# Entropic Out-of-Distribution Detection: Seamless Detection of Unknown Examples

arXiv: https://arxiv.org/abs/2006.04005 · HTML: https://mlsanity.com/paper/2006.04005/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2020.

## Built on by (most cited first, 16 of 16)

- [Block Selection Method for Using Feature Norm in Out-of-distribution Detection](https://mlsanity.com/paper/2212.02295/) (2022)
- [Provably Robust Detection of Out-of-distribution Data (almost) for free](https://mlsanity.com/paper/2106.04260/) (2021)
- [From Global to Local: Multi-scale Out-of-distribution Detection](https://mlsanity.com/paper/2308.10239/) (2023)
- [Reliable Few-shot Learning under Dual Noises](https://mlsanity.com/paper/2506.16330/) (2025)
- [Average of Pruning: Improving Performance and Stability of Out-of-Distribution Detection](https://mlsanity.com/paper/2303.01201/) (2023)
- [Enhanced Isotropy Maximization Loss: Seamless and High-Performance Out-of-Distribution Detection Simply Replacing the SoftMax Loss](https://mlsanity.com/paper/2105.14399/) (2021)
- [Revealing the Distributional Vulnerability of Discriminators by Implicit Generators](https://mlsanity.com/paper/2108.09976/) (2021)
- [Dense Out-of-Distribution Detection by Robust Learning on Synthetic Negative Data](https://mlsanity.com/paper/2112.12833/) (2021)
- [Fine-Grained Classification for Poisonous Fungi Identification with Transfer Learning](https://mlsanity.com/paper/2407.07492/) (2024)
- [Distinction Maximization Loss: Efficiently Improving Out-of-Distribution Detection and Uncertainty Estimation by Replacing the Loss and Calibrating](https://mlsanity.com/paper/2205.05874/) (2022)
- [Bi-discriminator Domain Adversarial Neural Networks with Class-Level Gradient Alignment](https://mlsanity.com/paper/2310.13959/) (2023)
- [Towards Robust Deep Learning using Entropic Losses](https://mlsanity.com/paper/2208.03566/) (2022)
- [POWN: Prototypical Open-World Node Classification](https://mlsanity.com/paper/2406.09926/) (2024)
- [Out-of-Distribution Detection with Overlap Index](https://mlsanity.com/paper/2412.06168/) (2024)
- [Confidence-Uncertainty Boundary Calibration for Bayesian Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/2602.11973/) (2026)
- [ECUASn: A family of metrics for principled evaluation of uncertainty-augmented systems](https://mlsanity.com/paper/2605.20490/) (2026)

## Abstract (arXiv)

In this paper, we argue that the unsatisfactory out-of-distribution (OOD) detection performance of neural networks is mainly due to the SoftMax loss anisotropy and propensity to produce low entropy probability distributions in disagreement with the principle of maximum entropy. Current out-of-distribution (OOD) detection approaches usually do not directly fix the SoftMax loss drawbacks, but rather build techniques to circumvent it. Unfortunately, those methods usually produce undesired side effects (e.g., classification accuracy drop, additional hyperparameters, slower inferences, and collecting extra data). In the opposite direction, we propose replacing SoftMax loss with a novel loss function that does not suffer from the mentioned weaknesses. The proposed IsoMax loss is isotropic (exclusively distance-based) and provides high entropy posterior probability distributions. Replacing the SoftMax loss by IsoMax loss requires no model or training changes. Additionally, the models trained with IsoMax loss produce as fast and energy-efficient inferences as those trained using SoftMax loss. Moreover, no classification accuracy drop is observed. The proposed method does not rely on outlier/background data, hyperparameter tuning, temperature calibration, feature extraction, metric learning, adversarial training, ensemble procedures, or generative models. Our experiments showed that IsoMax loss works as a seamless SoftMax loss drop-in replacement that significantly improves neural networks' OOD detection performance. Hence, it may be used as a baseline OOD detection approach to be combined with current or future OOD detection techniques to achieve even higher results.