# Convexified Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1609.01000 · HTML: https://mlsanity.com/paper/1609.01000/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2016.

## Built on by (most cited first, 9 of 9)

- [Approximation and Learning with Deep Convolutional Models: a Kernel Perspective](https://mlsanity.com/paper/2102.10032/) (2021)
- [Test-Time Dynamic Image Fusion](https://mlsanity.com/paper/2411.02840/) (2024)
- [Dual Convexified Convolutional Neural Networks](https://mlsanity.com/paper/2205.14056/) (2022)
- [Training a Two Layer ReLU Network Analytically](https://mlsanity.com/paper/2304.02972/) (2023)
- [Combining Neuro-Evolution of Augmenting Topologies with Convolutional Neural Networks](https://mlsanity.com/paper/2211.16978/) (2022)
- [Stability Analysis of Equivariant Convolutional Representations Through The Lens of Equivariant Multi-layered CKNs](https://mlsanity.com/paper/2408.04277/) (2024)
- [Convexified Message-Passing Graph Neural Networks](https://mlsanity.com/paper/2505.18289/) (2025)
- [Resource-Efficient Gesture Recognition through Convexified Attention](https://mlsanity.com/paper/2602.13030/) (2026)
- [Uncertainty Quantification in CNN Through the Bootstrap of Convex Neural Networks](https://mlsanity.com/paper/2604.11833/) (2026)

## Abstract (arXiv)

We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a reproducing kernel Hilbert space, the CNN parameters can be represented as a low-rank matrix, which can be relaxed to obtain a convex optimization problem. For learning two-layer convolutional neural networks, we prove that the generalization error obtained by a convexified CNN converges to that of the best possible CNN. For learning deeper networks, we train CCNNs in a layer-wise manner. Empirically, CCNNs achieve performance competitive with CNNs trained by backpropagation, SVMs, fully-connected neural networks, stacked denoising auto-encoders, and other baseline methods.