GPify : leveraging the combined strength of normalizing flow and softmax for an out-of-distribution aware confidence score
Kristoffersson Lind, Simon LU ; Triebel, Rudolph and Krueger, Volker LU
(2026)
In International Journal of Computer Vision
134.
- Abstract
- In order for any learning-based model to be considered reliable, it needs a well-behaved uncertainty or confidence estimate. Most modern neural networks do produce a confidence estimate in the form of their softmax output probability. However, the softmax probability is invalid for out-of-distribution data. Gaussian processes are known to produce a well-behaved confidence estimate that is aware of out-of-distribution samples. Inspired by Gaussian processes, we propose GPify, which combines the softmax probability with a Normalizing Flow in order to add out-of-distribution awareness to the confidence estimate from a neural network. The resulting confidence from GPify is an uncertainty measure that is interpretable and intuitive, while also... (More)
- In order for any learning-based model to be considered reliable, it needs a well-behaved uncertainty or confidence estimate. Most modern neural networks do produce a confidence estimate in the form of their softmax output probability. However, the softmax probability is invalid for out-of-distribution data. Gaussian processes are known to produce a well-behaved confidence estimate that is aware of out-of-distribution samples. Inspired by Gaussian processes, we propose GPify, which combines the softmax probability with a Normalizing Flow in order to add out-of-distribution awareness to the confidence estimate from a neural network. The resulting confidence from GPify is an uncertainty measure that is interpretable and intuitive, while also being probabilistically sound. We evaluate GPify in a selective classification framework, and conclude that it achieves comparable performance to state-of-the-art methods. In addition, we show that GPify has capabilities for detecting adversarial examples, which is a direct improvement over softmax confidence. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/a4e89db4-058c-4db4-acc4-1e538b98be19
- author
- Kristoffersson Lind, Simon
LU
; Triebel, Rudolph
and Krueger, Volker
LU
- organization
- publishing date
- 2026
- type
- Contribution to journal
- publication status
- published
- subject
- in
- International Journal of Computer Vision
- volume
- 134
- article number
- 185
- pages
- 12 pages
- publisher
- Springer
- external identifiers
-
- scopus:105033709285
- ISSN
- 1573-1405
- language
- English
- LU publication?
- yes
- id
- a4e89db4-058c-4db4-acc4-1e538b98be19
- alternative location
- https://link.springer.com/article/10.1007/s11263-026-02794-3
- date added to LUP
- 2026-04-10 14:08:14
- date last changed
- 2026-05-12 16:36:26
@article{a4e89db4-058c-4db4-acc4-1e538b98be19,
abstract = {{In order for any learning-based model to be considered reliable, it needs a well-behaved uncertainty or confidence estimate. Most modern neural networks do produce a confidence estimate in the form of their softmax output probability. However, the softmax probability is invalid for out-of-distribution data. Gaussian processes are known to produce a well-behaved confidence estimate that is aware of out-of-distribution samples. Inspired by Gaussian processes, we propose GPify, which combines the softmax probability with a Normalizing Flow in order to add out-of-distribution awareness to the confidence estimate from a neural network. The resulting confidence from GPify is an uncertainty measure that is interpretable and intuitive, while also being probabilistically sound. We evaluate GPify in a selective classification framework, and conclude that it achieves comparable performance to state-of-the-art methods. In addition, we show that GPify has capabilities for detecting adversarial examples, which is a direct improvement over softmax confidence.}},
author = {{Kristoffersson Lind, Simon and Triebel, Rudolph and Krueger, Volker}},
issn = {{1573-1405}},
language = {{eng}},
publisher = {{Springer}},
series = {{International Journal of Computer Vision}},
title = {{GPify : leveraging the combined strength of normalizing flow and softmax for an out-of-distribution aware confidence score}},
url = {{https://link.springer.com/article/10.1007/s11263-026-02794-3}},
volume = {{134}},
year = {{2026}},
}