, which is predetermined so as to be indicative of successful incoφoration ofthe desired knowledge domain within the artificial neural network. If the RMS ERROR has fallen below the THRESHOLD ERROR, the subroutine 198 ends at step 204. Conversely, if the RMS ERROR exceeds the THRESHOLD ERROR, step 206 is reached where N, the count of sets of training data, is evaluated to determine if it exceeds a THRESHOLD N number If N does not exceed the THRESHOLD N number, the subroutine 198 ends at step 204. However, if N exceeds the THRESHOLD N number, step 208 is reached The THRESHOLD N number should be chosen so as to indicate that the training operation has continued long enough to determine that the artificial neural network being trained is not large enough, and that in order to train the artificial neural network to be able to achieve the desired THRESHOLD ERROR, the artificial neural network must be enlarged. Thus, at step 208, a prototypical neuron with randomized weights is copied and added to the hidden layer. Similarly, at step 210, all cells necessary to perform the required operations associated with the new neuron are also copied and added to the network. The N value is then reset to zero (0) at step 212 and the subroutine 198 ends at 204. After the addition ofthe neuron as provided by steps 208 and 210, the training operation will continue except that the artificial neural network being trained will include one additional hidden layer neuron which should enable further reduction in the RMS error. For example, in the case ofthe 9-9-9 network associated with the integrated self training artificial neural network of Figs. 18-21, steps 208 and 210 ofthe subroutine will result in a 9-10-9 network. Thus, as described above, both dynamic pruning and dynamic growth may be achieved in combination with self training artificial neural networks. It is understood that the routines described herein are merely exemplary of implementations of dynamic pruning and dynamic neuron addition, and that such features may be incoφorated in alternative ways. DEVICE PROTOTYPING A system for device prototyping is advantageously provided in light ofthe ease of cascadability and the self training capability described above. An exemplary case of device prototyping is illustrated in Figs. 26 and 27. In Fig 26, a known input θ(t), which is a sinusoid 214 is shown. The desired output ofthe prototyped device, in response to the known input sinusoid 214, is a cyclic square pulse and the prototyped device is to be constructed from seven harmonic generating devices. Of course, such a problem may be approached through Fourier analysis, but it can also be solved through use of a prototyping neural network 216. The prototyping neural network 216 includes seven (7) hidden layer neurons 218, 220, 222, 224, 226, 228, and 230 respectively. Each hidden layer neuron is represented by a component neural network which is trained within a knowledge domain of one ofthe harmonic generating devices which will be used as components from which to construct the prototyped device. When the weights associated with the prototyping neural network are randomly assigned, the output F(θ) may appear as 232. Utilizing the techniques described above with reference to self training artificial neural network objects, the prototyping neural network can be trained within the desired knowledge domain ofthe prototyped device, which is reflected in a conversion ofthe sinusoid 214 to a cyclic square pulse. Fig. 27 illustrates the resulting prototyping neural network 216 after training, including weight values. As seen, all hidden layer weights approach one. With regard to the output layer weights, the weights for neurons 218, 222, 226, and 230 approach zero, and thus no connection to the output is shown. However, the illustrated weights for neurons 220, 224, and 228 approach (2/π), (2/3π), and (2/5π) respectively, along with a bias value of (1/2). With these weight values, the resulting output ofthe prototyping neural network is F(θ) as shown in the equation 234 and the graph 236. The weights which result from training the device prototyping neural network can then be correlated to how the components should be interconnected in order to construct the prototyped device. In this exemplary case, it is evident that odd harmonic generating devices would be directly re¬ connected to the input θ(t) and that the outputs therefrom would be multiplied by the respective weights and summed in order to construct the prototyped device This prototyping system can be utilized in conjunction with many types of components. The important aspect ofthe system is that if a neural network model for each component can be constructed, a prototyping neural network can be trained without requiring explicit knowledge ofthe functional relation between inputs and outputs ofthe components because the self training scheme is able to determine derivative values without knowing the functional relation On the contrary, traditional backpropagation algorithms require foreknowledge ofthe functional relation and its derivative Thus, combining the cascadability of neural networks implemented in spreadsheets with the self training artificial neural network facilitates the aforementioned device prototyping system DATA FILTERING/MONITORING Another neural network object which may be constructed is a data filtering neural network object or DFANNO 238 such as shown in Fig 28. The underlying theory ofthe DFANNO 238 is that of an autoassociative neural network 240 The autoassociative neural network 240 is an artificial neural network which is trained to map inputs to themselves. Accordingly, an input vector within the knowledge domain ofthe autoassociative neural network 240 results in an output vector therefrom which closely matches the input vector By way of example, if a vector v is applied at the input 242 ofthe autoassociative neural network 240, the network 240 will produce at its output 244 another vector v' representative ofthe closest vector seen in the training data or generalized from the training data. Using matrix notation, Av = lv', where A represents the autoassociative neural network 240 and 1 is the unitary matrix with diagonal elements of 1. Thus, the equation may be rearranged into a general eigenvalue form (Δ-l)v = δ, where δ represents the error or vector difference between input and output vectors ofthe autoassociative neural network 240 For a given input vector, if δ is 0, or close to 0, then the input vector fits the pattem ofthe training data the autoassociative neural network 240 was