# A Geometric Perspective towards Neural Calibration via Sensitivity Decomposition

arXiv: https://arxiv.org/abs/2110.14577 · HTML: https://mlsanity.com/paper/2110.14577/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Large-Margin Softmax Loss for Convolutional Neural Networks](https://mlsanity.com/paper/1612.02295/) (2016)
- [Decoupled Networks](https://mlsanity.com/paper/1804.08071/) (2018)
- [Angular Visual Hardness](https://mlsanity.com/paper/1912.02279/) (2019)
- [Deep Feature Space: A Geometrical Perspective](https://mlsanity.com/paper/2007.00062/) (2020)

## Built on by (most cited first, 19 of 19)

- [Better Uncertainty Calibration via Proper Scores for Classification and Beyond](https://mlsanity.com/paper/2203.07835/) (2022)
- [Trainable Projected Gradient Method for Robust Fine-tuning](https://mlsanity.com/paper/2303.10720/) (2023)
- [Exploring Predictive Uncertainty and Calibration in NLP: A Study on the Impact of Method & Data Scarcity](https://mlsanity.com/paper/2210.15452/) (2022)
- [Open-Set Semi-Supervised Object Detection](https://mlsanity.com/paper/2208.13722/) (2022)
- [Calibrating Multimodal Learning](https://mlsanity.com/paper/2306.01265/) (2023)
- [Consistent and Asymptotically Unbiased Estimation of Proper Calibration Errors](https://mlsanity.com/paper/2312.08589/) (2023)
- [Exploring Covariate and Concept Shift for Detection and Calibration of Out-of-Distribution Data](https://mlsanity.com/paper/2110.15231/) (2021)
- [Approaching Test Time Augmentation in the Context of Uncertainty Calibration for Deep Neural Networks](https://mlsanity.com/paper/2304.05104/) (2023)
- [Neural Clamping: Joint Input Perturbation and Temperature Scaling for Neural Network Calibration](https://mlsanity.com/paper/2209.11604/) (2022)
- [Information-theoretic Analysis of Test Data Sensitivity in Uncertainty](https://mlsanity.com/paper/2307.12456/) (2023)
- [Optimizing Estimators of Squared Calibration Errors in Classification](https://mlsanity.com/paper/2410.07014/) (2024)
- [Layer-Wise Partitioning and Merging for Efficient and Scalable Deep Learning](https://mlsanity.com/paper/2207.11019/) (2022)
- [NCTV: Neural Clamping Toolkit and Visualization for Neural Network Calibration](https://mlsanity.com/paper/2211.16274/) (2022)
- [h-calibration: Rethinking Classifier Recalibration with Probabilistic Error-Bounded Objective](https://mlsanity.com/paper/2506.17968/) (2025)
- [Adaptive Calibrator Ensemble for Model Calibration under Distribution Shift](https://mlsanity.com/paper/2303.05331/) (2023)
- [A Theoretical and Practical Framework for Evaluating Uncertainty Calibration in Object Detection](https://mlsanity.com/paper/2309.00464/) (2023)
- [Excess risk analysis for epistemic uncertainty with application to variational inference](https://mlsanity.com/paper/2206.01606/) (2022)
- [Explanation-based Counterfactual Retraining(XCR): A Calibration Method for Black-box Models](https://mlsanity.com/paper/2206.11126/) (2022)
- [MixBoost: Improving the Robustness of Deep Neural Networks by Boosting Data Augmentation](https://mlsanity.com/paper/2212.04059/) (2022)

## Abstract (arXiv)

It is well known that vision classification models suffer from poor calibration in the face of data distribution shifts. In this paper, we take a geometric approach to this problem. We propose Geometric Sensitivity Decomposition (GSD) which decomposes the norm of a sample feature embedding and the angular similarity to a target classifier into an instance-dependent and an instance-independent component. The instance-dependent component captures the sensitive information about changes in the input while the instance-independent component represents the insensitive information serving solely to minimize the loss on the training dataset. Inspired by the decomposition, we analytically derive a simple extension to current softmax-linear models, which learns to disentangle the two components during training. On several common vision models, the disentangled model outperforms other calibration methods on standard calibration metrics in the face of out-of-distribution (OOD) data and corruption with significantly less complexity. Specifically, we surpass the current state of the art by 30.8% relative improvement on corrupted CIFAR100 in Expected Calibration Error. Code available at https://github.com/GT-RIPL/Geometric-Sensitivity-Decomposition.git.