## Abstract

Neural networks are nowadays highly successful despite strong hardness results. The existing hardness results focus on the network architecture, and assume that the network’s weights are arbitrary. A natural approach to settle the discrepancy is to assume that the network’s weights are “well-behaved" and posses some generic properties that may allow efficient learning. This approach is supported by the intuition that the weights in real-world networks are not arbitrary, but exhibit some”random-like" properties with respect to some”natural" distributions. We prove negative results in this regard, and show that for depth-2 networks, and many “natural" weights distributions such as the normal and the uniform distribution, most networks are hard to learn. Namely, there is no efficient learning algorithm that is provably successful for most weights, and every input distribution. It implies that there is no generic property that holds with high probability in such random networks and allows efficient learning.

Original language | American English |
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Journal | Advances in Neural Information Processing Systems |

Volume | 2020-December |

State | Published - 2020 |

Event | 34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online Duration: 6 Dec 2020 → 12 Dec 2020 |

### Bibliographical note

Funding Information:This research is partially supported by ISF grant 2258/19.

Publisher Copyright:

© 2020 Neural information processing systems foundation. All rights reserved.