trained upon On the other hand, as δ is progressively different from the zero vector, there is a greater likelihood that the associated input vector does not fall within the pattem ofthe training data, and therefore a greater likelihood that the input vector is either novel or the result of systematic error or random noise. Prior to operation, the autoassociative neural network 240 should be trained on a plurality of sets of control data. Each set of control data should be carefully selected so as to reflect the desired knowledge domain and so as to ensure that each set of control data has not been affected by systematic error or random noise. Thus, as the DFANNO 238 moves through a data space 14 encountering different rows of data, such as 246, each representing an input vector thereto, an RMS error between each input vector and each output vector is determined as indicated at 248. If, for a given input vector, the error exceeds a predetermined level, the DFANNO 238 is then operable to perform some operation on the row 246 of data making up the input vector. For example, the row 246 of data may be deleted from the data space 14 entirely, relocated, or tagged as suspect. Thus, the DFANNO 238 is effective for moving through the data space 14, as indicated by arrow 250, and examining the data therein to find data which may have been caused by some systematic error or random noise introduced to the data or which occurred when the data was originally gathered. A Visual Basic program 252 which achieves these operations is illustrated in Fig. 29. The calculate line 254 triggers all calculations within the data space 14. The For-Next Loop 256 is provided to determine if the DFANNO 238 has reached a point in the data space 14 where there is no more data, as indicated by all cells of a particular row being zero. If there is no more data the operation of DFANNO 238 is halted. Line 258 and portion 260 determine the operation the DFANNO 238 will take with respect to a particular row of data. In each of these lines cell (1,10) ofthe data space 14 represents a flag. If the flag is zero (0) the DFANNO 238 is in the data tag mode but if the flag is set to one (1) the DFANNO 238 is in the data destroy mode. With respect to line 258, if the RMS error at 248, between inputs and outputs ofthe autoassociative neural network 240, is greater than thirty (30) and if the flag is zero (0) then the cell immediately to the right ofthe data row is tagged with an asterisk, *. With respect to the program portion 260, if the RMS error is greater than thirty (30) and if the flag is set to one (1), the data values in the row are cleared from the data space 14. The final portion 262 ofthe program 252 causes the DFANNO 238 to move on to another row of data. Of course, this program is merely representative of software which could be utilized in association with data filtering artificial neural network objects Altematively, the DFANNO 238 could be stationary within the data space 14 while data from some system or device to be monitored by the DFANNO 238 is fed into predetermined locations within the data space 14 through a dynamic data exchange, such that the DFANNO 238 operates on the data as it is fed through the data space 14. When suspect data is fed into the data space 14 and operated on by the DFANNO 238 the DFANNO 238 could be operable to shut down the system or device. Accordingly the DFANNO 238, either alone or in combination with other networks, provides an effective system monitor. Data filtering artificial neural networks can also advantageously be used in association with self training artificial neural networks. Such an association is illustrated in Fig. 30 wherein a DFANNO 238 has been appended to an STANNO 72 such that the two neural network objects move with each other through the data space 14 as shown by arrow 264. As the two objects move through the data space 14 the DFANNO 238 is operable to determine if the data at any given location is novel to the training ofthe STANNO 72. Thus, if the error determined by the DFANNO 238 exceeds a predetermined level, the data is considered novel and the STANNO 72 trains on such data. However, if the error is below the predetermined level the data at such location is considered old to the training ofthe STANNO 72, in which case the DFANNO 238 would be operable to cause the two associated neural network objects to move on to another set of data without allowing the STANNO 72 to train on the data, thereby reducing time wasted by retraining on redundant data. Thus, as described above data filtering neural network objects of various configurations have a variety of useful applications, particularly in the areas of data monitoring for the puφose of finding novel data or data which may be suspect. DATA SCANNING Fig. 31 illustrates a block diagram configuration of a data scanning artificial neural network object or DSANNO 266. The DSANNO 266 is stationary within the data space 14 but capable of directing its view to various groups of cells within the data space 14 utilizing relative cell referencing. The DSANNO 266 includes a search network 268, a detection network 270, and a field positioning network 272. The field positioning network 272 autonomously moves the viewing field 274 of the DSANNO 266 about the data. The graphical antenna 276 may be utilized as a guide to the human viewer as to where the DSANNO 266 is focusing its attention, however, the antenna 276 is not required for operation ofthe DSANNO 266. Viewing field 274 positioning is achieved utilizing an autoassociative neural network 278 in which the weights and biases are subjected to noise sources, as shown by arrow 280 in Fig. 32, so that the autoassociative neural network 278 imagines various possibilities within its training domain. In this case, the noise source may be random numbers applied to the weights and biases ofthe autoassociative neural network 278. The autoassociative neural network 278 used is trained on a table of (x, y) values having integer values associated with the cells containing the data. Therefore, as the autoassociative neural network 278 is subjected to noise, it generates outputs reflecting the constraints within the training database, namely that it generate only integer values corresponding to data containing cells. In essence, the perturbed autoassociative neural network 278 is a random integer generator. However, by recirculating the networks 278 outputs back to the inputs, see line 282 of Fig. 31 and lines 284 and 286 of Fig 32, a relatively smooth trajectory of viewing field 274 positions