# Gradient-Regularized Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2404.12368 · HTML: https://mlsanity.com/paper/2404.12368/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 80 references that are in the map.
- First posted on arXiv 18 Apr 2024.

## Builds on (most cited first, 30 of 57)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Towards Open Set Deep Networks](https://mlsanity.com/paper/1511.06233/) (2015)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Delving into Out-of-Distribution Detection with Vision-Language Representations](https://mlsanity.com/paper/2211.13445/) (2022)
- [OpenOOD v1.5: Enhanced Benchmark for Out-of-Distribution Detection](https://mlsanity.com/paper/2306.09301/) (2023)
- [DICE: Leveraging Sparsification for Out-of-Distribution Detection](https://mlsanity.com/paper/2111.09805/) (2021)
- [Reducing Network Agnostophobia](https://mlsanity.com/paper/1811.04110/) (2018)
- [Generative OpenMax for Multi-Class Open Set Classification](https://mlsanity.com/paper/1707.07418/) (2017)
- [C2AE: Class Conditioned Auto-Encoder for Open-set Recognition](https://mlsanity.com/paper/1904.01198/) (2019)
- [OpenGAN: Open-Set Recognition via Open Data Generation](https://mlsanity.com/paper/2104.02939/) (2021)
- [ATOM: Robustifying Out-of-distribution Detection Using Outlier Mining](https://mlsanity.com/paper/2006.15207/) (2020)
- [Learning Open Set Network with Discriminative Reciprocal Points](https://mlsanity.com/paper/2011.00178/) (2020)
- [Unsupervised Out-of-Distribution Detection by Maximum Classifier Discrepancy](https://mlsanity.com/paper/1908.04951/) (2019)
- [POEM: Out-of-Distribution Detection with Posterior Sampling](https://mlsanity.com/paper/2206.13687/) (2022)
- [Exactly Computing the Local Lipschitz Constant of ReLU Networks](https://mlsanity.com/paper/2003.01219/) (2020)
- [MOOD: Multi-level Out-of-distribution Detection](https://mlsanity.com/paper/2104.14726/) (2021)
- [Mixture Outlier Exposure: Towards Out-of-Distribution Detection in Fine-grained Environments](https://mlsanity.com/paper/2106.03917/) (2021)

## Built on by (most cited first, 13 of 13)

- [Follow the Rules: Reasoning for Video Anomaly Detection with Large Language Models](https://mlsanity.com/paper/2407.10299/) (2024)
- [AdaSCALE: Adaptive Scaling for OOD Detection](https://mlsanity.com/paper/2503.08023/) (2025)
- [Open-Insect: Benchmarking Open-Set Recognition of Novel Species in Biodiversity Monitoring](https://mlsanity.com/paper/2503.01691/) (2025)
- [GradPCA: Leveraging NTK Alignment for Reliable Out-of-Distribution Detection](https://mlsanity.com/paper/2505.16017/) (2025)
- [LoD: Loss-difference OOD Detection by Intentionally Label-Noisifying Unlabeled Wild Data](https://mlsanity.com/paper/2505.12952/) (2025)
- [Kernel PCA for Out-of-Distribution Detection: Non-Linear Kernel Selection and Approximation](https://mlsanity.com/paper/2505.15284/) (2025)
- [Local Background Features Matter in Out-of-Distribution Detection](https://mlsanity.com/paper/2510.12259/) (2025)
- [TSRE: Channel-Aware Typical Set Refinement for Out-of-Distribution Detection](https://mlsanity.com/paper/2511.17636/) (2025)
- [Vision Also You Need: Navigating Out-of-Distribution Detection with Multimodal Large Language Model](https://mlsanity.com/paper/2601.14052/) (2026)
- [Cognitive Fusion of ZC Sequences and Time-Frequency Images for Out-of-Distribution Detection of Drone Signals](https://mlsanity.com/paper/2601.18326/) (2026)
- [A New Framework to Analyse the Distributional Robustness of Deep Neural Networks](https://mlsanity.com/paper/2605.21313/) (2026)
- [Modality-Aware Out-of-Distribution Detection for Multi-Modal Action Recognition](https://mlsanity.com/paper/2606.24404/) (2026)
- [Dynamics to decision: A mathematical theory of Lyapunov spectra and decision boundaries in deep classifiers](https://mlsanity.com/paper/2609.39190/) (2026)

## Abstract (arXiv)

One of the challenges for neural networks in real-life applications is the overconfident errors these models make when the data is not from the original training distribution. Addressing this issue is known as Out-of-Distribution (OOD) detection. Many state-of-the-art OOD methods employ an auxiliary dataset as a surrogate for OOD data during training to achieve improved performance. However, these methods fail to fully exploit the local information embedded in the auxiliary dataset. In this work, we propose the idea of leveraging the information embedded in the gradient of the loss function during training to enable the network to not only learn a desired OOD score for each sample but also to exhibit similar behavior in a local neighborhood around each sample. We also develop a novel energy-based sampling method to allow the network to be exposed to more informative OOD samples during the training phase. This is especially important when the auxiliary dataset is large. We demonstrate the effectiveness of our method through extensive experiments on several OOD benchmarks, improving the existing state-of-the-art FPR95 by 4% on our ImageNet experiment. We further provide a theoretical analysis through the lens of certified robustness and Lipschitz analysis to showcase the theoretical foundation of our work. Our code is available at https://github.com/o4lc/Greg-OOD.