This is an interim version of our Electronic Legal Deposit Catalogue-eJournals and eBooks while we continue to recover from a cyber-attack.
Dynamics of stochastic gradient descent for two-layer neural networks in the teacher–student setup*This article is an updated version of: Goldt S, Advani M S, Saxe A M, Krzakala F and Zdeborova L 2019 Dynamics of stochastic gradient descent for two-layer neural networks in the teacher-student setup Advances in Neural Information Processing Systems pp 6981–91. (16th December 2020)
Record Type:
Journal Article
Title:
Dynamics of stochastic gradient descent for two-layer neural networks in the teacher–student setup*This article is an updated version of: Goldt S, Advani M S, Saxe A M, Krzakala F and Zdeborova L 2019 Dynamics of stochastic gradient descent for two-layer neural networks in the teacher-student setup Advances in Neural Information Processing Systems pp 6981–91. (16th December 2020)
Main Title:
Dynamics of stochastic gradient descent for two-layer neural networks in the teacher–student setup*This article is an updated version of: Goldt S, Advani M S, Saxe A M, Krzakala F and Zdeborova L 2019 Dynamics of stochastic gradient descent for two-layer neural networks in the teacher-student setup Advances in Neural Information Processing Systems pp 6981–91.
Abstract: Deep neural networks achieve stellar generalisation even when they have enough parameters to easily fit all their training data. We study this phenomenon by analysing the dynamics and the performance of over-parameterised two-layer neural networks in the teacher–student setup, where one network, the student, is trained on data generated by another network, called the teacher. We show how the dynamics of stochastic gradient descent (SGD) is captured by a set of differential equations and prove that this description is asymptotically exact in the limit of large inputs. Using this framework, we calculate the final generalisation error of student networks that have more parameters than their teachers. We find that the final generalisation error of the student increases with network size when training only the first layer, but stays constant or even decreases with size when training both layers. We show that these different behaviours have their root in the different solutions SGD finds for different activation functions. Our results indicate that achieving good generalisation in neural networks goes beyond the properties of SGD alone and depends on the interplay of at least the algorithm, the model architecture, and the data set.