is generated because x and y coordinates are only gradually altered with each feedthrough cycle of this recurrent net. The net effect is this configuration is to produce continuous random movement ofthe viewing field 274 ofthe DSANNO 266, and is similar to the population-polling process used to govern human eye movement. A group of imaging cells 288, see Fig. 31, utilize relative cell referencing to develop a working image ofthe viewing field 274. The working image may then be communicated to the search network 268 as indicated by arrow 290. By way of example, in Fig. 33 the imaging cells 288 ofthe DSANNO 266 are illustrated and include a 4x4 array of cells. The search network 268, illustrated in Fig. 34 is utilized to view the imaging cells 288 from a perspective such as that illustrated by the bold cells 292 of Fig. 33. The development of such a perspective is achieved utilizing an autoassociative neural network 294 which has been trained on numerous examples of data string configurations within the imaging cells 288. Noise 296 is then introduced to the network 294 such that the network 294 produces an imagined data string configuration at its output 298 which will be examined by the detection network 270 of Fig. 31. In this regard, an exemplary detection network 270 is illustrated in Fig. 35. This detection network 270 is trained to output a one at 300 if the inputs applied at input layer 302 obey the search criteria. The training domain can be chosen as required for a particular application. For example, the training domain may output a one when the inputs thereto have some predetermined relationship. The output of a one then acts to enable the DSANNO 266 to perform some operation such as tagging the data string, copying the data string to another portion ofthe data space 14, or enabling a wave file 304, see Fig. 31, which notifies a user that an appropriate data string was found. An appropriate program would be provided as required for a particular application. Of course other data scanning neural network objects could include different viewing field configurations and could develop different data strings to be viewed by appropriate detection networks and DSANNO 266 is merely exemplary ofthe overall configuration. Accordingly, data scanning artificial neural network objects are useful for examining large databases for data strings having some predetermined, desired relationship, and then in some way identifying such data strings. CREATIVITY MACHINES As mentioned previously, the creativity machine paradigm involves progressively purturbing a first neural network, or imagination engine (IE), having a predetermined knowledge domain such that the perturbed network continuously outputs a stream of concepts, and monitoring the outputs or stream of concepts with a second neural network, or alert associative center (AAC), which is trained to identify only useful concepts The perturbations may be achieved by different means, including the introduction of noise to the network, or degradation ofthe network. Such machines can be simulated within a data space in accordance with the present invention and also trained in as part of self training artificial neural network objects in accordance with the present invention In a spreadsheet, the resident rand() function may be utilized to alter the weights ofthe IE in order to achieve perturbation Moreover, relative cell referencing facilitates feeding the outputs ofthe IE to the inputs ofthe AAC. With respect to training, the simultaneous training capability illustrated in Fig 23 is particularly applicable to training ofthe IE and the AAC of creativity machines because both the IE and the AAC will typically have at least some training data in common. At times it may be desirable to change the knowledge domain ofthe IE and or the AAC. For example, if a creativity machine is trained in coffee mug design, the IE is initially trained on known, produced coffee mug shapes and the AAC is trained to recognize a good coffee mug shape from a bad coffee mug shape Over time, the range of known, produced coffee mug shapes may increase, or, the public's perception of what a good coffee mug shape is may change Thus, in order to keep the creativity machine up to date, both the IE and the AAC may need to be trained on new data Utilizing the hereinbefore described training technique, both networks can be trained on new data without having to completely retrain either network on the data it had been trained on previously Further, because the techniques described herein allow multiple neural network to n simultaneously, a creativity machine, including an IE and an AAC could run while replica IE and AAC networks train, with the replica IE and AAC networks being periodically copied and pasted into the IE and AAC networks ofthe creativty machine, thus continuously updatating the training ofthe creativity machine Accordingly, many ofthe inventive features described herein are advantageously applicable to creativity machines. From the preceding detailed description, it is evident that the objects ofthe invention are attained. In particular, a user friendly system of simulating neural net works has been provided. Further, various neural network object configurations have been described which provide self training artificial neural networks, data filtering, or data scanning, and a device prototyping system has also been described. Although these neural network objects and systems have been described and illustrated in detail, it is to be clearly understood that the same is intended by way of illustration and example only and is not to be taken by way of limitation. For example, with reference to Fig. 1, it is understood that the data space cells utilized in simulating the neuron 10 need not be arranged as shown, but could be located in various portions ofthe data space. With respect to self training artificial neural networks, it is understood that there are numerous configurations for achieving the underlying invention which is a network training another network. Further, numerous programs could be associated with the self training artificial neural networks, as well as the data filtering and data scanning neural networks. Moreover, while such programs are described as located in separate but associated spreadsheets or data spaces, the various routines could be included within individual cells ofthe same spreadsheet or data space in which the neural networks are constmcted. Accordingly, the spirit and scope ofthe invention are to be limited only by the terms ofthe appended claims.

