swMATH ID: 38983
Software Authors: Aubin, Benjamin; Maillard, Antoine; Barbier, Jean; Krzakala, Florent; Macris, Nicolas; Zdeborová, Lenka
Description: The committee machine: computational to statistical gaps in learning a two-layers neural network. 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. In this paper, we provide a rigorous justification of these approaches for a two-layers neural network model called the committee machine, under a technical assumption. We also introduce a version of the approximate message passing (AMP) algorithm for the committee machine that allows optimal learning in polynomial time for a large set of parameters. We find that there are regimes in which a low generalization error is information-theoretically achievable while the AMP algorithm fails to deliver it; strongly suggesting that no efficient algorithm exists for those cases, unveiling a large computational gap.
Homepage: https://arxiv.org/abs/1806.05451
Source Code:  https://github.com/benjaminaubin/TheCommitteeMachine
Related Software: lsd; dnner; PRMLT; AlexNet; ImageNet; gss; SigClust; AdaBoost.MH; GitHub; Entropy-SGD
Cited in: 7 Publications

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