# SPACR: Single-Pass Adaptive Training of Uncertainty-Aware Conformal Regressors

arXiv: https://arxiv.org/abs/2606.10734 · HTML: https://mlsanity.com/paper/2606.10734/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 14 of 14)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Uncertainty Quantification with Statistical Guarantees in End-to-End Autonomous Driving Control](https://mlsanity.com/paper/1909.09884/) (2019)
- [Optimized conformal classification using gradient descent approximation](https://mlsanity.com/paper/2105.11255/) (2021)
- [Training conformal predictors](https://mlsanity.com/paper/2005.07037/) (2020)
- [Reliable Prediction Intervals with Regression Neural Networks](https://mlsanity.com/paper/2312.09606/) (2023)
- [Conformal Risk Training: End-to-End Optimization of Conformal Risk Control](https://mlsanity.com/paper/2510.08748/) (2025)
- [Reliable Prediction Intervals with Directly Optimized Inductive Conformal Regression for Deep Learning](https://mlsanity.com/paper/2302.00872/) (2023)
- [Get Your Embedding Space in Order: Domain-Adaptive Regression for Forest Monitoring](https://mlsanity.com/paper/2405.00514/) (2024)

## Abstract (arXiv)

Conformal Prediction (CP) provides robust uncertainty guarantees for predictive models, but is typically applied post hoc, which misaligns model training with the conformal goal of producing efficient (i.e., narrow) intervals. We propose SPACR (Single-Pass Adaptive Conformal Regressor), a novel method for directly training uncertainty-aware regressors within a differentiable loss. SPACR jointly optimizes accuracy, efficiency, and validity without batch-splitting or a predefined confidence level during training. As a result, a single SPACR model yields valid prediction intervals at multiple confidence levels during inference, avoiding the costly retraining required by methods like Directly Optimized Inductive Conformal Regression (DOICR). Experiments on diverse tabular and image datasets show that SPACR consistently gives tighter intervals and better coverage-efficiency trade-offs compared to standard CP and DOICR, while significantly reducing computational costs relative to retraining-dependent baselines.