Learning High-Dimensional Parity Functions with Product Networks using Gradient Descent

This research project, conducted jointly by Orange Research and Télécom Paris, addresses a fundamental challenge in machine learning: learning parity (XOR) functions in high-dimensional spaces using gradient descent. Such functions are central to cryptography, error-correcting codes, and signal processing, yet notoriously hard to learn for standard neural networks.

The project shows, that combining a product-based neural architecture with sparse input data enables efficient parity learning with theoretical convergence guarantees, even at very large scales. These results were accepted at ICML 2026.

The source code to reproduce all experiments presented in the paper is available on GitHub under the MIT licence.

G. Larue, L.-A. Dufrène, Q. Lampin, H. Ghauch, and G. Rekaya, Learning High-Dimensional Parity Functions with Product Networks using Gradient Descent, accepted at ICML 2026, arXiv:2605.28612.