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

Benjamin Aubin (1) , Antoine Maillard (1) , Jean Barbier (2, 3) , Florent Krzakala (1) , Nicolas Macris (2) , Lenka Zdeborová (4)

1 LPS - Laboratoire de Physique Statistique de l'ENS
2 EPFL - Ecole Polytechnique Fédérale de Lausanne
3 QMUL - Queen Mary University of London
4 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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 contribution, we provide a rigorous justiication 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 nd 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 eecient algorithm exists for those cases, and unveiling a large computational gap.

Domaines: Physique [physics]

Benjamin Aubin, Antoine Maillard, Jean Barbier, Florent Krzakala, Nicolas Macris, et al.. The committee machine: Computational to statistical gaps in learning a two-layers neural network. Advances in Neural Information Processing Systems, 2018, 31, pp.3227-3238. ⟨cea-01933130⟩