# Ordinal Encoding as a Regularizer in Binary Loss for Solar Flare Prediction

arXiv: https://arxiv.org/abs/2510.04063 · HTML: https://mlsanity.com/paper/2510.04063/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Builds on (most cited first, 11 of 11)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [How to Train Your Flare Prediction Model: Revisiting Robust Sampling of Rare Events](https://mlsanity.com/paper/2103.07542/) (2021)
- [Towards Coupling Full-disk and Active Region-based Flare Prediction for Operational Space Weather Forecasting](https://mlsanity.com/paper/2209.07406/) (2022)
- [All-Clear Flare Prediction Using Interval-based Time Series Classifiers](https://mlsanity.com/paper/2105.01202/) (2021)
- [Explaining Full-disk Deep Learning Model for Solar Flare Prediction using Attribution Methods](https://mlsanity.com/paper/2307.15878/) (2023)
- [Challenges with Extreme Class-Imbalance and Temporal Coherence: A Study on Solar Flare Data](https://mlsanity.com/paper/1911.09061/) (2019)
- [Explainable Deep Learning-based Solar Flare Prediction with post hoc Attention for Operational Forecasting](https://mlsanity.com/paper/2308.02682/) (2023)
- [Towards Interpretable Solar Flare Prediction with Attention-based Deep Neural Networks](https://mlsanity.com/paper/2309.04558/) (2023)
- [Advancing Solar Flare Prediction using Deep Learning with Active Region Patches](https://mlsanity.com/paper/2406.11054/) (2024)
- [Embedding Ordinality to Binary Loss Function for Improving Solar Flare Forecasting](https://mlsanity.com/paper/2408.11768/) (2024)

## Abstract (arXiv)

The prediction of solar flares is typically formulated as a binary classification task, distinguishing events as either Flare (FL) or No-Flare (NF) according to a specified threshold (for example, greater than or equal to C-class, M-class, or X-class). However, this binary framework neglects the inherent ordinal relationships among the sub-classes contained within each category (FL and NF). Several studies on solar flare prediction have empirically shown that the most frequent misclassifications occur near this prediction threshold. This suggests that the models struggle to differentiate events that are similar in intensity but fall on opposite sides of the binary threshold. To mitigate this limitation, we propose a modified loss function that integrates the ordinal information among the sub-classes of the binarized flare labels into the conventional binary cross-entropy (BCE) loss. This approach serves as an ordinality-aware, data-driven regularization method that penalizes the incorrect predictions of flare events in close proximity to the prediction threshold more heavily than those away from the boundary during model optimization. By incorporating ordinal weighting into the loss function, we aim to enhance the model's learning process by leveraging the ordinal characteristics of the data, thereby improving its overall performance.