Claims: What is claimed is: 1. Means for electronically determining a numeric value representative of an activation level of a neuron within a neural network, utilizing a computer, comprising: processing means for electronically generating a data space including a plurality of identifiable cells, said processing means operable to interrelate said cells through relative cell referencing, means associated with said processing means for maintaining a numeric value associated with each cell, said plurality of identifiable cells including a first plurality of cells having associated predetermined numeric weighting values entered therein, each predetermined numeric weighting value being established during training ofthe neural network, a second plurality of cells having associated numeric values provided thereto, a numeric value associated with each cell of said second plurality representing an input to the neuron, and an activation cell having an associated numeric value which is determinable based upon a predetermined transfer function which references each of said first plurality of cells and each of said second plurality of cells, whereby, for a given set of numeric values representative of a given set of inputs to the neuron, the numeric value associated with said activation cell is representative ofthe activation level ofthe neuron. 2. Means for electronically determining a numeric value representative of an activation level of a neuron within a neural network in accordance with claim 1 wherein said transfer function is a sigmoid function. 3. Means for electronically determining a numeric value representative of an activation level of a neuron within a neural network in accordance with claim 1 wherein at least one of said second plurality of cells is an activation cell of another neuron within the neural network. 4. Means for electronically determining a numeric value representative of an activation level of a neuron within a neural network in accordance with claim 1 wherein said first plurality of cells comprise contiguous cells within said data space, and said second plurality of cells comprise contiguous cells within said data space. 5. Means for electronically determining a numeric value representative of an activation level of a neuron within a neural network in accordance with claim 1, further comprising a display device operable with said processing means for displaying at least a portion of said data space. 6. Means for electronically determining a numeric value representative of an activation level of a neuron within a neural network in accordance with claim 1 wherein said predetermined transfer function indirectly references at least one cell of said first and second plurality of cells. 7. A computer-readable storage medium and information stored thereon for conditioning a computer that has a processing means and is operable to mn a spreadsheet application, to be able to determine an output vector of a neural network including a plurality of hidden layer neurons and a plurality of output layer neurons, by implementing a simulated neural network within a spreadsheet ofthe spreadsheet application, the spreadsheet including a plurality of identifiable cells thereof, the computer-readable storage medium and information stored thereon comprising information to implement within the spreadsheet application a simulation of each hidden layer and each output layer neuron ofthe neural network, including, with respect to each simulated neuron: information to effect implementation of a first plurality of cells having associated numeric values provided thereto, the numeric value associated with each cell ofthe first plurality representing an input to the neuron, information to effect implementation of a second plurality of cells having associated predetermined numeric weighting values entered therein, each predetermined numeric weighting value being established during training ofthe neural network, and information to effect implementation of an activation cell having an associated numeric value determinable based upon a transfer function which references each of said first plurality of cells and each ofsaid second plurality of cells, whereby, for a given set of values representative of a given set of inputs to the neuron, the numeric value associated with the activation cell is representative ofthe activation level ofthe neuron and the numeric value associated with the activation cell of each output layer neuron is further representative of one variable ofthe output vector ofthe neural network. 8. A computer-readable storage medium and information stored thereon in accordance with claim 7, further comprising information to effect implementation of a plurality of imaging cells, each imaging cell having an associated numeric value provided thereto, the numeric value associated with at least one of said imaging cells representing an input to the neural network. 9. A computer-readable storage medium and information stored thereon in accordance with claim 7, further comprising information to automate the operation ofthe simulated neural network, including information to automate movement of the simulated neural network within the spreadsheet. 10. A method of electronically simulating a neural network including a hidden layer and an output layer, each layer including at least one neuron, utilizing a computer including a processing means and an associated spreadsheet application operable therewith, said method comprising the steps of: establishing a plurality of weighting values by training the neural network, providing a plurality of input cells within a spreadsheet, each input cell having an associated numeric value which is representative of an input to the artificial neural network, simulating each hidden layer neuron and each output layer neuron ofthe neural network within the spreadsheet such that each simulated neuron includes a first plurality of cells, each cell ofthe first plurality having an associated numeric value representative of an input to the simulated neuron, a second plurality of cells, each cell ofthe second plurality having an associated numeric value which is one of the established weighting values, and an activation cell, providing a predetermined transfer function to the activation cell of each simulated neuron, the transfer function referencing each ofthe first plurality of cells and each ofthe second plurality of cells associated with the simulated neuron, and activating a calculate function associated with the spreadsheet such that, for a given set of numeric values representative of inputs to the artificial neural network, a numeric value associated with each activation cell is determined, the numeric value associated with the activation cell of each output layer neuron representing an output ofthe artificial neural network. 11 A method of electronically simulating a neural network in accordance with claim 10, further comprising the step of dynamically inputting data to predetermined cells within the spreadsheet. 12. A method of electronically simulating a neural network in accordance with claim 10 wherein said step of activating a calculate function associated with the spreadsheet is performed manually. 13. A method of electronically simulating a neural network in accordance with claim 10 wherein said step of activating a calculate function associated with the spreadsheet is performed by a program associated with the neural network simulation. 