In this work, we study how the selection of examples affects the learning procedure in a boolean neural network and its relationship with the complexity of the function under study and its architecture. We analyze the generalization capacity for different target functions with particular architectures through an analytical calculation of the minimum number of examples needed to obtain full generalization (i.e., zero generalization error). The analysis of the training sets associated with such parameter leads us to propose a general architecture-independent criterion for selection of training examples. The criterion was checked through numerical simulations for various particular target functions with particular architectures, as well as for random target functions in a nonoverlapping receptive field perceptron. In all cases, the selection sampling criterion lead to an improvement in the generalization capacity compared with a pure random sampling. We also show that for the parity problem, one of the most used problems for testing learning algorithms, only the use of the whole set of examples ensures global learning in a depth two architecture. We show that this difficulty can be overcome by considering a tree-structured network of depth 2 log(2) (N) - 1.
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Imperial Coll London, Blackett Lab, London SW7 2AZ, England
London Inst Math Sci, 35a South St Mayfair, London W1K 2XF, EnglandImperial Coll London, Blackett Lab, London SW7 2AZ, England
Wan, Kwok Ho
Dahlsten, Oscar
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Imperial Coll London, Blackett Lab, London SW7 2AZ, England
London Inst Math Sci, 35a South St Mayfair, London W1K 2XF, England
Univ Oxford, Clarendon Lab, Parks Rd, Oxford OX1 3PU, England
South China Univ Sci & Technol SUSTech, Shenzhen, Peoples R ChinaImperial Coll London, Blackett Lab, London SW7 2AZ, England
Dahlsten, Oscar
Kristjansson, Hler
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Imperial Coll London, Blackett Lab, London SW7 2AZ, England
London Inst Math Sci, 35a South St Mayfair, London W1K 2XF, EnglandImperial Coll London, Blackett Lab, London SW7 2AZ, England
Kristjansson, Hler
Gardner, Robert
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Imperial Coll London, Blackett Lab, London SW7 2AZ, England
London Inst Math Sci, 35a South St Mayfair, London W1K 2XF, EnglandImperial Coll London, Blackett Lab, London SW7 2AZ, England
Gardner, Robert
Kim, M. S.
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Imperial Coll London, Blackett Lab, London SW7 2AZ, EnglandImperial Coll London, Blackett Lab, London SW7 2AZ, England