The committee machine: Computational to statistical gaps in learning a two-layers neural network

Aubin, BenjaminMaillard, AntoineBarbier, JeanKrzakala, FlorentMacris, NicolasZdeborova, Lenka2019-06-182019-06-182019-06-182018-01-01https://infoscience.epfl.ch/handle/20.500.14299/158004WOS:000461823303024Heuristic 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 contribution, we provide a rigorous justification of these approaches for a two-layers neural network model called the committee machine. We also introduce a version of the approximate message passing (AMP) algorithm for the committee machine that allows to perform 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, and unveiling a large computational gap.Computer Science, Artificial IntelligenceComputer Sciencemessage-passing algorithmsspaceThe committee machine: Computational to statistical gaps in learning a two-layers neural networktext::conference output::conference proceedings::conference paper