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Generative Models of Huge Objects

Authors Lunjia Hu, Inbal Rachel Livni Navon, Omer Reingold

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Author Details

Lunjia Hu
  • Department of Computer Science, Stanford University, CA, USA
Inbal Rachel Livni Navon
  • Department of Computer Science, Stanford University, CA, USA
Omer Reingold
  • Department of Computer Science, Stanford University, CA, USA

Funding

  • Hu, Lunjia: Supported by the Simons Foundation Collaboration on the Theory of Algorithmic Fairness, Omer Reingold’s NSF Award IIS-1908774, and Moses Charikar’s Simons Investigators award.
  • Livni Navon, Inbal Rachel: Supported by the Simons Foundation Collaboration on the Theory of Algorithmic Fairness, the Sloan Foundation Grant 2020-13941, and the Zuckerman STEM Leadership Program.
  • Reingold, Omer: Supported by the Simons Foundation Collaboration on the Theory of Algorithmic Fairness and the Simons Foundation Investigators award 689988.

Cite AsGet BibTex

Lunjia Hu, Inbal Rachel Livni Navon, and Omer Reingold. Generative Models of Huge Objects. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CCC.2023.5

Abstract

This work initiates the systematic study of explicit distributions that are indistinguishable from a single exponential-size combinatorial object. In this we extend the work of Goldreich, Goldwasser and Nussboim (SICOMP 2010) that focused on the implementation of huge objects that are indistinguishable from the uniform distribution, satisfying some global properties (which they coined truthfulness). Indistinguishability from a single object is motivated by the study of generative models in learning theory and regularity lemmas in graph theory. Problems that are well understood in the setting of pseudorandomness present significant challenges and at times are impossible when considering generative models of huge objects. We demonstrate the versatility of this study by providing a learning algorithm for huge indistinguishable objects in several natural settings including: dense functions and graphs with a truthfulness requirement on the number of ones in the function or edges in the graphs, and a version of the weak regularity lemma for sparse graphs that satisfy some global properties. These and other results generalize basic pseudorandom objects as well as notions introduced in algorithmic fairness. The results rely on notions and techniques from a variety of areas including learning theory, complexity theory, cryptography, and game theory.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pseudorandomness and derandomization
  • Theory of computation → Random network models
  • Theory of computation → Generating random combinatorial structures
Keywords
  • pseudorandomness
  • generative models
  • regularity lemma

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