# Meshes that trap random subspaces

arXiv: https://arxiv.org/abs/1304.0003 · HTML: https://mlsanity.com/paper/1304.0003/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2013.

## Built on by (most cited first, 8 of 8)

- [Asymptotics of feature learning in two-layer networks after one gradient-step](https://mlsanity.com/paper/2402.04980/) (2024)
- [A phase transition between positional and semantic learning in a solvable model of dot-product attention](https://mlsanity.com/paper/2402.03902/) (2024)
- [Fixed width treelike neural networks capacity analysis -- generic activations](https://mlsanity.com/paper/2402.05696/) (2024)
- [Injectivity capacity of ReLU gates](https://mlsanity.com/paper/2410.20646/) (2024)
- [Deep ReLU networks -- injectivity capacity upper bounds](https://mlsanity.com/paper/2412.19677/) (2024)
- [Exact objectives of random linear programs and mean widths of random polyhedrons](https://mlsanity.com/paper/2403.03637/) (2024)
- [Ridge interpolators in correlated factor regression models -- exact risk analysis](https://mlsanity.com/paper/2406.09183/) (2024)
- [Precise analysis of ridge interpolators under heavy correlations -- a Random Duality Theory view](https://mlsanity.com/paper/2406.09199/) (2024)

## 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.