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 OrthLoss, 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
CIFAR benchmarks without any additional data augmentation or sampling,
demonstrating the importance of feature separation in OOD detection. The code
will be published.

本文通过神经坍缩（Neural Collapse）的特性来界定问题，并提出了一种称为 OrthLoss 的简单而有效的损失函数，将 OOD 数据的特征束缚在与 ID 特征的主要子空间正交的一个子空间中，从而通过不同的维度分离 ID 和 OOD 样本的特征。通过优化特征分离损失，而不是仅仅扩大输出差异，我们的检测在 CIFAR 基准上达到了 SOTA 性能，无需任何额外的数据增强或采样，证明了 OOD 检测中特征分离的重要性。

基于神经坍缩的特征分离追求外域检测

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

In this paper, we extends original Neural Collapse Phenomenon by proving
Generalized Neural Collapse hypothesis. We obtain Grassmannian Frame structure
from the optimization and generalization of classification. This structure
maximally separates features of every two classes on a sphere and does not
require a larger feature dimension than the number of classes. Out of curiosity
about the symmetry of Grassmannian Frame, we conduct experiments to explore if
models with different Grassmannian Frames have different performance. As a
result, we discover the Symmetric Generalization phenomenon. We provide a
theorem to explain Symmetric Generalization of permutation. However, the
question of why different directions of features can lead to such different
generalization is still open for future investigation.

本文提出了广义神经崩溃假说，并通过优化和分类的推广获得 Grassmann 框架结构。该结构在球面上最大化地分离每两类的特征，不需要比类别数量更大的特征维度。我们发现了对称泛化现象，并提供了一个用于解释置换的对称泛化定理。尽管不同特征方向导致不同泛化的原因仍需未来研究。

神经塌陷现象的研究：Grassmann 框架，对称性，泛化

A Study of Neural Collapse Phenomenon: Grassmannian Frame, Symmetry,  Generalization

Although great progresses have been made in automatic speech recognition
(ASR), significant performance degradation is still observed when recognizing
multi-talker mixed speech. In this paper, we propose and evaluate several
architectures to address this problem under the assumption that only a single
channel of mixed signal is available. Our technique extends permutation
invariant training (PIT) by introducing the front-end feature separation module
with the minimum mean square error (MSE) criterion and the back-end recognition
module with the minimum cross entropy (CE) criterion. More specifically, during
training we compute the average MSE or CE over the whole utterance for each
possible utterance-level output-target assignment, pick the one with the
minimum MSE or CE, and optimize for that assignment. This strategy elegantly
solves the label permutation problem observed in the deep learning based
multi-talker mixed speech separation and recognition systems. The proposed
architectures are evaluated and compared on an artificially mixed AMI dataset
with both two- and three-talker mixed speech. The experimental results indicate
that our proposed architectures can cut the word error rate (WER) by 45.0% and
25.0% relatively against the state-of-the-art single-talker speech recognition
system across all speakers when their energies are comparable, for two- and
three-talker mixed speech, respectively. To our knowledge, this is the first
work on the multi-talker mixed speech recognition on the challenging
speaker-independent spontaneous large vocabulary continuous speech task.

本文探讨了如何通过扩展置换不变训练（PIT）方法并引入前端特征分离模块（最小均方误差标准）和后端识别模块（最小交叉熵标准），解决在多说话人混合语音识别中的问题，并且在 AMI 数据集（包括二人和三人的混音语音）的实验中，相对于同类不同说话人的语音识别系统，识别率提高了 45% 和 25%。