14. A computer based neural network training system, comprising: processing means operable to electronically generate a data space including a plurality of cells, means associated with said data space and said processing means for maintaining a numeric value associated with each cell, means associated with said data space and said processing means for interrelating said cells through relative cell referencing, a neural network simulated within said data space and having a plurality of imaging cells including a first plurality of imaging cells for relatively referencing a plurality of training inputs to said simulated neural network and a second plurality of imaging cells for relatively referencing a plurality of corresponding training outputs, a hidden layer including a plurality of neurons, an output layer including a plurality of neurons, each neuron having a plurality of cells including a first plurality of cells each for containing a numeric weight value of said neuron and an activation cell for containing a numeric value which is dependent upon said numeric weight values, and means associated with said simulated neural network for altering said numeric weight values of each neuron, whereby, for a given set of training inputs and corresponding training outputs, said numeric weight values of each neuron are altered to incoφorate into said simulated neural network a knowledge domain represented by said given set. 15. A computer based neural network training system in accordance with claim 14 wherein said means associated with said simulated neural network for altering said numeric weight values of each neuron includes a training network implemented in said data space. 16. A computer based neural network training system in accordance with claim 15 wherein at least a portion of said training network is integrated with said simulated neural network within said data space. 17. A computer based neural network training system in accordance with claim 15 wherein said training network is operable to determine, for each of said hidden layer neurons and each of said output layer neurons, a partial derivative of an activation level thereof with respect to a net input thereto. 18. A computer based neural network training system in accordance with claim 15 wherein said training network is operable to determine an error vector associated with said given set of training inputs and corresponding training outputs. 19. A computer based neural network training system in accordance with claim 15 wherein said means associated with said simulated neural network for altering said numeric weight values of each neuron further includes a program associated with said training network and said simulated neural network, at least a portion of said program operable to effect alteration of said numeric weight values of each neuron of said simulated neural network 20. A computer based neural network training system in accordance with claim 19 wherein at least a portion of said program is operable to effect movement of both said simulated neural network and said training network to a new location within said data space, whereby, for a given movement of said simulated neural network and said training network to a given new location, said numeric weight values of each neuron of said simulated neural network are altered to incoφorate a knowledge domain represented by a given set of training inputs and corresponding training outputs associated with said given new location within said data space. 21. A computer based neural network training system in accordance with claim 14, further comprising means for providing a dynamic data exchange between said data space and an external system so that sets of training inputs and corresponding training outputs are input into predetermined cells within said data space, whereby, as said sets of training inputs and corresponding training outputs flow through said data space, said numeric weight values of each ofsaid neurons of said simulated neural network are altered to incoφorate a knowledge domain represented by at least some ofsaid sets of training inputs and corresponding training outputs. 22. A computer based neural network training system in accordance with claim 14, further comprising a data filtering neural network including an autoassociative neural network implemented in said data space, said autoassociative neural network having been trained on a plurality of control sets of training inputs, whereby, for a given set of training inputs within a knowledge domain represented by said plurality of control sets of training inputs, said autoassociative neural network is operable to map said given set of training inputs to themselves. 23. A computer based neural network training system in accordance with claim 22, further comprising a program associated with said data filtering neural network, said simulated neural network and said training network, at least a portion of said data filtering neural network operable to determine an error between a given set of training inputs and a resulting set of outputs ofsaid autoassociative neural network, at least a portion of said program operable to determine if said error exceeds a predetermined value, and, only if said error exceeds said predetermined value, to alter said numeric weight values of each neuron of said simulated neural network, so that only novel sets of training inputs and corresponding training outputs result in alteration of said numeric weight values of each neuron of said simulated neural network. 24. A computer based neural network training system in accordance with claim 14, further comprising means for dynamically pruning at least one ofsaid hidden layer neurons from said simulated neural network. 25. A computer based neural network training system in accordance with claim 24 wherein said means for dynamically pruning at least one hidden layer neuron from said simulated neural network includes a program associated with said at least one hidden layer neuron, said program effecting determination of whether said at least one hidden layer neuron is significantly involved in training, and, if said at least one hidden layer neuron is not significantly involved in training, to set a transfer function associated with said at least one hidden layer neuron to zero (0) 26. A computer based neural network training system in accordance with claim 14, further comprising means for adding a new hidden layer neuron to said simulated neural network. 27. A computer based neural network training system in accordance with claim 26 wherein said means for adding a new hidden layer neuron to said simulated neural network includes a program associated with said simulated neural network, said program effecting determination of whether an error value associated therewith exceeds a predetermined threshold. 28. A computer based neural network training system in accordance with claim 27 wherein said program further effects, at predetermined intervals, addition of a new hidden layer neuron to said simulated neural network if said error exceeds said predetermined threshold. 29. A self training neural network object implemented utilizing a computer including processing means operable to mn a spreadsheet application, comprising: a neural network simulated in a spreadsheet ofthe spreadsheet application, said simulated neural network including a plurality of neurons each simulated in said spreadsheet, each simulated neuron having a plurality of cells including a first plurality of cells each with an associated numeric weighting value entered therein, a training network implemented in the spreadsheet, a program associated with said training network and said simulated neural network, said training network operable in conjunction with said program to alter said numeric weighting value associated with each cell of said first plurality of cells of each simulated neuron, whereby, for a given set of training inputs and corresponding training outputs applied to said self training neural network object, said numeric weighting value associated with each cell of said plurality of cells of each simulated neuron is alterable to incoφorate into said simulated neural network a knowledge domain represented by said given set of training inputs and corresponding training outputs 30 A self training neural network object in accordance with claim 29 wherein, for said given set of training inputs and corresponding training outputs, said training