# Deep Neural Networks with Ordinal Loss for Medical Applications

arXiv: https://arxiv.org/abs/2606.25769 · HTML: https://mlsanity.com/paper/2606.25769/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 24 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Deep Learning for Medical Image Analysis](https://mlsanity.com/paper/1708.08987/) (2017)
- [Rank consistent ordinal regression for neural networks with application to age estimation](https://mlsanity.com/paper/1901.07884/) (2019)
- [Making Better Mistakes: Leveraging Class Hierarchies with Deep Networks](https://mlsanity.com/paper/1912.09393/) (2019)
- [End-to-end Training for Whole Image Breast Cancer Diagnosis using An All Convolutional Design](https://mlsanity.com/paper/1711.05775/) (2017)
- [Deep Neural Networks for Rank-Consistent Ordinal Regression Based On Conditional Probabilities](https://mlsanity.com/paper/2111.08851/) (2021)
- [Unimodal probability distributions for deep ordinal classification](https://mlsanity.com/paper/1705.05278/) (2017)
- [DeepLung: 3D Deep Convolutional Nets for Automated Pulmonary Nodule Detection and Classification](https://mlsanity.com/paper/1709.05538/) (2017)
- [An ordinal CNN approach for the assessment of neurological damage in Parkinson's disease patients](https://mlsanity.com/paper/2106.05230/) (2021)

## Abstract (arXiv)

In many prediction problems in medical applications, target labels exhibit an inherent ordinal structure, where class ordering reflects clinically meaningful severity levels. The cost associated with misclassification is often non-uniform and asymmetric, as errors between distant ordinal categories may have substantially more severe consequences than errors between adjacent ones, and overestimating disease severity may have different clinical implications than underestimating it. Traditional loss functions such as multi-class cross-entropy treat all misclassifications equally and fail to incorporate this ordering information. Recent advances in ordinal regression aim to address this limitation by integrating rank-based structures into deep learning models. In this work, we introduce the Ordinal Cross-Entropy (OCE) framework, a general and architecture-independent approach for learning from ordinal data. The proposed method extends the standard cross-entropy formulation to account for misclassification severity through an ordinal cost matrix while preserving the probabilistic interpretation and optimization benefits of the conventional loss. We provide a theoretical analysis of the OCE gradient behavior and show that it yields smoother optimization dynamics and improved ordinal consistency. Experiments on benchmark datasets show that our method achieves lower prediction error costs and better calibration compared to existing state-of-the-art ordinal approaches, establishing OCE as a simple yet effective solution for ordinal regression in deep neural networks.