# Flexible Moment-Invariant Bases from Irreducible Tensors

arXiv: https://arxiv.org/abs/2503.21939 · HTML: https://mlsanity.com/paper/2503.21939/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2025.

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

- [Optimal Invariant Bases for Atomistic Machine Learning](https://mlsanity.com/paper/2503.23515/) (2025)
- [On Making SE(2)-Invariant Networks Optimal](https://mlsanity.com/paper/2610.17424/) (2026)

## Abstract (arXiv)

Moment invariants are a powerful tool for the generation of rotation-invariant descriptors needed for many applications in pattern detection, classification, and machine learning. A set of invariants is optimal if it is complete, independent, and robust against degeneracy in the input. In this paper, we show that the current state of the art for the generation of these bases of moment invariants, despite being robust against moment tensors being identically zero, is vulnerable to a degeneracy that is common in real-world applications, namely spherical functions. We show how to overcome this vulnerability by combining two popular moment invariant approaches: one based on spherical harmonics and one based on Cartesian tensor algebra.