# Balancing Two Classifiers via A Simplex ETF Structure for Model Calibration

arXiv: https://arxiv.org/abs/2504.10007 · HTML: https://mlsanity.com/paper/2504.10007/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 54 references that are in the map.
- First posted on arXiv 14 Apr 2025.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [YOLOv3: An Incremental Improvement](https://mlsanity.com/paper/1804.02767/) (2018)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [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)
- [Neural Collapse Inspired Feature-Classifier Alignment for Few-Shot Class Incremental Learning](https://mlsanity.com/paper/2302.03004/) (2023)
- [Extended Unconstrained Features Model for Exploring Deep Neural Collapse](https://mlsanity.com/paper/2202.08087/) (2022)
- [Inducing Neural Collapse in Imbalanced Learning: Do We Really Need a Learnable Classifier at the End of Deep Neural Network?](https://mlsanity.com/paper/2203.09081/) (2022)
- [The Devil is in the Margin: Margin-based Label Smoothing for Network Calibration](https://mlsanity.com/paper/2111.15430/) (2021)
- [End-to-end Training for Whole Image Breast Cancer Diagnosis using An All Convolutional Design](https://mlsanity.com/paper/1711.05775/) (2017)
- [Imbalance Trouble: Revisiting Neural-Collapse Geometry](https://mlsanity.com/paper/2208.05512/) (2022)
- [Posterior calibration and exploratory analysis for natural language processing models](https://mlsanity.com/paper/1508.05154/) (2015)
- [Neural Collapse Inspired Attraction-Repulsion-Balanced Loss for Imbalanced Learning](https://mlsanity.com/paper/2204.08735/) (2022)
- [Sequential Deep Learning for Credit Risk Monitoring with Tabular Financial Data](https://mlsanity.com/paper/2012.15330/) (2020)
- [Dual Focal Loss for Calibration](https://mlsanity.com/paper/2305.13665/) (2023)
- [AdaFocal: Calibration-aware Adaptive Focal Loss](https://mlsanity.com/paper/2211.11838/) (2022)
- [Machine learning based disease diagnosis: A comprehensive review](https://mlsanity.com/paper/2112.15538/) (2021)
- [Understanding and Improving Transfer Learning of Deep Models via Neural Collapse](https://mlsanity.com/paper/2212.12206/) (2022)

## Built on by (most cited first, 3 of 3)

- [Towards Understanding The Calibration Benefits of Sharpness-Aware Minimization](https://mlsanity.com/paper/2505.23866/) (2025)
- [Deep Neural Network Calibration by Reducing Classifier Shift with Stochastic Masking](https://mlsanity.com/paper/2508.09116/) (2025)
- [Bayesian Sparse Low-Rank Adaptation for Large Language Model Uncertainty Estimation](https://mlsanity.com/paper/2607.02182/) (2026)

## Abstract (arXiv)

In recent years, deep neural networks (DNNs) have demonstrated state-of-the-art performance across various domains. However, despite their success, they often face calibration issues, particularly in safety-critical applications such as autonomous driving and healthcare, where unreliable predictions can have serious consequences. Recent research has started to improve model calibration from the view of the classifier. However, the exploration of designing the classifier to solve the model calibration problem is insufficient. Let alone most of the existing methods ignore the calibration errors arising from underconfidence. In this work, we propose a novel method by balancing learnable and ETF classifiers to solve the overconfidence or underconfidence problem for model Calibration named BalCAL. By introducing a confidence-tunable module and a dynamic adjustment method, we ensure better alignment between model confidence and its true accuracy. Extensive experimental validation shows that ours significantly improves model calibration performance while maintaining high predictive accuracy, outperforming existing techniques. This provides a novel solution to the calibration challenges commonly encountered in deep learning.