# Convex Relaxations of Convolutional Neural Nets

arXiv: https://arxiv.org/abs/1901.00035 · HTML: https://mlsanity.com/paper/1901.00035/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2018.

## Built on by (most cited first, 2 of 2)

- [Training Quantized Neural Networks to Global Optimality via Semidefinite Programming](https://mlsanity.com/paper/2105.01420/) (2021)
- [Convex Approximation of Two-Layer ReLU Networks for Hidden State Differential Privacy](https://mlsanity.com/paper/2407.04884/) (2024)

## Abstract (arXiv)

We propose convex relaxations for convolutional neural nets with one hidden layer where the output weights are fixed. For convex activation functions such as rectified linear units, the relaxations are convex second order cone programs which can be solved very efficiently. We prove that the relaxation recovers the global minimum under a planted model assumption, given sufficiently many training samples from a Gaussian distribution. We also identify a phase transition phenomenon in recovering the global minimum for the relaxation.