This repository contains Matlab demo code for our Nonlinear Spectral Methods presented at NIPS 2016.

For citation of our paper
@inproceedings{AQM2016,
title={Globally Optimal Training of Generalized Polynomial Neural Networks with Nonlinear Spectral Methods},
author={A. Gautier and Q. Nguyen and M. Hein},
booktitle={Advances in Neural Information Processing Systems (NIPS)},
year={2016}
}

The following version presents our general theory for a certain class of non-convex optimization problems:
@inproceedings{QAM2016,
title={Nonlinear Spectral Methods for Nonconvex Optimization with Global Optimality},
author={Q. Nguyen and A. Gautier and M. Hein},
booktitle={NIPS Workshop on Optimization for Machine Learning},
year={2016}
}

Installation:
cvx is required: http:https://cvxr.com/cvx/download/

Guideline:
Please see the following files to run our experiments
0. NLSM_demo.m: demo our NLSM on cancer/iris dataset 1. main_NLSM.m: testing our Nonlinear Spectral Methods 2. main_ReLU1.m: testing one-hidden-layer ReLU nets by Batch-SGD
3. main_ReLU2.m: testing two-hidden-layer ReLU nets by Batch-SGD

In all experiments, we use UCI-datasets obtained from:
https://archive.ics.uci.edu/ml/datasets.html