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The committee machine: Computational to statistical gaps in learning a two-layers neural network
Benjamin Aubin · Antoine Maillard · jean barbier · Florent Krzakala · Nicolas Macris · Lenka Zdeborová

Thu Dec 06 07:45 AM -- 09:45 AM (PST) @ Room 517 AB #111

Heuristic tools from statistical physics have been used in the past to 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.

Author Information

Benjamin Aubin (Ipht Saclay)
Antoine Maillard (Ecole Normale Supérieure)
jean barbier (EPFL)
Florent Krzakala (École Normale Supérieure)
Nicolas Macris (EPFL)
Lenka Zdeborová (CEA Saclay)

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