# Multi-Head Multi-Loss Model Calibration

arXiv: https://arxiv.org/abs/2303.01099 · HTML: https://mlsanity.com/paper/2303.01099/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 33 references that are in the map.
- First posted on arXiv 2 Mar 2023.

## Builds on (most cited first, 25 of 25)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Deeply-Supervised Nets](https://mlsanity.com/paper/1409.5185/) (2014)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Calibrating Deep Neural Networks using Focal Loss](https://mlsanity.com/paper/2002.09437/) (2020)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysis](https://mlsanity.com/paper/2010.14925/) (2020)
- [Why M Heads are Better than One: Training a Diverse Ensemble of Deep Networks](https://mlsanity.com/paper/1511.06314/) (2015)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [Local Temperature Scaling for Probability Calibration](https://mlsanity.com/paper/2008.05105/) (2020)
- [The Devil is in the Margin: Margin-based Label Smoothing for Network Calibration](https://mlsanity.com/paper/2111.15430/) (2021)
- [A Deeper Look into Aleatoric and Epistemic Uncertainty Disentanglement](https://mlsanity.com/paper/2204.09308/) (2022)
- [Understanding metric-related pitfalls in image analysis validation](https://mlsanity.com/paper/2302.01790/) (2023)
- [A Stitch in Time Saves Nine: A Train-Time Regularizing Loss for Improved Neural Network Calibration](https://mlsanity.com/paper/2203.13834/) (2022)
- [Hard Sample Aware Noise Robust Learning for Histopathology Image Classification](https://mlsanity.com/paper/2112.03694/) (2021)
- [Improved Trainable Calibration Method for Neural Networks on Medical Imaging Classification](https://mlsanity.com/paper/2009.04057/) (2020)
- [Spatially Varying Label Smoothing: Capturing Uncertainty from Expert Annotations](https://mlsanity.com/paper/2104.05788/) (2021)
- [Test-time Adaptation with Calibration of Medical Image Classification Nets for Label Distribution Shift](https://mlsanity.com/paper/2207.00769/) (2022)
- [Orthogonal Ensemble Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/2105.10827/) (2021)
- [Analysis and Comparison of Classification Metrics](https://mlsanity.com/paper/2209.05355/) (2022)
- [Failure Detection in Medical Image Classification: A Reality Check and Benchmarking Testbed](https://mlsanity.com/paper/2205.14094/) (2022)

## Built on by (most cited first, 8 of 8)

- [Dynamically Scaled Temperature in Self-Supervised Contrastive Learning](https://mlsanity.com/paper/2308.01140/) (2023)
- [h-calibration: Rethinking Classifier Recalibration with Probabilistic Error-Bounded Objective](https://mlsanity.com/paper/2506.17968/) (2025)
- [Data-Centric Label Smoothing for Explainable Glaucoma Screening from Eye Fundus Images](https://mlsanity.com/paper/2406.03903/) (2024)
- [Beyond H&E: Unlocking Pathological Insights with Polarization Imaging](https://mlsanity.com/paper/2503.05933/) (2025)
- [Multi-Rater Calibrated Segmentation Models](https://mlsanity.com/paper/2605.02437/) (2026)
- [ClinReadNet: A clinical reading-inspired network for low-dose abdominal CT image quality assessment](https://mlsanity.com/paper/2606.10372/) (2026)
- [Covariance Last-Layer Ensembles: Function-Space Diversity for Efficient Uncertainty Quantification](https://mlsanity.com/paper/2607.23856/) (2026)
- [Uncertainty quantification for trustworthy deep learning: Methods and measures](https://mlsanity.com/paper/2607.28248/) (2026)

## Abstract (arXiv)

Delivering meaningful uncertainty estimates is essential for a successful deployment of machine learning models in the clinical practice. A central aspect of uncertainty quantification is the ability of a model to return predictions that are well-aligned with the actual probability of the model being correct, also known as model calibration. Although many methods have been proposed to improve calibration, no technique can match the simple, but expensive approach of training an ensemble of deep neural networks. In this paper we introduce a form of simplified ensembling that bypasses the costly training and inference of deep ensembles, yet it keeps its calibration capabilities. The idea is to replace the common linear classifier at the end of a network by a set of heads that are supervised with different loss functions to enforce diversity on their predictions. Specifically, each head is trained to minimize a weighted Cross-Entropy loss, but the weights are different among the different branches. We show that the resulting averaged predictions can achieve excellent calibration without sacrificing accuracy in two challenging datasets for histopathological and endoscopic image classification. Our experiments indicate that Multi-Head Multi-Loss classifiers are inherently well-calibrated, outperforming other recent calibration techniques and even challenging Deep Ensembles' performance. Code to reproduce our experiments can be found at urlhttps://github.com/agaldran/mhmlcalibration .