Evolution in Neural Networks-Computer Sciences Applications-Project Report, Study Guides, Projects, Research of Applications of Computer Sciences

Download Evolution in Neural Networks-Computer Sciences Applications-Project Report and more Study Guides, Projects, Research Applications of Computer Sciences in PDF only on Docsity! 1 1. Evolution in Neural Networks: Evolutionary Neural Networks (ENNs) refer to a special class of Artificial Neural Networks (ANNs). ENNs can be considered as the combination of ANNs and evolutionary computation techniques. Training artificial neural networks for a particular task using evolutionary computation is a hot topic of research for several past years, and this training is done by using genetic algorithms discussed above. Evolution is introduced at three different levels in ANNs. These three levels are Connection Weights, Architecture, and Learning Rule. These levels are described below. 1.1. The Evolution of Connection Weights: Global search procedures like GAs can be used effectively in the evolution to find a near optimal set of connection weights for the ENN. The fitness of an ENN can be defined according to different needs. The fitness function does not have to be differentiable or even continuous since GAs do not depend on gradient information in search. Two important factors, which often appear in the fitness function, are the error between target outputs and actual outputs and the complexity of the ENN, Because GAs are good at dealing with large complex non-differentiable and multimodal spaces which are the typical space defined by an error function or fitness function. The evolution of connection weights provides an alternative approach to training ENNs. Following is a typical cycle of the evolution of connection weights [1, 2]:  Decode each individual in the current generation into a set of connection weights and construct a corresponding ENN with these weights (with architecture and learning rule fixed.)  Calculate the total mean square error between actual output and target output for each ENN by feeding training patterns to it, and define a fitness function.  Reproduce a number of children in the current generation with according to its fitness using some appropriate evolutionary algorithm.  Apply generic operators such as crossover, mutation and / or inversion to the child individual produced above, and get a new generation. docsity.com 2  Stop the evolution when the desired results are obtained. In ANNs, the evolution of connection weights consists of two major phases. The first phase decides the representation of connection weights i.e. whether in the form of binary strings or not. In the second phase, the evolutionary process is simulated by an evolutionary algorithm, in which search operators such as crossover, mutation and / or inversion are used. Different representations and different evolutionary algorithms can lead to quite different training performance [1, 2]. 1.1.1. Binary Representation: It is found that the binary representation is very beneficial in GAs search [3, 4]. So one way to represent connection weights is to encode them in some binary strings[5]. In binary representation scheme, each connection weight is represented by a number of binary bits having certain length. Here the bit length is of utmost importance. The bit length must be selected with care. If each connection weight is represented by too few bits, it may cause the training to fail because some combinations of real connection weight are unable or very hard to be approximated by discrete values. On the other hand, if we are using too many bit to represent each connection weight, the chromosome representing a very large neural network will become extremely long and that will make the evolution very inefficient [1, 2]. Figure 1 shows a binary representation of weights. Each connection weight is represented by four bits, and the whole network is represented by 24 bits. Figure 2 represents another neural network having the same representation. Figure 1: Binary Representation of Weights [2] docsity.com 5 1. The surface is infinitely large as the number of possible nodes and connections is unbounded. 2. The surface is non-differentiable since changes in the number of nodes or connections are discrete and can have a discontinuous effect on ENN’s performance. 3. The surface is complex and noisy since the mapping from an architecture to its performance is indirect and dependent on the evaluation method used. 4. The surface is deceptive since similar architectures may have quite different performance. 5. The surface is multimodal since different architectures may have similar performance. The typical evolution of architecture is described by the cycle given below [1, 2]:  Decode each individual in the current generation into an architecture.  Train each ENN by a predefined learning rule. Start form random initial connection weights and learning rule parameters.  Compute the fitness of each encoded architecture.  Select parents from the population based on their fitness.  Apply search operations to the parents and generate offspring to produce the next generation. One of the key issues in encoding ENN architectures is to decide how much information about an architecture should be encoded in the chromosome. The following two types of encoding schemes are used to represent the information about the architecture of an ENN [1, 2]. 