# The Multiclass Score-Oriented Loss (MultiSOL) on the Simplex Source: [The Multiclass Score-Oriented Loss (MultiSOL) on the Simplex]() Collection index: [llms.txt]() Data updated: 2025-12-02T05:05:21.382Z Authors: Francesco Marchetti, Edoardo Legnaro, Sabrina Guastavino Published: 2025-11-27T16:20:55.000Z ## Abstract 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 \\textit{a posteriori} threshold tuning. To do this, in their construction, the decision threshold is treated as a random variable provided with a certain \\textit{a 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Image Classification on CIFAR10 (test) (Run Statistics)](): Image Classification; CIFAR10 (test); Mean Accuracy: 82.05. ## Original sources and implementation [Original paper]() [PDF]()