# Cardinality augmented loss functions

arXiv: https://arxiv.org/abs/2601.04941 · HTML: https://mlsanity.com/paper/2601.04941/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 15 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Builds on (most cited first, 2 of 2)

- [Metric Space Magnitude and Generalisation in Neural Networks](https://mlsanity.com/paper/2305.05611/) (2023)
- [Self-Supervised Learning for Glass Composition Screening](https://mlsanity.com/paper/2410.24083/) (2024)

## Abstract (arXiv)

Class imbalance is a common and pernicious issue for the training of neural networks. Often, an imbalanced majority class can dominate training to skew classifier performance towards the majority outcome. To address this problem we introduce cardinality augmented loss functions, derived from cardinality-like invariants in modern mathematics literature such as magnitude and the spread. These invariants enrich the concept of cardinality by evaluating the `effective diversity' of a metric space, and as such represent a natural solution to overly homogeneous training data. In this work, we establish a methodology for applying cardinality augmented loss functions in the training of neural networks and report results on both artificially imbalanced datasets as well as a real-world imbalanced material science dataset. We observe significant performance improvement among minority classes, as well as improvement in overall performance metrics.