# Calibration of Neural Networks using Splines

arXiv: https://arxiv.org/abs/2006.12800 · HTML: https://mlsanity.com/paper/2006.12800/

## Key facts

- Cited by 97 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2020.

## Built on by (most cited first, 30 of 97)

- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Soft Calibration Objectives for Neural Networks](https://mlsanity.com/paper/2108.00106/) (2021)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Stop Measuring Calibration When Humans Disagree](https://mlsanity.com/paper/2210.16133/) (2022)
- [Better Uncertainty Calibration via Proper Scores for Classification and Beyond](https://mlsanity.com/paper/2203.07835/) (2022)
- [Smooth ECE: Principled Reliability Diagrams via Kernel Smoothing](https://mlsanity.com/paper/2309.12236/) (2023)
- [A Close Look into the Calibration of Pre-trained Language Models](https://mlsanity.com/paper/2211.00151/) (2022)
- [A Unifying Theory of Distance from Calibration](https://mlsanity.com/paper/2211.16886/) (2022)
- [Parameterized Temperature Scaling for Boosting the Expressive Power in Post-Hoc Uncertainty Calibration](https://mlsanity.com/paper/2102.12182/) (2021)
- [A Consistent and Differentiable Lp Canonical Calibration Error Estimator](https://mlsanity.com/paper/2210.07810/) (2022)
- [Top-label calibration and multiclass-to-binary reductions](https://mlsanity.com/paper/2107.08353/) (2021)
- [A Closer Look at the Robustness of Contrastive Language-Image Pre-Training (CLIP)](https://mlsanity.com/paper/2402.07410/) (2024)
- [Rethinking Confidence Calibration for Failure Prediction](https://mlsanity.com/paper/2303.02970/) (2023)
- [Uncertainty in Language Models: Assessment through Rank-Calibration](https://mlsanity.com/paper/2404.03163/) (2024)
- [What Makes Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/2210.06391/) (2022)
- [Towards Calibrated Robust Fine-Tuning of Vision-Language Models](https://mlsanity.com/paper/2311.01723/) (2023)
- [Dual Focal Loss for Calibration](https://mlsanity.com/paper/2305.13665/) (2023)
- [Metrics of calibration for probabilistic predictions](https://mlsanity.com/paper/2205.09680/) (2022)
- [Beyond calibration: estimating the grouping loss of modern neural networks](https://mlsanity.com/paper/2210.16315/) (2022)
- [AdaFocal: Calibration-aware Adaptive Focal Loss](https://mlsanity.com/paper/2211.11838/) (2022)
- [Block Selection Method for Using Feature Norm in Out-of-distribution Detection](https://mlsanity.com/paper/2212.02295/) (2022)
- [Local Calibration: Metrics and Recalibration](https://mlsanity.com/paper/2102.10809/) (2021)
- [Confidence and Dispersity Speak: Characterising Prediction Matrix for Unsupervised Accuracy Estimation](https://mlsanity.com/paper/2302.01094/) (2023)
- [An Empirical Study Into What Matters for Calibrating Vision-Language Models](https://mlsanity.com/paper/2402.07417/) (2024)
- [Understanding Model Calibration -- A gentle introduction and visual exploration of calibration and the expected calibration error (ECE)](https://mlsanity.com/paper/2501.19047/) (2025)
- [Intermediate Layers Matter in Momentum Contrastive Self Supervised Learning](https://mlsanity.com/paper/2110.14805/) (2021)
- [RankMixup: Ranking-Based Mixup Training for Network Calibration](https://mlsanity.com/paper/2308.11990/) (2023)
- [FairCal: Fairness Calibration for Face Verification](https://mlsanity.com/paper/2106.03761/) (2021)
- [Reliability in Semantic Segmentation: Are We on the Right Track?](https://mlsanity.com/paper/2303.11298/) (2023)
- [Interpreting Predictive Probabilities: Model Confidence or Human Label Variation?](https://mlsanity.com/paper/2402.16102/) (2024)

## Abstract (arXiv)

Calibrating neural networks is of utmost importance when employing them in safety-critical applications where the downstream decision making depends on the predicted probabilities. Measuring calibration error amounts to comparing two empirical distributions. In this work, we introduce a binning-free calibration measure inspired by the classical Kolmogorov-Smirnov (KS) statistical test in which the main idea is to compare the respective cumulative probability distributions. From this, by approximating the empirical cumulative distribution using a differentiable function via splines, we obtain a recalibration function, which maps the network outputs to actual (calibrated) class assignment probabilities. The spine-fitting is performed using a held-out calibration set and the obtained recalibration function is evaluated on an unseen test set. We tested our method against existing calibration approaches on various image classification datasets and our spline-based recalibration approach consistently outperforms existing methods on KS error as well as other commonly used calibration measures. Our Code is available at https://github.com/kartikgupta-at-anu/spline-calibration.