Institutional Research Information Service
UCL Logo
Please report any queries concerning the funding data grouped in the sections named "Externally Awarded" or "Internally Disbursed" (shown on the profile page) to your Research Finance Administrator. Your can find your Research Finance Administrator at https://www.ucl.ac.uk/finance/research/rs-contacts.php by entering your department
Please report any queries concerning the student data shown on the profile page to:

Email: portico-services@ucl.ac.uk

Help Desk: http://www.ucl.ac.uk/ras/portico/helpdesk
Publication Detail
Dynamics of stochastic gradient descent for two-layer neural networks in the teacher–student setup
  • Publication Type:
    Journal article
  • Publication Sub Type:
  • Authors:
    Goldt S, Advani MS, Saxe AM, Krzakala F, Zdeborová L
  • Publication date:
  • Pagination:
  • Journal:
    Journal of Statistical Mechanics: Theory and Experiment
  • Volume:
  • Article number:
  • Status:
  • Print ISSN:
  • Language:
  • Notes:
    Number: 12 Publisher: IOP Publishing urldate: 2021-12-10 keywords: publications
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.
Publication data is maintained in RPS. Visit https://rps.ucl.ac.uk
 More search options
UCL Researchers
Gatsby Computational Neurosci Unit
University College London - Gower Street - London - WC1E 6BT Tel:+44 (0)20 7679 2000

© UCL 1999–2011

Search by