network is operable to determine a plurality of weight update terms, and said program is operable to effect addition of one of said weight update terms to said numeric weighting value associated with each cell of said first plurality of cells of each simulated neuron 31 A self training neural network object in accordance with claim 29 wherein, for said given set of training inputs and corresponding training outputs, said training network is operable to determine, for each cell of said first plurality of cells of each neuron, a new numeric value, and said program is operable to effect replacement of said numeric weighting value associated with each cell ofsaid first plurality of cells of each simulated neuron with said corresponding new numeric value 32 A self training neural network object in accordance with claim 29, further comprising an autoassociative neural network implemented in said spreadsheet, said autoassociative neural network operable to determine, for a given set of inputs thereto, an error value, said error value representing a difference between said given set of inputs thereto and a resulting set of outputs therefrom, wherein said program is operable to effect determination of whether said error exceeds some predetermined value and, if said error is less than said predetermined value, to prevent alteration of said numeric weighting value associated with each cell of said first plurality of cells of each simulated neuron. 33. A method of training a neural network, utilizing a computer including a processing means and an associated spreadsheet application operable therewith, wherein the neural network is simulated within a spreadsheet ofthe spreadsheet application such that each hidden layer neuron and each output layer neuron ofthe simulated neural network includes a plurality of cells each having a numeric weighting value associated therewith and an activation cell having an associated numeric value which is representative of an activation level ofthe neuron, said method comprising the steps of: (a) applying a set of training data including a plurality of training inputs and a plurality of corresponding training outputs to the simulated neural network, (b) comparing a set of outputs ofthe simulated neural network to the training outputs, and (c) altering the numeric weighting value associated with each cell of each plurality of cells to reflect a knowledge domain represented by the set of training data. 34. A method of training a neural network in accordance with claim 33 wherein step (b) includes determining, within the spreadsheet, a weight update term for the numeric weighting value associated with each cell of each plurality of cells, and step (c) includes adding each weight update term to its corresponding numeric weighting value. 35. A method of training a neural network in accordance with claim 33 wherein step (b) includes determining, within the spreadsheet, a new numeric value for the numeric weighting value associated with each cell of each plurality of cells, and step (c) includes replacing each numeric weighting value with its corresponding new numeric value. 36. A method of training a neural network in accordance with claim 33 wherein step (b) includes determining, within the spreadsheet, for each ofthe activation cells, a derivative of activation level with respect to net input. 37. A method of training a neural network according to claim 33 wherein step (b) includes determining, within the spreadsheet, an error representative of a difference between the set of outputs ofthe simulated neural network and the training outputs. 38. A method of training a neural network in accordance with claim 37, further comprising the step of: (d) repeating steps (a), (b), and (c) until said error falls below a predetermined value. 39. A method of training a neural network in accordance with claim 33 wherein step (a) includes providing relative movement between the simulated neural network and a plurality of sets of training data located within the spreadsheet. 40. A method of simultaneously training at least two neural networks, utilizing a computer including processing means and an associated spreadsheet application operable therewith, said method comprising the steps of: (a) implementing each neural network within a spreadsheet ofthe spreadsheet application, (b) simultaneously applying a set of training data located within the spreadsheet to each ofthe neural networks, and (c) altering at least a portion of each ofthe neural networks in accordance with a predetermined training scheme. 41. A method of simultaneously training at least two neural networks in accordance with claim 40 wherein step (b) includes applying a first set of training data to a first neural network and simultaneously applying a second set of training data to a second neural network, said first set of training data and said second set of training data having at least one variable in common 42. A neural network based prototyping system for prototyping constmction of a device from a plurality of known components, wherein a desired relationship between inputs and outputs ofthe device being prototyped is known, comprising: a computer operable to electronically generate a data space including a plurality of cells which are interrelatable through relative cell referencing, a plurality of component neural networks, each component neural network trained within a knowledge domain of one ofthe known components so as to emulate a relationship between inputs and outputs to the known component, each component neural network implemented in said data space, a prototyping neural network implemented in said data space and including at least one hidden layer having a plurality of neurons, at least one hidden layer neuron represented by one of said component neural networks, and an output layer having at least one neuron, each hidden layer neuron and each output layer neuron having at least one numeric weighting value associated therewith for weighting inputs thereto, and means for adjusting at least some of said numeric weighting values so as to incoφorate into said prototyping neural network a knowledge domain represented by the known desired relationship between inputs and outputs ofthe device being prototyped, so that, after said knowledge domain represented by the known desired relationship between inputs and outputs ofthe device being prototyped has been incoφorated into said prototyping neural network, said numeric weighting values are indicative of how the known components should be interconnected in order to construct the device being prototyped. 43. A neural network based prototyping system in accordance with claim 42 wherein at least one output layer neuron being represented by one of said component neural networks. 44. A neural network based prototyping system in accordance with claim 42 wherein said means for adjusting at least some of said numeric weighting values includes a training network implemented in said data space, said training network operable to determine, for each hidden layer neuron and each output layer neuron, a derivative of an activation level thereof with respect to a net input thereto. 45. A neural network based prototyping system in accordance with claim 44 wherein said training network is further operable to determine a weight update term for each numeric weighting value to be adjusted, and said means for adjusting at least some ofsaid numeric weighting values further includes a program associated with said prototyping neural network and said training network, said program operable to add each weight update term to its corresponding numeric weighting value. 46. A neural network based prototyping system in accordance with claim 44 wherein said training network is further operable to determine a new numeric value for each numeric weighting value to be adjusted, and said means for adjusting at least some of said numeric weighting values further includes a program associated with said prototyping neural network and said training network, said program operable to replace each numeric weighting value which is to be adjusted with its new numeric value. 