134 research outputs found

    Traveling Salesman Problem

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    This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering

    Dynamics analysis and applications of neural networks

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    Ph.DDOCTOR OF PHILOSOPH

    Exploratory Combinatorial Optimization with Reinforcement Learning

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    Many real-world problems can be reduced to combinatorial optimization on a graph, where the subset or ordering of vertices that maximize some objective function must be found. With such tasks often NP-hard and analytically intractable, reinforcement learning (RL) has shown promise as a framework with which efficient heuristic methods to tackle these problems can be learned. Previous works construct the solution subset incrementally, adding one element at a time, however, the irreversible nature of this approach prevents the agent from revising its earlier decisions, which may be necessary given the complexity of the optimization task. We instead propose that the agent should seek to continuously improve the solution by learning to explore at test time. Our approach of exploratory combinatorial optimization (ECO-DQN) is, in principle, applicable to any combinatorial problem that can be defined on a graph. Experimentally, we show our method to produce state-of-the-art RL performance on the Maximum Cut problem. Moreover, because ECO-DQN can start from any arbitrary configuration, it can be combined with other search methods to further improve performance, which we demonstrate using a simple random search.Comment: In Proceedings of the 34th National Conference on Artificial Intelligence, AAAI 202

    Recurrent neural network for optimization with application to computer vision.

