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Heuristic tools from statistical physics have been used in the past to locate the phase transitions and compute the optimal learning and generalization errors in the teacher-student scenario in multi-layer neural networks.
Solution of’solvable model of a spin glass’
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Generalization in a large committee machine
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The statistical mechanics of learning a rule
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Learning a rule in a multilayer neural network
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Generalization in fully connected committee machines
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Weight space structure and internal representations: a direct approach to learning and generalization in multilayer neural networks
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On-line learning in soft committee machines
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Broken replica symmetry bounds in the mean field spin glass model
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Spin glasses: a challenge for mathematicians: cavity and mean field models
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Efficient supervised learning in networks with binary synapses
C. Baldassi, A. Braunstein, N. Brunel, and R. Zecchina · 2007
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Inference from correlated patterns: a unified theory for perceptron learning and linear vector channels
Y. Kabashima · 2008
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Graphical models, exponential families, and variational inference
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Information, physics, and computation
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Message-passing algorithms for compressed sensing
D. L. Donoho, A. Maleki, and A. Montanari · 2009
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Understanding deep learning requires rethinking generalization
C. Zhang, S. Bengio, M. Hardt, B. Recht, and O. Vinyals · 2017
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Entropy-sgd: Biasing gradient descent into wide valleys
P. Chaudhari, A. Choromanska, S. Soatto, Y. LeCun, C. Baldassi, C. Borgs, J. Chayes, L. Sagun, and R. Zecchina · 2017
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Decoding from pooled data: Phase transitions of message passing
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Performance limits for noisy multimeasurement vector problems
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AMP implementation of the committee machine
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