# Interval Neural Networks: Uncertainty Scores

arXiv: https://arxiv.org/abs/2003.11566 · HTML: https://mlsanity.com/paper/2003.11566/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2020.

## Built on by (most cited first, 14 of 14)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [On the Posterior Distribution in Denoising: Application to Uncertainty Quantification](https://mlsanity.com/paper/2309.13598/) (2023)
- [Semantic uncertainty intervals for disentangled latent spaces](https://mlsanity.com/paper/2207.10074/) (2022)
- [Distributionally Robust Statistical Verification with Imprecise Neural Networks](https://mlsanity.com/paper/2308.14815/) (2023)
- [A Structured Review of Literature on Uncertainty in Machine Learning & Deep Learning](https://mlsanity.com/paper/2406.00332/) (2024)
- [Transitional Uncertainty with Layered Intermediate Predictions](https://mlsanity.com/paper/2405.17494/) (2024)
- [TEDL: A Two-stage Evidential Deep Learning Method for Classification Uncertainty Quantification](https://mlsanity.com/paper/2209.05522/) (2022)
- [Target-agnostic Source-free Domain Adaptation for Regression Tasks](https://mlsanity.com/paper/2312.00540/) (2023)
- [Introducing Interval Neural Networks for Uncertainty-Aware System Identification](https://mlsanity.com/paper/2504.18845/) (2025)
- [Selective classification using a robust meta-learning approach](https://mlsanity.com/paper/2212.05987/) (2022)
- [Boosting Verified Training for Robust Image Classifications via Abstraction](https://mlsanity.com/paper/2303.11552/) (2023)
- [Uncertainty Quantification for Image-based Traffic Prediction across Cities](https://mlsanity.com/paper/2308.06129/) (2023)
- [Beyond Prediction: Interval Neural Networks for Uncertainty-Aware System Identification](https://mlsanity.com/paper/2605.11460/) (2026)

## Abstract (arXiv)

We propose a fast, non-Bayesian method for producing uncertainty scores in the output of pre-trained deep neural networks (DNNs) using a data-driven interval propagating network. This interval neural network (INN) has interval valued parameters and propagates its input using interval arithmetic. The INN produces sensible lower and upper bounds encompassing the ground truth. We provide theoretical justification for the validity of these bounds. Furthermore, its asymmetric uncertainty scores offer additional, directional information beyond what Gaussian-based, symmetric variance estimation can provide. We find that noise in the data is adequately captured by the intervals produced with our method. In numerical experiments on an image reconstruction task, we demonstrate the practical utility of INNs as a proxy for the prediction error in comparison to two state-of-the-art uncertainty quantification methods. In summary, INNs produce fast, theoretically justified uncertainty scores for DNNs that are easy to interpret, come with added information and pose as improved error proxies - features that may prove useful in advancing the usability of DNNs especially in sensitive applications such as health care.