1,721,009 research outputs found
Weight Space Structure and Internal Representations: aDirect Approach to Learning and Generalization in Multilayer Neural Network
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Analytical and Numerical Study of Internal Representationsin Multilayer Neural Networks with Binary Weights
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Statistical mechanics methods and phase transitions inoptimization problems
No full textAbstractRecently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer science and statistical physics. This review aims at presenting the tools and concepts designed by physicists to deal with optimization or decision problems in a language accessible for computer scientists and mathematicians, with no prerequisites in physics. We first introduce some elementary methods of statistical mechanics and then progressively cover the tools appropriate for disordered systems. In each case, we apply these methods to study the phase transitions or the statistical properties of the optimal solutions in various combinatorial problems. We cover in detail the Random Graph, the Satisfiability, and the Traveling Salesman problems. References to the physics literature on optimization are provided. We also give our perspective regarding the interdisciplinary contribution of physics to computer science
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