Unsupervised learning by a 'softened' correlation game: Duality and convergence

Kyle L. Luther, Runzhe Yang, H. Sebastian Seung

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Neural networks with Hebbian excitation and anti-Hebbian inhibition form an interesting class of biologically plausible unsupervised learning algorithms. It has recently been shown that such networks can be regarded as online gradient descent-ascent algorithms for solving min-max problems that are dual to unsupervised learning principles formulated with no explicit reference to neural networks. Here we generalize one such formulation, the correlation game, by replacing a hard constraint with a soft penalty function. Our 'softened' correlation game contains the nonnegative similarity matching principle as a special case. For solving the primal problem, we derive a projected gradient ascent algorithm that achieves speed through sorting. For solving the dual problem, we derive a projected gradient descent-ascent algorithm, the stochastic online variant of which can be interpreted as a neural network algorithm. We prove strong duality when the inhibitory connection matrix is positive definite, a condition that also prohibits multistability of neural activity dynamics. We show empirically that the neural net algorithm can converge when inhibitory plasticity is faster than excitatory plasticity, and may fail to converge in the opposing case. This is intuitively interpreted using the structure of the min-max problem.

Original languageEnglish (US)
Title of host publicationConference Record - 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages876-883
Number of pages8
ISBN (Electronic)9781728143002
DOIs
StatePublished - Nov 2019
Event53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019 - Pacific Grove, United States
Duration: Nov 3 2019Nov 6 2019

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
Volume2019-November
ISSN (Print)1058-6393

Conference

Conference53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019
CountryUnited States
CityPacific Grove
Period11/3/1911/6/19

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Networks and Communications

Keywords

  • Hebbian learning
  • neural networks

Fingerprint Dive into the research topics of 'Unsupervised learning by a 'softened' correlation game: Duality and convergence'. Together they form a unique fingerprint.

Cite this