On Uncertainty Calibration for Equivariant Functions
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Abstract (arXiv)
Data-sparse settings such as robotic manipulation, molecular physics, and galaxy morphology classification are some of the hardest domains for deep learning. For these problems, equivariant networks can help improve modeling across undersampled parts of the input space, and uncertainty estimation can guard against overconfidence. However, until now, the relationships between equivariance and model confidence, and more generally equivariance and model calibration, has yet to be studied. Since traditional classification and regression error terms show up in the definitions of calibration error, it is natural to suspect that previous work can be used to help understand the relationship between equivariance and calibration error. In this work, we present a theory relating equivariance to uncertainty estimation. By proving lower and upper bounds on uncertainty calibration errors (ECE and ENCE) under various equivariance conditions, we elucidate the generalization limits of equivariant models and illustrate how symmetry mismatch can result in miscalibration in both classification and regression. We complement our theoretical framework with numerical experiments that clarify the relationship between equivariance and uncertainty using a variety of real and simulated datasets, and we comment on trends with symmetry mismatch, group size, and aleatoric and epistemic uncertainties.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 73 of its 122 references that are in the map. First posted on arXiv 24 Oct 2025.
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73 of 122 references.
References · 73
- 2017On Calibration of Modern Neural Networkscited by 4,960
- 2018How Powerful are Graph Neural Networks?cited by 4,393
- 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,352
- 2015Variational Inference with Normalizing Flowscited by 2,170
- 2017Deep Setscited by 1,421
- 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
- 2019Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shiftcited by 1,287
- 2021Alias-Free Generative Adversarial Networkscited by 1,184
- 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
- 2021E(n) Equivariant Graph Neural Networkscited by 965
- 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 913
- 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
38 more
- 2018QT-Opt: Scalable Deep Reinforcement Learning for Vision-Based Robotic Manipulationcited by 743
- 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
- 2021Implicit Behavioral Cloningcited by 452
- 2019Measuring Calibration in Deep Learningcited by 446
- 2019General E(2)-Equivariant Steerable CNNscited by 446
- 2018Accurate Uncertainties for Deep Learning Using Calibrated Regressioncited by 422
- 2019Making Convolutional Networks Shift-Invariant Againcited by 391
- 2018Invertible Residual Networkscited by 365
- 2019Deep Evidential Regressioncited by 355
- 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
- 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 264
- 2019Residual Flows for Invertible Generative Modelingcited by 257
- 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
- 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 204
- 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 171
- 2019Evaluating model calibration in classificationcited by 168
- 2019On the Universality of Invariant Networkscited by 152
- 2018Universal approximations of invariant maps by neural networkscited by 127
- 2022Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?cited by 125
- 2021Epistemic Neural Networkscited by 120
- 2022On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networkscited by 120
- 2020On Learning Sets of Symmetric Elementscited by 98
- 2019Evaluating and Calibrating Uncertainty Prediction in Regression Taskscited by 87
- 2022A Deeper Look into Aleatoric and Epistemic Uncertainty Disentanglementcited by 87
- 2021Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimationcited by 71
- 2022Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisationcited by 66
- 2022Benchmarking Graphormer on Large-Scale Molecular Modeling Datasetscited by 64
- 2021Equivariant Q Learning in Spatial Action Spacescited by 62
- 2023Swallowing the Bitter Pill: Simplified Scalable Conformer Generationcited by 56
- 2022The Lie Derivative for Measuring Learned Equivariancecited by 54
- 2024Does equivariance matter at scale?cited by 52
- 2023Sampling-Based Accuracy Testing of Posterior Estimators for General Inferencecited by 46
- 2023Approximation-Generalization Trade-offs under (Approximate) Group Equivariancecited by 46
- 2024Equivariant Frames and the Impossibility of Continuous Canonicalizationcited by 43
- 2022On-Robot Learning With Equivariant Modelscited by 42
- 2022The Unreasonable Effectiveness of Deep Evidential Regressioncited by 40
- 2022Edge Grasp Network: A Graph-Based SE(3)-invariant Approach to Grasp Detectioncited by 35
- 2024Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?cited by 35
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