# Low-Dimensional Gradient Helps Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2310.17163 · HTML: https://mlsanity.com/paper/2310.17163/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 77 references that are in the map.
- First posted on arXiv 26 Oct 2023.

## Builds on (most cited first, 30 of 48)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [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)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [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)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [Mitigating Neural Network Overconfidence with Logit Normalization](https://mlsanity.com/paper/2205.09310/) (2022)
- [Gradient Descent Happens in a Tiny Subspace](https://mlsanity.com/paper/1812.04754/) (2018)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [TurkerGaze: Crowdsourcing Saliency with Webcam based Eye Tracking](https://mlsanity.com/paper/1504.06755/) (2015)
- [How to Exploit Hyperspherical Embeddings for Out-of-Distribution Detection?](https://mlsanity.com/paper/2203.04450/) (2022)
- [POEM: Out-of-Distribution Detection with Posterior Sampling](https://mlsanity.com/paper/2206.13687/) (2022)

## Built on by (most cited first, 6 of 6)

- [Kernel PCA for Out-of-Distribution Detection](https://mlsanity.com/paper/2402.02949/) (2024)
- [Pursuing Feature Separation based on Neural Collapse for Out-of-Distribution Detection](https://mlsanity.com/paper/2405.17816/) (2024)
- [Controlling Neural Collapse Enhances Out-of-Distribution Detection and Transfer Learning](https://mlsanity.com/paper/2502.10691/) (2025)
- [GradPCA: Leveraging NTK Alignment for Reliable Out-of-Distribution Detection](https://mlsanity.com/paper/2505.16017/) (2025)
- [Kernel PCA for Out-of-Distribution Detection: Non-Linear Kernel Selection and Approximation](https://mlsanity.com/paper/2505.15284/) (2025)
- [General OOD Detection via Model-aware and Subspace-aware Variable Priority](https://mlsanity.com/paper/2512.13003/) (2025)

## Abstract (arXiv)

Detecting out-of-distribution (OOD) samples is essential for ensuring the reliability of deep neural networks (DNNs) in real-world scenarios. While previous research has predominantly investigated the disparity between in-distribution (ID) and OOD data through forward information analysis, the discrepancy in parameter gradients during the backward process of DNNs has received insufficient attention. Existing studies on gradient disparities mainly focus on the utilization of gradient norms, neglecting the wealth of information embedded in gradient directions. To bridge this gap, in this paper, we conduct a comprehensive investigation into leveraging the entirety of gradient information for OOD detection. The primary challenge arises from the high dimensionality of gradients due to the large number of network parameters. To solve this problem, we propose performing linear dimension reduction on the gradient using a designated subspace that comprises principal components. This innovative technique enables us to obtain a low-dimensional representation of the gradient with minimal information loss. Subsequently, by integrating the reduced gradient with various existing detection score functions, our approach demonstrates superior performance across a wide range of detection tasks. For instance, on the ImageNet benchmark with ResNet50 model, our method achieves an average reduction of 11.15% in the false positive rate at 95% recall (FPR95) compared to the current state-of-the-art approach. The code would be released.