# The Multiclass Score-Oriented Loss (MultiSOL) on the Simplex

arXiv: https://arxiv.org/abs/2511.22587 · HTML: https://mlsanity.com/paper/2511.22587/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 27 Nov 2025.

## Builds on (most cited first, 15 of 15)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysis](https://mlsanity.com/paper/2010.14925/) (2020)
- [Influence-Balanced Loss for Imbalanced Visual Classification](https://mlsanity.com/paper/2110.02444/) (2021)
- [Score-oriented loss (SOL) functions](https://mlsanity.com/paper/2103.15522/) (2021)
- [f-Divergence Based Classification: Beyond the Use of Cross-Entropy](https://mlsanity.com/paper/2401.01268/) (2024)
- [Building a stable classifier with the inflated argmax](https://mlsanity.com/paper/2405.14064/) (2024)
- [Operational solar flare forecasting via video-based deep learning](https://mlsanity.com/paper/2209.05128/) (2022)
- [Geometry-Aware Adaptation for Pretrained Models](https://mlsanity.com/paper/2307.12226/) (2023)
- [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)
- [Deep Learning for Active Region Classification: A Systematic Study from Convolutional Neural Networks to Vision Transformers](https://mlsanity.com/paper/2410.17816/) (2024)
- [Multiclass threshold-based classification](https://mlsanity.com/paper/2505.11276/) (2025)

## Abstract (arXiv)

In the supervised binary classification setting, score-oriented losses have been introduced with the aim of optimizing a chosen performance metric directly during the training phase, thus avoiding textita posteriori threshold tuning. To do this, in their construction, the decision threshold is treated as a random variable provided with a certain textita priori distribution. In this paper, we use a recently introduced multidimensional threshold-based classification framework to extend such score-oriented losses to multiclass classification, defining the Multiclass Score-Oriented Loss (MultiSOL) functions. As also demonstrated by several classification experiments, this proposed family of losses is designed to preserve the main advantages observed in the binary setting, such as the direct optimization of the target metric and the robustness to class imbalance, achieving performance comparable to other state-of-the-art loss functions and providing new insights into the interaction between simplex geometry and score-oriented learning.