mlsanityData to 14 Oct 2026

Another look at the Gardner problem

arXiv 1306.3979 ↗First posted 17 Jun 2013math.OC math-ph math.MPcited by 24

Not on the map. Why?

Abstract (arXiv)

In this paper we revisit one of the classical perceptron problems from the neural networks and statistical physics. In citeGar88 Gardner presented a neat statistical physics type of approach for analyzing what is now typically referred to as the Gardner problem. The problem amounts to discovering a statistical behavior of a spherical perceptron. Among various quantities citeGar88 determined the so-called storage capacity of the corresponding neural network and analyzed its deviations as various perceptron parameters change. In a more recent work citeSchTir02,SchTir03 many of the findings of citeGar88 (obtained on the grounds of the statistical mechanics replica approach) were proven to be mathematically correct. In this paper, we take another look at the Gardner problem and provide a simple alternative framework for its analysis. As a result we reprove many of now known facts and rigorously reestablish a few other results.

Key facts. Cited by 24 papers in the map (data through 14 Oct 2026). First posted on arXiv 17 Jun 2013.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 5; 2024: 9; 2025: 7; 2026: 3.

24 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. 2023Injectivity of ReLU networks: perspectives from statistical physicscited by 10
  4. 2024No Free Prune: Information-Theoretic Barriers to Pruning at Initializationcited by 8
  5. 2025Rare dense solutions clusters in asymmetric binary perceptrons -- local entropy via fully lifted RDTcited by 5
  6. 2025A CLuP algorithm to practically achieve ~ 0.76 SK--model ground state free energycited by 5
  7. 2024Fixed width treelike neural networks capacity analysis -- generic activationscited by 4
  8. 2024Injectivity capacity of ReLU gatescited by 4
  9. 2023Capacity of the treelike sign perceptrons neural networks with one hidden layer -- RDT based upper boundscited by 3
  10. 2023Lifted RDT based capacity analysis of the 1-hidden layer treelike sign perceptrons neural networkscited by 3
  11. 2024Deep ReLU networks -- injectivity capacity upper boundscited by 3
  12. 2025Binary perceptron computational gap -- a parametric fl RDT viewcited by 3
12 more
  1. 2024Capacity of the Hebbian-Hopfield network associative memorycited by 1
  2. 2026Parametric RDT approach to computational gap of symmetric binary perceptroncited by 1
  3. 2026How abundant are good interpolators?cited by 1
  4. 2024Exact objectives of random linear programs and mean widths of random polyhedronscited by 0
  5. 2024Ridge interpolators in correlated factor regression models -- exact risk analysiscited by 0
  6. 2024Precise analysis of ridge interpolators under heavy correlations -- a Random Duality Theory viewcited by 0
  7. 2024Theoretical limits of descending ℓ0 sparse-regression ML algorithmscited 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. 2025A large deviation view of stationarized fully lifted blirp interpolationcited by 0
  12. 2026Ultrametric OGP - parametric RDT symmetric binary perceptron connectioncited by 0