# Multiclass threshold-based classification and model evaluation

arXiv: https://arxiv.org/abs/2511.21794 · HTML: https://mlsanity.com/paper/2511.21794/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 35 references that are in the map.
- First posted on arXiv 26 Nov 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)

## 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 textita posteriori optimization of the classification score by means of threshold tuning, as usually carried out in the binary setting, thus allowing for a further refinement of the prediction capability of any network. Our experiments show indeed that multidimensional threshold tuning yields performance improvements across various networks and datasets. Moreover, we derive a multiclass ROC analysis based on ROC clouds -- the attainable (FPR,TPR) operating points induced by a single multiclass threshold -- and summarize them via a Distance From Point (DFP) score to (0,1). This yields a coherent alternative to standard One-vs-Rest (OvR) curves and aligns with the observed tuning gains.