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    by Cheung Kwok-wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 1993.Includes bibliographical references (leaves [146-154]).Chapter Chapter 1 --- IntroductionChapter 1.1 --- Programmed computing vs. neurocomputing --- p.1-1Chapter 1.2 --- Development of neural networks - feedforward and feedback models --- p.1-2Chapter 1.3 --- State of art of applying recurrent neural network towards computer vision problem --- p.1-3Chapter 1.4 --- Objective of the Research --- p.1-6Chapter 1.5 --- Plan of the thesis --- p.1-7Chapter Chapter 2 --- BackgroundChapter 2.1 --- Short history on development of Hopfield-like neural network --- p.2-1Chapter 2.2 --- Hopfield network model --- p.2-3Chapter 2.2.1 --- Neuron's transfer function --- p.2-3Chapter 2.2.2 --- Updating sequence --- p.2-6Chapter 2.3 --- Hopfield energy function and network convergence properties --- p.2-1Chapter 2.4 --- Generalized Hopfield network --- p.2-13Chapter 2.4.1 --- Network order and generalized Hopfield network --- p.2-13Chapter 2.4.2 --- Associated energy function and network convergence property --- p.2-13Chapter 2.4.3 --- Hardware implementation consideration --- p.2-15Chapter Chapter 3 --- Recurrent neural network for optimizationChapter 3.1 --- Mapping to Neural Network formulation --- p.3-1Chapter 3.2 --- Network stability verse Self-reinforcement --- p.3-5Chapter 3.2.1 --- Quadratic problem and Hopfield network --- p.3-6Chapter 3.2.2 --- Higher-order case and reshaping strategy --- p.3-8Chapter 3.2.3 --- Numerical Example --- p.3-10Chapter 3.3 --- Local minimum limitation and existing solutions in the literature --- p.3-12Chapter 3.3.1 --- Simulated Annealing --- p.3-13Chapter 3.3.2 --- Mean Field Annealing --- p.3-15Chapter 3.3.3 --- Adaptively changing neural network --- p.3-16Chapter 3.3.4 --- Correcting Current Method --- p.3-16Chapter 3.4 --- Conclusions --- p.3-17Chapter Chapter 4 --- A Novel Neural Network for Global Optimization - Tunneling NetworkChapter 4.1 --- Tunneling Algorithm --- p.4-1Chapter 4.1.1 --- Description of Tunneling Algorithm --- p.4-1Chapter 4.1.2 --- Tunneling Phase --- p.4-2Chapter 4.2 --- A Neural Network with tunneling capability Tunneling network --- p.4-8Chapter 4.2.1 --- Network Specifications --- p.4-8Chapter 4.2.2 --- Tunneling function for Hopfield network and the corresponding updating rule --- p.4-9Chapter 4.3 --- Tunneling network stability and global convergence property --- p.4-12Chapter 4.3.1 --- Tunneling network stability --- p.4-12Chapter 4.3.2 --- Global convergence property --- p.4-15Chapter 4.3.2.1 --- Markov chain model for Hopfield network --- p.4-15Chapter 4.3.2.2 --- Classification of the Hopfield markov chain --- p.4-16Chapter 4.3.2.3 --- Markov chain model for tunneling network and its convergence towards global minimum --- p.4-18Chapter 4.3.3 --- Variation of pole strength and its effect --- p.4-20Chapter 4.3.3.1 --- Energy Profile analysis --- p.4-21Chapter 4.3.3.2 --- Size of attractive basin and pole strength required --- p.4-24Chapter 4.3.3.3 --- A new type of pole eases the implementation problem --- p.4-30Chapter 4.4 --- Simulation Results and Performance comparison --- p.4-31Chapter 4.4.1 --- Simulation Experiments --- p.4-32Chapter 4.4.2 --- Simulation Results and Discussions --- p.4-37Chapter 4.4.2.1 --- Comparisons on optimal path obtained and the convergence rate --- p.4-37Chapter 4.4.2.2 --- On decomposition of Tunneling network --- p.4-38Chapter 4.5 --- Suggested hardware implementation of Tunneling network --- p.4-48Chapter 4.5.1 --- Tunneling network hardware implementation --- p.4-48Chapter 4.5.2 --- Alternative implementation theory --- p.4-52Chapter 4.6 --- Conclusions --- p.4-54Chapter Chapter 5 --- Recurrent Neural Network for Gaussian FilteringChapter 5.1 --- Introduction --- p.5-1Chapter 5.1.1 --- Silicon Retina --- p.5-3Chapter 5.1.2 --- An Active Resistor Network for Gaussian Filtering of Image --- p.5-5Chapter 5.1.3 --- Motivations of using recurrent neural network --- p.5-7Chapter 5.1.4 --- Difference between the active resistor network model and recurrent neural network model for gaussian filtering --- p.5-8Chapter 5.2 --- From Problem formulation to Neural Network formulation --- p.5-9Chapter 5.2.1 --- One Dimensional Case --- p.5-9Chapter 5.2.2 --- Two Dimensional Case --- p.5-13Chapter 5.3 --- Simulation Results and Discussions --- p.5-14Chapter 5.3.1 --- Spatial impulse response of the 1-D network --- p.5-14Chapter 5.3.2 --- Filtering property of the 1-D network --- p.5-14Chapter 5.3.3 --- Spatial impulse response of the 2-D network and some filtering results --- p.5-15Chapter 5.4 --- Conclusions --- p.5-16Chapter Chapter 6 --- Recurrent Neural Network for Boundary DetectionChapter 6.1 --- Introduction --- p.6-1Chapter 6.2 --- From Problem formulation to Neural Network formulation --- p.6-3Chapter 6.2.1 --- Problem Formulation --- p.6-3Chapter 6.2.2 --- Recurrent Neural Network Model used --- p.6-4Chapter 6.2.3 --- Neural Network formulation --- p.6-5Chapter 6.3 --- Simulation Results and Discussions --- p.6-7Chapter 6.3.1 --- Feasibility study and Performance comparison --- p.6-7Chapter 6.3.2 --- Smoothing and Boundary Detection --- p.6-9Chapter 6.3.3 --- Convergence improvement by network decomposition --- p.6-10Chapter 6.3.4 --- Hardware implementation consideration --- p.6-10Chapter 6.4 --- Conclusions --- p.6-11Chapter Chapter 7 --- Conclusions and Future ResearchesChapter 7.1 --- Contributions and Conclusions --- p.7-1Chapter 7.2 --- Limitations and Suggested Future Researches --- p.7-3References --- p.R-lAppendix I The assignment of the boundary connection of 2-D recurrent neural network for gaussian filtering --- p.Al-1Appendix II Formula for connection weight assignment of 2-D recurrent neural network for gaussian filtering and the proof on symmetric property --- p.A2-1Appendix III Details on reshaping strategy --- p.A3-

    The hardware implementation of an artificial neural network using stochastic pulse rate encoding principles

