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<p>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.</p>

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GPify: Leveraging the Combined Strength of Normalizing Flow and Softmax For an Out-of-Distribution aware Confidence Score

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月9日

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  • Simon Kristoffersson Lind,
  • Rudolph Triebel,
  • Volker Krüger

摘要

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.