# Multiclass threshold-based classification

arXiv: https://arxiv.org/abs/2505.11276 · HTML: https://mlsanity.com/paper/2505.11276/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 35 references that are in the map.
- First posted on arXiv 16 May 2025.

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

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [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)
- [Score-oriented loss (SOL) functions](https://mlsanity.com/paper/2103.15522/) (2021)
- [Building a stable classifier with the inflated argmax](https://mlsanity.com/paper/2405.14064/) (2024)
- [Geometry-Aware Adaptation for Pretrained Models](https://mlsanity.com/paper/2307.12226/) (2023)
- [Calibrated simplex-mapping classification](https://mlsanity.com/paper/2103.02926/) (2021)
- [Deep Learning for Active Region Classification: A Systematic Study from Convolutional Neural Networks to Vision Transformers](https://mlsanity.com/paper/2410.17816/) (2024)

## Built on by (most cited first, 1 of 1)

- [The Multiclass Score-Oriented Loss (MultiSOL) on the Simplex](https://mlsanity.com/paper/2511.22587/) (2025)

## Abstract (arXiv)

In this paper, we introduce a threshold-based framework for multiclass classification that generalizes the standard argmax rule. This is done by replacing the probabilistic interpretation of softmax outputs with a geometric one on the multidimensional simplex, where the classification depends on a multidimensional threshold. This change of perspective enables for any trained classification network an a posteriori optimization of the classification score by means of threshold tuning, as usually carried out in the binary setting. This allows a further refinement of the prediction capability of any network. Moreover, this multidimensional threshold-based setting makes it possible to define score-oriented losses, which are based on the interpretation of the threshold as a random variable. Our experiments show that the multidimensional threshold tuning yields consistent performance improvements across various networks and datasets, and that the proposed multiclass score-oriented losses are competitive with standard loss functions, resembling the advantages observed in the binary case.