1.2.1. Direct Encoding Scheme: Direct encoding scheme encodes all the details i.e. every connection and node of an architecture can be specified by the chromosome. In direct encoding scheme, two different approaches are used. In the first approach, the evolution of architecture is separated form the evolution of architecture [5, 8]. Here each connection of an architecture is directly specified by its docsity.com 6 binary representation. The second approach evolves the architecture and connection weights simultaneously [9]. Figure 3: Direct Encoding [2] An example of direct encoding is shown in Figure 3 [2]. Here a feedforward neural network is shown having two inputs and one output. The connectivity matrix is also shown. the first row indicates connections from node 1 to all other nodes. The first two columns are 0’s because there is no connection from node 1 to itself and no connection to node 2. However, node 1 is connected to nodes 3 and 4. Hence columns 3 and 4 have 1’s. Now by concatenating all the rows we can obtain the chromosome and that is in this case 00110 00101 00001 00001 00000. As this is a feedforward network, we only need the upper right triangle of the connectivity matrix. So the chromosome length can then be reduced to 0110 101 01 1. The direct encoding scheme is quite simple to implement. It is very suitable for the precise and fine-tuned search of a compact ANN architecture, since a single connection can be added or removed from the ANN easily. It may facilitate rapid generation and optimization of tightly pruned interesting designs that no one has hit upon so far [1, 2, 8]. One of the problems of the direct encoding scheme is scalability. A large ANN would require a very large connectivity matrix and thus it would increase the computation time of the evolution. The permutation problem still exists and it can cause unwanted side effects in the evolution of architectures [2]. 1.2.2. Indirect Encoding Scheme: Indirect encoding scheme encodes only the most important parameters of an architecture e.g. the number of hidden layers and hidden nodes in each layer. Other details about the architecture are left to the training process to decide [1]. docsity.com 7 This scheme can produce more compact genotypical representation of an ANN architectures, but it may not be very good at finding a compact ANN having good generalization ability. Some researchers have argued that the indirect encoding scheme is biologically more reasonable than the direct encoding scheme because it is impossible for genetic information encoded in chromosomes to specify independently the whole nervous system according to the discoveries of neuroscience [10]. Some of the types of the indirect encoding scheme are given below. 1.2.2.1. Parametric Representation: One way to represent the ANN architectures is to use a set of parameters such as the number of hidden layers, the number of hidden nodes in each layer, the number of connections between two layers, etc. These parameters can then be encoded in various forms in a chromosome [2]. Though the parametric representation can reduces the length of binary chromosome specifying ANN’s architecture, but EAs can only search a limited subset of the whole feasible architecture space e.g. if we encode only the number of hidden nodes, we basically assume strictly a layered feedforward network with a single hidden layer, and we also will have to assume that the two neighboring layers are fully connected. Simply we can say that the parametric representation will be the most suitable only if we know the kind of architectures we are trying to find [2]. 1.2.2.2. Developmental Rule Representation: A quite different indirect encoding method is to encode developmental rules, which are used to construct architectures, in chromosomes [2, 10]. The developmental rule representation has brought some benefits such as it provides more compact genotypical representation, and the destructive effect of crossover is also be lessened as the developmental rule representation is capable of preserving promising building blocks [2]. Developmental rule representation has certain limitations as described below [2]: 1. It doesn’t allow recursive rules. 2. It doesn’t give good results in evolving detailed connectivity patterns among individual nodes. docsity.com 10 References: [1]. Xin Yao, “Evolutionary Artificial Neural Networks”, International Journal of Neural Systems, 1993. [2]. Xin Yao, “Evolving Artificial Neural Networks”, IEEE, New York, USA, 1999 [3]. J. H. Holland. Adaptation in Natural and Artificial Systems, The MIT Press, Cambridge, MA, 1992. [4]. David E. Goldberg, Genetic Algorithms in Search, Optimization & Machine Learning, Dorling Kindersley, Delhi, India, 2006. [5]. D. Whitley, T. Starkweather and C. Bogart, Genetic Algorithms and Neural Networks: Optimizing Connections and Connectivity, Parallel Computing, 14: 347- 361, 1990. [6]. F. Menczer and D. Parisi, “Evidence of Hyperplanes in the Genetic Learning of Neural Networks,” Biological Cybern., vol. 66, pp. 283–289, 1992. [7]. D. B. Fogel, L. J. Fogel, and V. W. Porto, “Evolving Neural Networks,” Biological Cybern., vol. 63, no. 6, pp. 487–493, 1990. [8]. G. F. Miller, P. M. Todd, and S. U. Hegde, “Designing neural networks using genetic algorithms,” in Proc. 3rd Int. Conf. Genetic Algorithms and Their Applications, J. D. Schaffer, Ed. San Mateo, CA: Morgan Kaufmann, 1989, pp. 379–384. [9]. P. J. Angeline, G. M. Sauders, and J. B. Pollack, “An Evolutionary Algorithm that Constructs Recurrent Neural Networks,” IEEE Trans. Neural Networks, vol. 5, pp. 54–65, Jan. 1994. [10]. H. Kitano, “Designing Neural Networks using Genetic Algorithms with Graph Generation System,” Complex Syst., vol. 4, no. 4, pp. 461–476, 1990. [11]. J. W. L. Merrill and R. F. Port, “Fractally Configured Neural Networks,” Neural Networks, vol. 4, pp. 53–60, 1991. [12]. Ajith Abraham, Nature and Scope of AI Techniques, Handbook for Measurement Systems Design, Peter Sydenham and Richard Thorn (Eds.), John Wiley and Sons Ltd., London, pp. 893-900, 2005. docsity.com 11 [13]. Ajith Abraham, Evolutionary Computation, Handbook for Measurement Systems Design, Peter Sydenham and Richard Thorn (Eds.), John Wiley and Sons Ltd., London, pp. 920-931, 2005. [14]. Introduction to Genetic Algorithms URL: http://www.rennard.org/alife/english/gavintrgb.html [15]. “Evolutionary Algorithms: Genetic Algorithms, Evolutionary Programming and Genetic Programming” URL: http://www.cs.sandia.gov/opt/survey/ea.html docsity.com