# Towards Unbiased Calibration using Meta-Regularization

arXiv: https://arxiv.org/abs/2303.15057 · HTML: https://mlsanity.com/paper/2303.15057/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 50 references that are in the map.
- First posted on arXiv 27 Mar 2023.

## Builds on (most cited first, 29 of 29)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [Regularizing Neural Networks by Penalizing Confident Output Distributions](https://mlsanity.com/paper/1701.06548/) (2017)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [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)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Improving model calibration with accuracy versus uncertainty optimization](https://mlsanity.com/paper/2012.07923/) (2020)
- [Soft Calibration Objectives for Neural Networks](https://mlsanity.com/paper/2108.00106/) (2021)
- [The Devil is in the Margin: Margin-based Label Smoothing for Network Calibration](https://mlsanity.com/paper/2111.15430/) (2021)
- [Scalable Gradient-Based Tuning of Continuous Regularization Hyperparameters](https://mlsanity.com/paper/1511.06727/) (2015)
- [A Stitch in Time Saves Nine: A Train-Time Regularizing Loss for Improved Neural Network Calibration](https://mlsanity.com/paper/2203.13834/) (2022)
- [Well-calibrated Model Uncertainty with Temperature Scaling for Dropout Variational Inference](https://mlsanity.com/paper/1909.13550/) (2019)
- [Calibrated Interpretation: Confidence Estimation in Semantic Parsing](https://mlsanity.com/paper/2211.07443/) (2022)
- [AdaFocal: Calibration-aware Adaptive Focal Loss](https://mlsanity.com/paper/2211.11838/) (2022)
- [Meta-Calibration: Learning of Model Calibration Using Differentiable Expected Calibration Error](https://mlsanity.com/paper/2106.09613/) (2021)
- [Attended Temperature Scaling: A Practical Approach for Calibrating Deep Neural Networks](https://mlsanity.com/paper/1810.11586/) (2018)
- [Calibrating Deep Neural Networks using Explicit Regularisation and Dynamic Data Pruning](https://mlsanity.com/paper/2212.10005/) (2022)

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

- [Bag of Coins: A Statistical Probe into Neural Confidence Structures](https://mlsanity.com/paper/2507.19774/) (2025)

## Abstract (arXiv)

Model miscalibration has been frequently identified in modern deep neural networks. Recent work aims to improve model calibration directly through a differentiable calibration proxy. However, the calibration produced is often biased due to the binning mechanism. In this work, we propose to learn better-calibrated models via meta-regularization, which has two components: (1) gamma network (gamma-net), a meta learner that outputs sample-wise gamma values (continuous variable) for Focal loss for regularizing the backbone network; (2) smooth expected calibration error (SECE), a Gaussian-kernel based, unbiased, and differentiable surrogate to ECE that enables the smooth optimization of gamma-Net. We evaluate the effectiveness of the proposed approach in regularizing neural networks towards improved and unbiased calibration on three computer vision datasets. We empirically demonstrate that: (a) learning sample-wise gamma as continuous variables can effectively improve calibration; (b) SECE smoothly optimizes gamma-net towards unbiased and robust calibration with respect to the binning schemes; and (c) the combination of gamma-net and SECE achieves the best calibration performance across various calibration metrics while retaining very competitive predictive performance as compared to multiple recently proposed methods.