mlsanityData to 7 Oct 2026

Meshes that trap random subspaces

arXiv 1304.0003 ↗First posted 29 Mar 2013cs.IT math.IT math.OCcited by 8

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Abstract (arXiv)

In our recent work citeStojnicCSetam09,StojnicUpper10 we considered solving under-determined systems of linear equations with sparse solutions. In a large dimensional and statistical context we proved results related to performance of a polynomial ℓ1-optimization technique when used for solving such systems. As one of the tools we used a probabilistic result of Gordon citeGordon88. In this paper we revisit this classic result in its core form and show how it can be reused to in a sense prove its own optimality.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Mar 2013.

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Citing papers per year: 2024: 8.

8 papers.

  1. 2024Asymptotics of feature learning in two-layer networks after one gradient-stepcited by 35
  2. 2024A phase transition between positional and semantic learning in a solvable model of dot-product attentioncited by 30
  3. 2024Fixed width treelike neural networks capacity analysis -- generic activationscited by 4
  4. 2024Injectivity capacity of ReLU gatescited by 4
  5. 2024Deep ReLU networks -- injectivity capacity upper boundscited by 3
  6. 2024Exact objectives of random linear programs and mean widths of random polyhedronscited by 0
  7. 2024Ridge interpolators in correlated factor regression models -- exact risk analysiscited by 0
  8. 2024Precise analysis of ridge interpolators under heavy correlations -- a Random Duality Theory viewcited by 0