47. A neural network based prototyping system in accordance with claim 42 wherein said means for adjusting at least some of said numeric weighting values includes a training network implemented in said data space, and means for applying a plurality of sets of training data to said prototyping neural network. 48. A neural network based prototyping system in accordance with claim 47 wherein said plurality of sets of training data are located within said data space and said means for applying a plurality of sets of training data to said prototyping neural network includes a program associated with said prototyping neural network and said training network, said program operable to effect movement said prototyping network within said data space such that with each movement thereof, a set of training data is applied to said prototyping neural network. 49. A method of utilizing neural networks to prototype a configuration of a device which will achieve a predetermined relationship between inputs thereto and outputs therefrom, wherein the device is to be constmcted from a plurality of known components, each component simulated by a component neural network within a spreadsheet of a spreadsheet application, the component neural networks associated within the spreadsheet to form a prototyping neural network including a plurality of neurons, each neuron including at least one input, each input having an associated weight, wherein at least some ofthe neurons ofthe prototyping neural network are represented by one ofthe component neural networks, said method comprising the steps of: (a) assigning a value to the weight associated with each input, (b) performing a training operation, said training operation comprising the steps of: (i) applying a training input to the prototyping neural network, (ii) determining within the spreadsheet, for each weight, a weight update term, (iii) adjusting each weight to reflect the determined weight update term, (iv) determining an error indicative ofthe training status of the prototyping neural network by comparing a desired training output to an actual output ofthe prototyping neural network, (c) repeating steps b(i) through b(iv) until said error falls below a predetermined value, and (d) correlating the weights ofthe prototyping neural network to how the known components should be interconnected to construct the device. 50. A method of utilizing neural networks to prototype a configuration of a device which will achieve a predetermined relationship between inputs thereto and outputs therefrom in accordance with claim 49, the predetermined relationship between inputs thereto and outputs therefrom represented by a plurality of known inputs and associated desired outputs, wherein step (b)(i) includes the prototyping neural network relatively referencing said training input. 51. A method of utilizing neural networks to prototype a configuration of a device which will achieve a predetermined relationship between inputs thereto and outputs therefrom in accordance with claim 49 wherein step (a) includes assigning a random value to the weight associated with each input. 52. A method of utilizing neural networks to prototype a configuration of a device which will achieve a predetermined relationship between inputs thereto and outputs therefrom in accordance with claim 49 wherein steps (b)(i) through (b)(iv) are performed each time a calculate function associated with the spreadsheet is activated. 53. A method of utilizing neural networks to prototype a configuration of a device which will achieve a predetermined relationship between inputs thereto and outputs therefrom in accordance with claim 49 wherein the repetition of steps (b)(i) through (b)(iv) is achieved by a program associated with the prototyping neural network. 54. A method of utilizing neural networks to prototype a configuration of a device which will achieve a predetermined relationship between inputs thereto and outputs therefrom in accordance with claim 49 wherein step (b)(ii) includes determining, for each neuron ofthe plurality of neurons, a derivative of activation level thereof with respect to net input thereto. 55 Means for examining a plurality of data values in order to detect those data values which are uncharacteristic of an overall pattem ofthe plurality of data values, comprising. an autoassociative neural network having a knowledge domain wherein a vector within said knowledge domain which is input to said autoassociative neural network is mapped to itself, resulting in an output vector from said autoassociative neural network which is similar to said input vector, means associated with said autoassociative neural network for determining an error value representative of a difference between said input vector and said output vector ofsaid autoassociative neural network, and means for determining if said error value exceeds a predetermined value, such that, for a given input vector which includes at least two of said data values, said error value exceeding said predetermined value is indicative ofsaid given input vector being uncharacteristic ofthe overall pattem ofthe plurality of data values. 56. Means for examining a plurality of data values in order to detect those data values which are uncharacteristic of an overall pattem ofthe plurality of data values in accordance with claim 55 wherein said autoassociative neural network is implemented within a spreadsheet of a spreadsheet application. 57 Means for examining a plurality of data values in order to detect those data values which are uncharacteristic of an overall pattern ofthe plurality of data values in accordance with claim 56, the plurality of data values being located within said spreadsheet, further comprising means associated with said autoassociative neural network for controlling movement thereof within said spreadsheet, whereby, for a given movement of said autoassociative neural network, a corresponding input vector is applied thereto 58 Means for examining a plurality of data values in order to detect those data values which are uncharacteristic of an overall pattem ofthe plurality of data values in accordance with claim 56, further comprising means for providing a dynamic data exchange between said spreadsheet and an external system such that the plurality of data values flow through predetermined positions within said spreadsheet 59 Means for examining a plurality of data values in order to detect those data values which are uncharacteristic of an overall pattem ofthe plurality of data values in accordance with claim 56, further comprising means associated with said autoassociative neural network for tagging all input vectors which result in said error exceeding said predetermined value 60 Means for examining a plurality of data values in order to detect those data values which are uncharacteristic of an overall pattem ofthe plurality of data values in accordance with claim 56, further comprising means associated with said autoassociative neural network for eliminating all input vectors which result in said error exceeding said predetermined level 61. A method of determining if a particular set of data falls within an overall pattem of a plurality of sets of data, each set of data including n data values, said method comprising the steps of (a) establishing a plurality of control sets of data wherein each control set of data falls within the overall pattem ofthe plurality of sets of data, (b) constructing a neural network having an input layer, an output layer, and at least one hidden layer, wherein said input layer and said output layer each include n nodes, (c) training said neural network on said plurality of control sets of data so that, once trained, in response to input of a given control set of data, said trained neural network outputs a set of data similar thereto, (d) inputting the particular set of data to said trained neural network so that said trained neural network produces an output set of data in response thereto, (e) determining an error value representative of a difference between the particular set of data and said output set of data, (f) comparing said error value with a predetermined value to determine if said applied set of data falls within the overall pattem ofthe plurality of sets of data. 62. A method of determining if a particular set of data falls within an overall pattem of a plurality of sets of data in accordance with claim 61 wherein step (b) includes implementing said neural network in a spreadsheet of a spreadsheet application. 