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    In this thesis the development of a hardware artificial neuron device and artificial neural network using stochastic pulse rate encoding principles is considered. After a review of neural network architectures and algorithmic approaches suitable for hardware implementation, a critical review of hardware techniques which have been considered in analogue and digital systems is presented. New results are presented demonstrating the potential of two learning schemes which adapt by the use of a single reinforcement signal. The techniques for computation using stochastic pulse rate encoding are presented and extended with new novel circuits relevant to the hardware implementation of an artificial neural network. The generation of random numbers is the key to the encoding of data into the stochastic pulse rate domain. The formation of random numbers and multiple random bit sequences from a single PRBS generator have been investigated. Two techniques, Simulated Annealing and Genetic Algorithms, have been applied successfully to the problem of optimising the configuration of a PRBS random number generator for the formation of multiple random bit sequences and hence random numbers. A complete hardware design for an artificial neuron using stochastic pulse rate encoded signals has been described, designed, simulated, fabricated and tested before configuration of the device into a network to perform simple test problems. The implementation has shown that the processing elements of the artificial neuron are small and simple, but that there can be a significant overhead for the encoding of information into the stochastic pulse rate domain. The stochastic artificial neuron has the capability of on-line weight adaption. The implementation of reinforcement schemes using the stochastic neuron as a basic element are discussed

    A new approach to Decimation in High Order Boltzmann Machines

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    La Màquina de Boltzmann (MB) és una xarxa neuronal estocàstica amb l'habilitat tant d'aprendre com d'extrapolar distribucions de probabilitat. Malgrat això, mai ha arribat a ser tant emprada com d'altres models de xarxa neuronal, com ara el perceptró, degut a la complexitat tan del procés de simulació com d'aprenentatge: les quantitats que es necessiten al llarg del procés d'aprenentatge són normalment estimades mitjançant tècniques Monte Carlo (MC), a través de l'algorisme del Temprat Simulat (SA). Això ha portat a una situació on la MB és més ben aviat considerada o bé com una extensió de la xarxa de Hopfield o bé com una implementació paral·lela del SA. Malgrat aquesta relativa manca d'èxit, la comunitat científica de l'àmbit de les xarxes neuronals ha mantingut un cert interès amb el model. Una de les extensions més rellevants a la MB és la Màquina de Boltzmann d'Alt Ordre (HOBM), on els pesos poden connectar més de dues neurones simultàniament. Encara que les capacitats d'aprenentatge d'aquest model han estat analitzades per d'altres autors, no s'ha pogut establir una equivalència formal entre els pesos d'una MB i els pesos d'alt ordre de la HOBM. En aquest treball s'analitza l'equivalència entre una MB i una HOBM a través de l'extensió del mètode conegut com a decimació. Decimació és una eina emprada a física estadística que es pot també aplicar a cert tipus de MB, obtenint expressions analítiques per a calcular les correlacions necessàries per a dur a terme el procés d'aprenentatge. Per tant, la decimació evita l'ús del costós algorisme del SA. Malgrat això, en la seva forma original, la decimació podia tan sols ser aplicada a cert tipus de topologies molt poc densament connectades. La extensió que es defineix en aquest treball permet calcular aquests valors independentment de la topologia de la xarxa neuronal; aquest model es basa en afegir prou pesos d'alt ordre a una MB estàndard com per a assegurar que les equacions de la decimació es poden solucionar. Després, s'estableix una equivalència directa entre els pesos d'un model d'alt ordre, la distribució de probabilitat que pot aprendre i les matrius de Hadamard: les propietats d'aquestes matrius es poden emprar per a calcular fàcilment els pesos del sistema. Finalment, es defineix una MB estàndard amb una topologia específica que permet entendre millor la equivalència exacta entre unitats ocultes de la MB i els pesos d'alt ordre de la HOBM.La Máquina de Boltzmann (MB) es una red neuronal estocástica con la habilidad de aprender y extrapolar distribuciones de probabilidad. Sin embargo, nunca ha llegado a ser tan popular como otros modelos de redes neuronals como, por ejemplo, el perceptrón. Esto es debido a la complejidad tanto del proceso de simulación como de aprendizaje: las cantidades que se necesitan a lo largo del proceso de aprendizaje se estiman mediante el uso de técnicas Monte Carlo (MC), a través del algoritmo del Temple Simulado (SA). En definitiva, la MB es generalmente considerada o bien una extensión de la red de Hopfield o bien como una implementación paralela del algoritmo del SA. Pese a esta relativa falta de éxito, la comunidad científica del ámbito de las redes neuronales ha mantenido un cierto interés en el modelo. Una importante extensión es la Màquina de Boltzmann de Alto Orden (HOBM), en la que los pesos pueden conectar más de dos neuronas a la vez. Pese a que este modelo ha sido analizado en profundidad por otros autores, todavía no se ha descrito una equivalencia formal entre los pesos de una MB i las conexiones de alto orden de una HOBM. En este trabajo se ha analizado la equivalencia entre una MB i una HOBM, a través de la extensión del método conocido como decimación. La decimación es una herramienta propia de la física estadística que también puede ser aplicada a ciertos modelos de MB, obteniendo expresiones analíticas para el cálculo de las cantidades necesarias en el algoritmo de aprendizaje. Por lo tanto, la decimación evita el alto coste computacional asociado al al uso del costoso algoritmo del SA. Pese a esto, en su forma original la decimación tan solo podía ser aplicada a ciertas topologías de MB, distinguidas por ser poco densamente conectadas. La extensión definida en este trabajo permite calcular estos valores independientemente de la topología de la red neuronal: este modelo se basa en añadir suficientes pesos de alto orden a una MB estándar como para asegurar que las ecuaciones de decimación pueden solucionarse. Más adelante, se establece una equivalencia directa entre los pesos de un modelo de alto orden, la distribución de probabilidad que puede aprender y las matrices tipo Hadamard. Las propiedades de este tipo de matrices se pueden usar para calcular fácilmente los pesos del sistema. Finalmente, se define una BM estándar con una topología específica que permite entender mejor la equivalencia exacta entre neuronas ocultas en la MB y los pesos de alto orden de la HOBM.The Boltzmann Machine (BM) is a stochastic neural network with the ability of both learning and extrapolating probability distributions. However, it has never been as widely used as other neural networks such as the perceptron, due to the complexity of both the learning and recalling algorithms, and to the high computational cost required in the learning process: the quantities that are needed at the learning stage are usually estimated by Monte Carlo (MC) through the Simulated Annealing (SA) algorithm. This has led to a situation where the BM is rather considered as an evolution of the Hopfield Neural Network or as a parallel implementation of the Simulated Annealing algorithm. Despite this relative lack of success, the neural network community has continued to progress in the analysis of the dynamics of the model. One remarkable extension is the High Order Boltzmann Machine (HOBM), where weights can connect more than two neurons at a time. Although the learning capabilities of this model have already been discussed by other authors, a formal equivalence between the weights in a standard BM and the high order weights in a HOBM has not yet been established. We analyze this latter equivalence between a second order BM and a HOBM by proposing an extension of the method known as decimation. Decimation is a common tool in statistical physics that may be applied to some kind of BMs, that can be used to obtain analytical expressions for the n-unit correlation elements required in the learning process. In this way, decimation avoids using the time consuming Simulated Annealing algorithm. However, as it was first conceived, it could only deal with sparsely connected neural networks. The extension that we define in this thesis allows computing the same quantities irrespective of the topology of the network. This method is based on adding enough high order weights to a standard BM to guarantee that the system can be solved. Next, we establish a direct equivalence between the weights of a HOBM model, the probability distribution to be learnt and Hadamard matrices. The properties of these matrices can be used to easily calculate the value of the weights of the system. Finally, we define a standard BM with a very specific topology that helps us better understand the exact equivalence between hidden units in a BM and high order weights in a HOBM

