# Symmetry constrained machine learning

arXiv: https://arxiv.org/abs/1811.07051 · HTML: https://mlsanity.com/paper/1811.07051/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2018.

## Built on by (most cited first, 3 of 3)

- [Symmetry Discovery Beyond Affine Transformations](https://mlsanity.com/paper/2406.03619/) (2024)
- [Knowledge-Integrated Informed AI for National Security](https://mlsanity.com/paper/2202.03188/) (2022)
- [Switchable Lightweight Anti-symmetric Processing (SLAP) with CNN Outspeeds Data Augmentation by Smaller Sample -- Application in Gomoku Reinforcement Learning](https://mlsanity.com/paper/2301.04746/) (2023)

## Abstract (arXiv)

Symmetry, a central concept in understanding the laws of nature, has been used for centuries in physics, mathematics, and chemistry, to help make mathematical models tractable. Yet, despite its power, symmetry has not been used extensively in machine learning, until rather recently. In this article we show a general way to incorporate symmetries into machine learning models. We demonstrate this with a detailed analysis on a rather simple real world machine learning system - a neural network for classifying handwritten digits, lacking bias terms for every neuron. We demonstrate that ignoring symmetries can have dire over-fitting consequences, and that incorporating symmetry into the model reduces over-fitting, while at the same time reducing complexity, ultimately requiring less training data, and taking less time and resources to train.