It was “all” for “nothing”: sharp phase transitions for noiseless discrete channels

Jonathan Niles-Weed, Ilias Zadik

Research output: Contribution to journalConference articlepeer-review


We prove a phase transition known as the “all-or-nothing” phenomenon for noiseless discrete channels. This class of models includes the Bernoulli group testing model and the planted Gaussian perceptron model. Previously, the existence of the all-or-nothing phenomenon for such models was only known in a limited range of parameters. Our work extends the results to all signals with sublinear sparsity.

Original languageEnglish (US)
Pages (from-to)3546-3547
Number of pages2
JournalProceedings of Machine Learning Research
StatePublished - 2021
Event34th Conference on Learning Theory, COLT 2021 - Boulder, United States
Duration: Aug 15 2021Aug 19 2021


  • Phase transitions
  • all-or-nothing
  • group testing
  • perceptron
  • teacher-student

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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