    Reinforcing connectionism: learning the statistical way

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    Connectionism's main contribution to cognitive science will prove to be the renewed impetus it has imparted to learning. Learning can be integrated into the existing theoretical foundations of the subject, and the combination, statistical computational theories, provide a framework within which many connectionist mathematical mechanisms naturally fit. Examples from supervised and reinforcement learning demonstrate this. Statistical computational theories already exist for certainn associative matrix memories. This work is extended, allowing real valued synapses and arbitrarily biased inputs. It shows that a covariance learning rule optimises the signal/noise ratio, a measure of the potential quality of the memory, and quantifies the performance penalty incurred by other rules. In particular two that have been suggested as occuring naturally are shown to be asymptotically optimal in the limit of sparse coding. The mathematical model is justified in comparison with other treatments whose results differ. Reinforcement comparison is a way of hastening the learning of reinforcement learning systems in statistical environments. Previous theoretical analysis has not distinguished between different comparison terms, even though empirically, a covariance rule has been shown to be better than just a constant one. The workings of reinforcement comparison are investigated by a second order analysis of the expected statistical performance of learning, and an alternative rule is proposed and empirically justified. The existing proof that temporal difference prediction learning converges in the mean is extended from a special case involving adjacent time steps to the general case involving arbitary ones. The interaction between the statistical mechanism of temporal difference and the linear representation is particularly stark. The performance of the method given a linearly dependent representation is also analysed
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