63. A method of determining if a particular set of data falls within an overall pattem of a plurality of sets of data in accordance with claim 62 wherein step (e) includes determining said error value within said spreadsheet. 64. A method of determining if a particular set of data falls within an overall pattem of a plurality of sets of data in accordance with claim 61 wherein step (c) includes establishing a plurality of weight values to be associated with said trained neural network. 65. A method of determining if a particular set of data falls within an overall pattem of a plurality of sets of data in accordance with claim 61 wherein step (f) includes selecting said predetermined value such that said error value exceeding said predetermined value indicates the particular set of data does not fall within the overall pattem ofthe plurality of sets of data 66. Means for examining a database which includes a plurality of sets of data in order to detect a set of data having a predetermined pattem, wherein each set of data includes n data values and the predetermined pattem is indicated by a predetermined relationship between the n data values, comprising: a first neural network trained within a knowledge domain represented by the predetermined pattem, such that input of a given set of data having the predetermined pattem results in a predetermined pattem indicative output from said first neural network, said first neural network implemented in a spreadsheet of a spreadsheet application, said spreadsheet including a plurality of cells, means associated with said first neural network for developing a working image of a portion of said spreadsheet, and means associated with said first neural network for applying at least one set of data from said working image as an input to said first neural network. 67. Means for examining a database which includes a plurality of sets of data in order to detect a set of data having a predetermined pattem, in accordance with claim 66, wherein said means associated with said first neural network for developing a working image of a portion ofsaid spreadsheet includes: a plurality of imaging cells each having an associated relative reference to said portion of said spreadsheet. 68. Means for examining a database which includes a plurality of sets of data in order to detect a set of data having a predetermined pattem, in accordance with claim 67, wherein said means associated with said first neural network for developing a working image of a portion of said spreadsheet further includes: a second neural network which is trained as an autoassociative neural network with a knowledge domain of spreadsheet cell designations, an output of said second neural network being applied as a feedback input to said second neural network, and means associated with said second neural network for modifying the knowledge domain thereof by altering at least some of a plurality of weight values associated therewith, whereby, a series of spreadsheet cell designations are output from said second neural network, each spreadsheet cell designation indicative of a portion of said spreadsheet. 69. Means for examining a database which includes a plurality of sets of data in order to detect a set of data having a predetermined pattem, in accordance with claim 68, further comprising: means for modifying said relative reference associated with each of said imaging cells each time a spreadsheet cell designation is output from said second neural network. 70. Means for examining a database which includes a plurality of sets of data in order to detect a set of data having a predetermined pattem, in accordance with claim 67, wherein said means associated with said first neural network for applying at least one set of data from said working image as an input to said first neural network includes: a searching neural network which is trained as an autoassociative neural network having a knowledge domain of multiple spreadsheet cell designations corresponding to said imaging cells, an output of said searching neural network being applied as an input to said first neural network, and means associated with said searching neural network for modifying the knowledge domain thereof by adjusting at least some of a plurality of weight values associated therewith, whereby, said searching neural network selects a set of n imaging cells, and a numeric value associated with each of said n imaging cells is input to said first neural network. 71. Means for examining a database which includes a plurality of sets of data in order to detect a set of data having a predetermined pattem, in accordance with claim 67, further comprising: means for eliminating a given set of data from said spreadsheet if said given set of data fits the predetermined pattem. 72. Means for examining a database which includes a plurality of sets of data in order to detect a set of data having a predetermined pattem, in accordance with claim 67, further comprising: means for copying a given set of data to a predetermined location if said given set of data fits the predetermined pattem. 73 A database scanning pattem recognition device capable of scanning a database for any set of n data values having a predetermined pattern, comprising a first neural network including a knowledge domain defined by the predetermined pattem, said first neural network including n inputs and at least one output, said first neural network operable to output a predetermined output in response to a given set of n inputs if said given set of n inputs falls within said knowledge domain thereof, means for applying a series of sets of n data values from said database to said first neural network as inputs thereto 74 A database scanning pattem recognition device in accordance with claim 73 wherein said means for applying a series of sets of n data values from said database to said first neural network as inputs thereto includes a second neural network for selecting a portion ofsaid database to be scanned, said second neural network comprising an autoassociative neural network including a knowledge domain of various positions within said database, means associated with said second neural network for obtaining a series of outputs therefrom, each output representative of a database position, and means for selecting a set of n data values from each of said database positions to be applied as inputs to said first neural network 75. A method of electronically simulating a neural network, utilizing a computer and a spreadsheet application operable therewith, comprising (a) electronically generating a spreadsheet including a plurality of identifiable cells, (b) determining a desired stmcture ofthe neural network, including a number of neurons thereof, (c) simulating each neuron activation level within a cell ofthe spreadsheet, (d) interrerlating each cell of step (c) so as to construct the neural network, and (e) activating a calculate function associated with the spreadsheet so as to produce an output from the simulated neural network

Inventors: THALER STEPHEN L, THALER, STEPHEN, L.
Applicants: THALER STEPHEN L, THALER, STEPHEN, L.
Application year: 1997
Main classification: G06F
IPC codes: G06F15, G06N3