TY - GEN
T1 - Learning a Single Neuron with Bias Using Gradient Descent
AU - Vardi, Gal
AU - Yehudai, Gilad
AU - Shamir, Ohad
N1 - Publisher Copyright: © 2021 Neural information processing systems foundation. All rights reserved.
PY - 2021
Y1 - 2021
N2 - We theoretically study the fundamental problem of learning a single neuron with a bias term (x 7→ σ(hw, xi + b)) in the realizable setting with the ReLU activation, using gradient descent. Perhaps surprisingly, we show that this is a significantly different and more challenging problem than the bias-less case (which was the focus of previous works on single neurons), both in terms of the optimization geometry as well as the ability of gradient methods to succeed in some scenarios. We provide a detailed study of this problem, characterizing the critical points of the objective, demonstrating failure cases, and providing positive convergence guarantees under different sets of assumptions. To prove our results, we develop some tools which may be of independent interest, and improve previous results on learning single neurons.
AB - We theoretically study the fundamental problem of learning a single neuron with a bias term (x 7→ σ(hw, xi + b)) in the realizable setting with the ReLU activation, using gradient descent. Perhaps surprisingly, we show that this is a significantly different and more challenging problem than the bias-less case (which was the focus of previous works on single neurons), both in terms of the optimization geometry as well as the ability of gradient methods to succeed in some scenarios. We provide a detailed study of this problem, characterizing the critical points of the objective, demonstrating failure cases, and providing positive convergence guarantees under different sets of assumptions. To prove our results, we develop some tools which may be of independent interest, and improve previous results on learning single neurons.
UR - http://www.scopus.com/inward/record.url?scp=85131873458&partnerID=8YFLogxK
M3 - منشور من مؤتمر
T3 - Advances in Neural Information Processing Systems
SP - 28690
EP - 28700
BT - Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
A2 - Ranzato, Marc'Aurelio
A2 - Beygelzimer, Alina
A2 - Dauphin, Yann
A2 - Liang, Percy S.
A2 - Wortman Vaughan, Jenn
T2 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
Y2 - 6 December 2021 through 14 December 2021
ER -