Hyperbolic Metric Learning for Visual Outlier Detection

TL;DR

This work proposes a metric framework that leverages the strengths of Hyperbolic geometry for OOD detection, and explores the relationship between OOD detection performance and Hyperbolic embedding dimension, addressing practical concerns in resource-constrained environments.

Abstract

Out-Of-Distribution (OOD) detection is critical to deploy deep learning models in safety-critical applications. However, the inherent hierarchical concept structure of visual data, which is instrumental to OOD detection, is often poorly captured by conventional methods based on Euclidean geometry. This work proposes a metric framework that leverages the strengths of Hyperbolic geometry for OOD detection. Inspired by previous works that refine the decision boundary for OOD data with synthetic outliers, we extend this method to Hyperbolic space. Interestingly, we find that synthetic outliers do not benefit OOD detection in Hyperbolic space as they do in Euclidean space. Furthermore we explore the relationship between OOD detection performance and Hyperbolic embedding dimension, addressing practical concerns in resource-constrained environments. Extensive experiments show that our framework improves the FPR95 for OOD detection from 22\% to 15\% and from 49% to 28% on CIFAR-10 and CIFAR-100 respectively compared to Euclidean methods.

Figures (6)

• Figure 1: Illustration of the Hyperbolic outliers synthesis. First, the embeddings are optimized using \ref{['eq:Hyperbolic_contrastive_loss']} which encourages low intra-class variation and high inter-class separation. Second, the most uncertain embeddings are selected by their distance towards the origin. Third, the outliers are synthesized by sampling from the wrapped Gaussian distribution centered around the selected embeddings. Finally, only those with a higher level of certainty are kept.
• Figure 2: UMAP visualization of learned feature embeddings of CIFAR-10 projected to the Poincaré disk using $\mathcal{L}_{\text{hsup}}$.
• Figure 3: Histogram displaying scores for both and datasets. Visualization reveals that distances to the in-distribution data are consistently lower than those to the out-of-distribution data.
• Figure 4: Boxplot illustrating detection performance using CIFAR-10 as the dataset across three distinct training runs. We present and metrics upon reducing the dimensionality of the ResNet-18 projection layer. The Hyperbolic space maintains robustness to dimensionality reduction for detection, which offers a promising solution for limited resource devices.
• Figure 5: Average OOD detection performance using CIFAR-10/100 and ImageNet-200 as $D_\text{id}$ and with ResNet-18, ResNet-34 and ResNet-50 backbones.

Theorems & Definitions (3)

• definition thmcounterdefinition: Geodesic
• definition thmcounterdefinition: Tangent space
• definition thmcounterdefinition: Exponential and Logarithmic maps