Width of Minima Reached by Stochastic Gradient Descent is Influenced by Learning Rate to Batch Size Ratio

  • Stanislaw JastrzębskiEmail author
  • Zachary Kenton
  • Devansh Arpit
  • Nicolas Ballas
  • Asja Fischer
  • Yoshua Bengio
  • Amos Storkey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11141)


We show that the dynamics and convergence properties of SGD are set by the ratio of learning rate to batch size. We observe that this ratio is a key determinant of the generalization error, which we suggest is mediated by controlling the width of the final minima found by SGD. We verify our analysis experimentally on a range of deep neural networks and datasets.



We thank NSERC, Canada Research Chairs, IVADO and CIFAR for funding. SJ was in part supported by Grant No. DI 2014/016644 and ETIUDA stipend No. 2017/24/T/ST6/00487. This project has received funding from the European Union’s Horizon 2020 programme under grant agreement No 732204 and Swiss State Secretariat for Education,Research and Innovation under contract No. 16.0159.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Stanislaw Jastrzębski
    • 1
    • 2
    • 3
    Email author
  • Zachary Kenton
    • 1
    • 2
  • Devansh Arpit
    • 2
  • Nicolas Ballas
    • 3
  • Asja Fischer
    • 4
  • Yoshua Bengio
    • 2
    • 5
  • Amos Storkey
    • 6
  1. 1.Jagiellonian UniversityKrakówPoland
  2. 2.MILAUniversité de MontréalMontrealCanada
  3. 3.Facebook AI ResearchParisFrance
  4. 4.Faculty of MathematicsRuhr-University BochumBochumGermany
  5. 5.CIFAR Senior FellowTorontoCanada
  6. 6.School of InformaticsUniversity of EdinburghEdinburghScotland

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