Pursuing Feature Separation based on Neural Collapse for Out-of-Distribution Detection

TL;DR

This paper proposes a simple but effective loss called Separation Loss, which binds the features of OOD data in a subspace orthogonal to the principal subspace of ID features formed by Neural Collapse, and achieves SOTA performance on CIFAR10, CIFAR100 and ImageNet benchmarks without any additional data augmentation or sampling.

Abstract

In the open world, detecting out-of-distribution (OOD) data, whose labels are disjoint with those of in-distribution (ID) samples, is important for reliable deep neural networks (DNNs). To achieve better detection performance, one type of approach proposes to fine-tune the model with auxiliary OOD datasets to amplify the difference between ID and OOD data through a separation loss defined on model outputs. However, none of these studies consider enlarging the feature disparity, which should be more effective compared to outputs. The main difficulty lies in the diversity of OOD samples, which makes it hard to describe their feature distribution, let alone design losses to separate them from ID features. In this paper, we neatly fence off the problem based on an aggregation property of ID features named Neural Collapse (NC). NC means that the penultimate features of ID samples within a class are nearly identical to the last layer weight of the corresponding class. Based on this property, we propose a simple but effective loss called Separation Loss, which binds the features of OOD data in a subspace orthogonal to the principal subspace of ID features formed by NC. In this way, the features of ID and OOD samples are separated by different dimensions. By optimizing the feature separation loss rather than purely enlarging output differences, our detection achieves SOTA performance on CIFAR10, CIFAR100 and ImageNet benchmarks without any additional data augmentation or sampling, demonstrating the importance of feature separation in OOD detection. Code is available at https://github.com/Wuyingwen/Pursuing-Feature-Separation-for-OOD-Detection.

Figures (7)

• Figure 1: Overview of our method. An example of a well-trained binary classification network, where $w_i$ denotes the $i$-th weight of the last fully connected layer. The features of ID samples within a class are nearly identical to the weight of the corresponding class, which is called Neural Collapse. Based on this property, we propose to constrain OOD features on dimensions orthogonal to FC weight subspace to explicitly separate the feature manifolds between ID and OOD data.
• Figure 2: Visualization of features projected into the two-dimensional space consisted of $w_1$ and $w_2$ (ref. Figure \ref{['overview']}) and the three-dimensional space consisted of $w_1$, $w_2$ and the principal eigenvector of OOD features on CIFAR10 benchmark. The Class-1 and Class-2 represent features of test ID samples of class-1 and class-2, and the Outlier means features of test unseen OOD data, i.e. SVHN. It can be observed that the feature separability between ID and OOD data gradually increases from left (Vanilla model) to right (Our model).
• Figure 3: ID sample: Class-0 and Class-1, OOD sample: SVHN
• Figure 4: ID sample: Class-2 and Class-3, OOD sample: SVHN
• Figure 5: ID sample: Class-4 and Class-5, OOD sample: SVHN