Size-noise tradeoffs in generative networks

Bolton Bailey, Matus Telgarsky

Research output: Contribution to journalConference articlepeer-review


This paper investigates the ability of generative networks to convert their input noise distributions into other distributions. Firstly, we demonstrate a construction that allows ReLU networks to increase the dimensionality of their noise distribution by implementing a “space-filling” function based on iterated tent maps. We show this construction is optimal by analyzing the number of affine pieces in functions computed by multivariate ReLU networks. Secondly, we provide efficient ways (using polylog(1/ε) nodes) for networks to pass between univariate uniform and normal distributions, using a Taylor series approximation and a binary search gadget for computing function inverses. Lastly, we indicate how high dimensional distributions can be efficiently transformed into low dimensional distributions.

Original languageEnglish (US)
Pages (from-to)6489-6499
Number of pages11
JournalAdvances in Neural Information Processing Systems
StatePublished - 2018
Event32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada
Duration: Dec 2 2018Dec 8 2018

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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