# Proximity-Informed Calibration for Deep Neural Networks

arXiv: https://arxiv.org/abs/2306.04590 · HTML: https://mlsanity.com/paper/2306.04590/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 49 references that are in the map.
- First posted on arXiv 7 Jun 2023.

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

- [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)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [BEiT: BERT Pre-Training of Image Transformers](https://mlsanity.com/paper/2106.08254/) (2021)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [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)
- [XCiT: Cross-Covariance Image Transformers](https://mlsanity.com/paper/2106.09681/) (2021)
- [To Trust Or Not To Trust A Classifier](https://mlsanity.com/paper/1805.11783/) (2018)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Benchmarking Representation Learning for Natural World Image Collections](https://mlsanity.com/paper/2103.16483/) (2021)
- [Parameterized Temperature Scaling for Boosting the Expressive Power in Post-Hoc Uncertainty Calibration](https://mlsanity.com/paper/2102.12182/) (2021)
- ["The Human Body is a Black Box": Supporting Clinical Decision-Making with Deep Learning](https://mlsanity.com/paper/1911.08089/) (2019)
- [Calibrated and Sharp Uncertainties in Deep Learning via Density Estimation](https://mlsanity.com/paper/2112.07184/) (2021)
- [Beyond calibration: estimating the grouping loss of modern neural networks](https://mlsanity.com/paper/2210.16315/) (2022)
- [Multi-Class Uncertainty Calibration via Mutual Information Maximization-based Binning](https://mlsanity.com/paper/2006.13092/) (2020)
- [Taking a Step Back with KCal: Multi-Class Kernel-Based Calibration for Deep Neural Networks](https://mlsanity.com/paper/2202.07679/) (2022)
- [Birds of a Feather Trust Together: Knowing When to Trust a Classifier via Adaptive Neighborhood Aggregation](https://mlsanity.com/paper/2211.16466/) (2022)

## Built on by (most cited first, 18 of 18)

- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [SteerConf: Steering LLMs for Confidence Elicitation](https://mlsanity.com/paper/2503.02863/) (2025)
- [Your Pre-trained LLM is Secretly an Unsupervised Confidence Calibrator](https://mlsanity.com/paper/2505.16690/) (2025)
- [Open-Vocabulary Calibration for Fine-tuned CLIP](https://mlsanity.com/paper/2402.04655/) (2024)
- [Confidence Calibration of Classifiers with Many Classes](https://mlsanity.com/paper/2411.02988/) (2024)
- [Beyond Probability Partitions: Calibrating Neural Networks with Semantic Aware Grouping](https://mlsanity.com/paper/2306.04985/) (2023)
- [Understanding and Mitigating Miscalibration in Prompt Tuning for Vision-Language Models](https://mlsanity.com/paper/2410.02681/) (2024)
- [Optimizing Calibration by Gaining Aware of Prediction Correctness](https://mlsanity.com/paper/2404.13016/) (2024)
- [Consistency Calibration: Improving Uncertainty Calibration via Consistency among Perturbed Neighbors](https://mlsanity.com/paper/2410.12295/) (2024)
- [Enhancing Out-of-Distribution Detection with Extended Logit Normalization](https://mlsanity.com/paper/2504.11434/) (2025)
- [Sample Margin-Aware Recalibration of Temperature Scaling](https://mlsanity.com/paper/2506.23492/) (2025)
- [Towards Unveiling Predictive Uncertainty Vulnerabilities in the Context of the Right to Be Forgotten](https://mlsanity.com/paper/2508.07458/) (2025)
- [Weighted Risk Invariance: Domain Generalization under Invariant Feature Shift](https://mlsanity.com/paper/2407.18428/) (2024)
- [Beyond One-Hot Labels: Semantic Mixing for Model Calibration](https://mlsanity.com/paper/2504.13548/) (2025)
- [Multiclass Local Calibration with the Jensen-Shannon Distance](https://mlsanity.com/paper/2510.26566/) (2025)
- [Quantile Adaptive Temperature Scaling for Confidence Calibration](https://mlsanity.com/paper/2606.21749/) (2026)
- [Model-Free Local Recalibration of Neural Networks](https://mlsanity.com/paper/2403.05756/) (2024)
- [Divide et Calibra: Multiclass Local Calibration via Vector Quantization](https://mlsanity.com/paper/2605.21060/) (2026)

## Abstract (arXiv)

Confidence calibration is central to providing accurate and interpretable uncertainty estimates, especially under safety-critical scenarios. However, we find that existing calibration algorithms often overlook the issue of *proximity bias*, a phenomenon where models tend to be more overconfident in low proximity data (i.e., data lying in the sparse region of the data distribution) compared to high proximity samples, and thus suffer from inconsistent miscalibration across different proximity samples. We examine the problem over 504 pretrained ImageNet models and observe that: 1) Proximity bias exists across a wide variety of model architectures and sizes; 2) Transformer-based models are relatively more susceptible to proximity bias than CNN-based models; 3) Proximity bias persists even after performing popular calibration algorithms like temperature scaling; 4) Models tend to overfit more heavily on low proximity samples than on high proximity samples. Motivated by the empirical findings, we propose ProCal, a plug-and-play algorithm with a theoretical guarantee to adjust sample confidence based on proximity. To further quantify the effectiveness of calibration algorithms in mitigating proximity bias, we introduce proximity-informed expected calibration error (PIECE) with theoretical analysis. We show that ProCal is effective in addressing proximity bias and improving calibration on balanced, long-tail, and distribution-shift settings under four metrics over various model architectures. We believe our findings on proximity bias will guide the development of *fairer and better-calibrated* models, contributing to the broader pursuit of trustworthy AI. Our code is available at: https://github.com/MiaoXiong2320/ProximityBias-Calibration.