# A Functional Data Perspective and Baseline On Multi-Layer Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2306.03522 · HTML: https://mlsanity.com/paper/2306.03522/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 72 references that are in the map.
- First posted on arXiv 6 Jun 2023.

## Builds on (most cited first, 30 of 49)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [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)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [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)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [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)
- [Recent Advances in Open Set Recognition: A Survey](https://mlsanity.com/paper/1811.08581/) (2018)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [MOS: Towards Scaling Out-of-distribution Detection for Large Semantic Space](https://mlsanity.com/paper/2105.01879/) (2021)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detection](https://mlsanity.com/paper/2106.09022/) (2021)

## Built on by (most cited first, 2 of 2)

- [Signature Isolation Forest](https://mlsanity.com/paper/2403.04405/) (2024)
- [Combine and Conquer: A Meta-Analysis on Data Shift and Out-of-Distribution Detection](https://mlsanity.com/paper/2406.16045/) (2024)

## Abstract (arXiv)

A key feature of out-of-distribution (OOD) detection is to exploit a trained neural network by extracting statistical patterns and relationships through the multi-layer classifier to detect shifts in the expected input data distribution. Despite achieving solid results, several state-of-the-art methods rely on the penultimate or last layer outputs only, leaving behind valuable information for OOD detection. Methods that explore the multiple layers either require a special architecture or a supervised objective to do so. This work adopts an original approach based on a functional view of the network that exploits the sample's trajectories through the various layers and their statistical dependencies. It goes beyond multivariate features aggregation and introduces a baseline rooted in functional anomaly detection. In this new framework, OOD detection translates into detecting samples whose trajectories differ from the typical behavior characterized by the training set. We validate our method and empirically demonstrate its effectiveness in OOD detection compared to strong state-of-the-art baselines on computer vision benchmarks.