# Score-oriented loss (SOL) functions

arXiv: https://arxiv.org/abs/2103.15522 · HTML: https://mlsanity.com/paper/2103.15522/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 43 references that are in the map.
- First posted on arXiv 29 Mar 2021.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Large-Margin Softmax Loss for Convolutional Neural Networks](https://mlsanity.com/paper/1612.02295/) (2016)
- [Temporal Convolutional Neural Network for the Classification of Satellite Image Time Series](https://mlsanity.com/paper/1811.10166/) (2018)
- [On Loss Functions for Deep Neural Networks in Classification](https://mlsanity.com/paper/1702.05659/) (2017)
- [Addressing the Loss-Metric Mismatch with Adaptive Loss Alignment](https://mlsanity.com/paper/1905.05895/) (2019)
- [A New Loss Function for CNN Classifier Based on Pre-defined Evenly-Distributed Class Centroids](https://mlsanity.com/paper/1904.06008/) (2019)
- [Bad and good errors: value-weighted skill scores in deep ensemble learning](https://mlsanity.com/paper/2103.02881/) (2021)
- [Machine learning as a flaring storm warning machine: Was a warning machine for the September 2017 solar flaring storm possible?](https://mlsanity.com/paper/2007.02425/) (2020)

## Built on by (most cited first, 11 of 11)

- [Prediction of severe thunderstorm events with ensemble deep learning and radar data](https://mlsanity.com/paper/2109.09791/) (2021)
- [Physics-driven machine learning for the prediction of coronal mass ejections' travel times](https://mlsanity.com/paper/2305.10057/) (2023)
- [Operational solar flare forecasting via video-based deep learning](https://mlsanity.com/paper/2209.05128/) (2022)
- [A comprehensive theoretical framework for the optimization of neural networks classification performance with respect to weighted metrics](https://mlsanity.com/paper/2305.13472/) (2023)
- [Forecasting Geoffective Events from Solar Wind Data and Evaluating the Most Predictive Features through Machine Learning Approaches](https://mlsanity.com/paper/2403.09847/) (2024)
- [AnyLoss: Transforming Classification Metrics into Loss Functions](https://mlsanity.com/paper/2405.14745/) (2024)
- [Multiclass threshold-based classification](https://mlsanity.com/paper/2505.11276/) (2025)
- [Multiclass threshold-based classification and model evaluation](https://mlsanity.com/paper/2511.21794/) (2025)
- [The Multiclass Score-Oriented Loss (MultiSOL) on the Simplex](https://mlsanity.com/paper/2511.22587/) (2025)
- [Don't stop me now: How Validation Criteria Affect Checkpoint Selection and Early Stopping](https://mlsanity.com/paper/2602.22107/) (2026)
- [Weighted Score-Oriented Losses for Temporally Localized Event Prediction](https://mlsanity.com/paper/2606.23145/) (2026)

## Abstract (arXiv)

Loss functions engineering and the assessment of forecasting performances are two crucial and intertwined aspects of supervised machine learning. This paper focuses on binary classification to introduce a class of loss functions that are defined on probabilistic confusion matrices and that allow an automatic and a priori maximization of the skill scores. The performances of these loss functions are validated during the training phase of two experimental forecasting problems, thus showing that the probability distribution function associated with the confusion matrices significantly impacts the outcome of the score maximization process.