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Bounding Box Anomaly Scoring for simple and efficient Out-of-Distribution detection

Mohamed Bahi Yahiaoui, Geoffrey Daniel, Loïc Giraldi, Jérémie Bruyelle, Julyan Arbel

Abstract

Out-of-distribution (OOD) detection aims to identify inputs that differ from the training distribution in order to reduce unreliable predictions by deep neural networks. Among post-hoc feature-space approaches, OOD detection is commonly performed by approximating the in-distribution support in the representation space of a pretrained network. Existing methods often reflect a trade-off between compact parametric models, such as Mahalanobis-based scores, and more flexible but reference-based methods, such as k-nearest neighbors. Bounding-box abstraction provides an attractive intermediate perspective by representing in-distribution support through compact axis-aligned summaries of hidden activations. In this paper, we introduce Bounding Box Anomaly Scoring (BBAS), a post-hoc OOD detection method that leverages bounding-box abstraction. BBAS combines graded anomaly scores based on interval exceedances, monitoring variables adapted to convolutional layers, and decoupled clustering and box construction for richer and multi-layer representations. Experiments on image-classification benchmarks show that BBAS provides robust separation between in-distribution and out-of-distribution samples while preserving the simplicity, compactness, and updateability of the bounding-box approach.

Bounding Box Anomaly Scoring for simple and efficient Out-of-Distribution detection

Abstract

Out-of-distribution (OOD) detection aims to identify inputs that differ from the training distribution in order to reduce unreliable predictions by deep neural networks. Among post-hoc feature-space approaches, OOD detection is commonly performed by approximating the in-distribution support in the representation space of a pretrained network. Existing methods often reflect a trade-off between compact parametric models, such as Mahalanobis-based scores, and more flexible but reference-based methods, such as k-nearest neighbors. Bounding-box abstraction provides an attractive intermediate perspective by representing in-distribution support through compact axis-aligned summaries of hidden activations. In this paper, we introduce Bounding Box Anomaly Scoring (BBAS), a post-hoc OOD detection method that leverages bounding-box abstraction. BBAS combines graded anomaly scores based on interval exceedances, monitoring variables adapted to convolutional layers, and decoupled clustering and box construction for richer and multi-layer representations. Experiments on image-classification benchmarks show that BBAS provides robust separation between in-distribution and out-of-distribution samples while preserving the simplicity, compactness, and updateability of the bounding-box approach.
Paper Structure (52 sections, 4 theorems, 49 equations, 4 figures, 17 tables)

This paper contains 52 sections, 4 theorems, 49 equations, 4 figures, 17 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Outline
  4. Out-of-Distribution problem setting
  5. Related work
  6. Mahalanobis-based detectors
  7. k-Nearest-Neighbor (kNN) OOD detection
  8. Bounding box abstraction
  9. Bounding Box Anomaly Scoring
  10. Monitoring variables
  11. Clustering for bounding box construction
  12. Fully connected neural networks
  13. Adaptation for CNNs
  14. Clustering algorithm choice
  15. Clustering application
  16. ...and 37 more sections

Key Result

Lemma 1

For $\mathcal{N}$ a neural network with $\mathop{\mathrm{ReLU}}\nolimits$ activation on the first layer and $A \subset \mathbb{R}^{n_{\mathrm{in}}}$ a finite point set, we have:

Figures (4)

  • Figure 1: Complete BBAS pipeline processing: from constructing the monitor to runtime monitoring.
  • Figure 2: Two-moons regression example illustrating the geometric interpretation of activation regions and cluster-wise bounding boxes for a ReLU neural network trained on $f(x)=\sin(\pi x_1)+\sin(\pi x_2)$.
  • Figure 3: t-SNE visualizations of different feature representations extracted from a ResNet trained on CIFAR-10. Across all representations, samples form compact, well-separated class clusters, demonstrating robust class-dependent structure.
  • Figure 4: Effect of the clustering algorithm and the number of clusters per class on AUROC. Agglomerative clustering with complete linkage consistently yields the strongest performance for Far-OOD detection, while Near-OOD performance is less sensitive to the clustering choice.

Theorems & Definitions (11)

  • Definition 1
  • Definition 2
  • Definition 3
  • Lemma 1
  • proof
  • Definition 4
  • Lemma 2
  • Lemma 3
  • Definition 5
  • Lemma 4
  • ...and 1 more