mlsanityData to 7 Oct 2026

Regularly random duality

arXiv 1303.7295 ↗First posted 29 Mar 2013cs.IT math.IT math.OCcited by 23

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Abstract (arXiv)

In this paper we look at a class of random optimization problems. We discuss ways that can help determine typical behavior of their solutions. When the dimensions of the optimization problems are large such an information often can be obtained without actually solving the original problems. Moreover, we also discover that fairly often one can actually determine many quantities of interest (such as, for example, the typical optimal values of the objective functions) completely analytically. We present a few general ideas and emphasize that the range of applications is enormous.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Mar 2013.

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Citing papers per year: 2021: 2; 2022: 0; 2023: 6; 2024: 8; 2025: 5; 2026: 2.

23 papers.

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  1. 2023Binary perceptrons capacity via fully lifted random duality theorycited by 13
  2. 2023Fl RDT based ultimate lowering of the negative spherical perceptron capacitycited by 11
  3. 2021Sharp global convergence guarantees for iterative nonconvex optimization: A Gaussian process perspectivecited by 10
  4. 2025Rare dense solutions clusters in asymmetric binary perceptrons -- local entropy via fully lifted RDTcited by 5
  5. 2025A CLuP algorithm to practically achieve ~ 0.76 SK--model ground state free energycited by 5
  6. 2024Fixed width treelike neural networks capacity analysis -- generic activationscited by 4
  7. 2024Injectivity capacity of ReLU gatescited by 4
  8. 2023Capacity of the treelike sign perceptrons neural networks with one hidden layer -- RDT based upper boundscited by 3
  9. 2023Lifted RDT based capacity analysis of the 1-hidden layer treelike sign perceptrons neural networkscited by 3
  10. 2024Deep ReLU networks -- injectivity capacity upper boundscited by 3
  11. 2026Parametric RDT approach to computational gap of symmetric binary perceptroncited by 1
  12. 2021Phase Transitions in Recovery of Structured Signals from Corrupted Measurementscited by 0
11 more
  1. 2023Causal Inference (C-inf) -- closed form worst case typical phase transitionscited by 0
  2. 2023Causal Inference (C-inf) -- asymmetric scenario of typical phase transitionscited by 0
  3. 2024Exact objectives of random linear programs and mean widths of random polyhedronscited by 0
  4. 2024Ridge interpolators in correlated factor regression models -- exact risk analysiscited by 0
  5. 2024Precise analysis of ridge interpolators under heavy correlations -- a Random Duality Theory viewcited by 0
  6. 2024Theoretical limits of descending ℓ0 sparse-regression ML algorithmscited by 0
  7. 2024Sparsifying Suprema of Gaussian Processescited by 0
  8. 2025Phase transition of descending phase retrieval algorithmscited by 0
  9. 2025Optimal spectral initializers impact on phase retrieval phase transitions -- an RDT viewcited by 0
  10. 2025Phase retrieval with rank d measurements -- descending algorithms phase transitionscited by 0
  11. 2026Precise sample covariance spectral norm error -- an RDT viewcited by 0