Global Convergence of SGD For Logistic Loss on Two Layer Neural Nets

Pulkit Gopalani, Samyak Jha, Anirbit Mukherjee

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Abstract

In this note, we demonstrate a first-of-its-kind provable convergence of SGD to the global minima of appropriately regularized logistic empirical risk of depth 2 nets -- for arbitrary data and with any number of gates with adequately smooth and bounded activations like sigmoid and tanh. We also prove an exponentially fast convergence rate for continuous time SGD that also applies to smooth unbounded activations like SoftPlus. Our key idea is to show the existence of Frobenius norm regularized logistic loss functions on constant-sized neural nets which are "Villani functions" and thus be able to build on recent progress with analyzing SGD on such objectives.
Original languageUndefined
Number of pages21
JournalTransactions on Machine Learning Research
Publication statusPublished - 25 Feb 2024

Keywords

  • stochastic differential equations
  • deep-learning
  • stochastic gradient descent
  • stochastic optimization

Research Beacons, Institutes and Platforms

  • Institute for Data Science and AI
  • MCAIF: Centre for AI Fundamentals

    Kaski, S. (PI), Alvarez, M. (Researcher), Pan, W. (Researcher), Mu, T. (Researcher), Rivasplata, O. (PI), Sun, M. (Researcher), Mukherjee, A. (Researcher), Caprio, M. (PI), Sonee, A. (Researcher), Leroy, A. (Researcher), Wang, J. (Researcher), Lee, J. (Researcher), Parakkal Unni, M. (Researcher), Sloman, S. (Researcher), Menary, S. (Researcher), Quilter, T. (Researcher), Hosseinzadeh, A. (PGR student), Mousa, A. (PGR student), Glover, E. (PGR student), Das, A. (PGR student), DURSUN, F. (PGR student), Zhu, H. (PGR student), Abdi, H. (PGR student), Dandago, K. (PGR student), Piriyajitakonkij, M. (PGR student), Rachman, R. (PGR student), Shi, X. (PGR student), Keany, T. (PGR student), Liu, X. (PGR student), Jiang, Y. (PGR student), Wan, Z. (PGR student), Evans, I. (Support team), Harrison, M. (Support team) & Machado, M. (PI)

    1/10/2130/09/26

    Project: Research

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