We provide the detailed of the PQ retrieval performance trends of Glint360K trained using the CosFace loss in Tab. 1.

When training overparameterized deep networks for classification tasks, it has been widely observed that the learned features exhibit a so-called neural collapse' phenomenon. More specifically, for the output features of the penultimate layer, for each class the within-class features converge to their means, and the means of different classes exhibit a certain tight frame structure, which is also aligned with the last layer's classifier. As feature normalization in the last layer becomes a common practice in modern representation learning, in this work we theoretically justify the neural collapse phenomenon under normalized features. Based on an unconstrained feature model, we simplify the empirical loss function in a multi-class classification task into a nonconvex optimization problem over the Riemannian manifold by constraining all features and classifiers over the sphere. In this context, we analyze the nonconvex landscape of the Riemannian optimization problem over the product of spheres, showing a benign global landscape in the sense that the only global minimizers are the neural collapse solutions while all other critical points are strict saddle points with negative curvature. Experimental results on practical deep networks corroborate our theory and demonstrate that better representations can be learned faster via feature normalization.

Recent work has explored a range of model families for human motion generation, including Variational Autoencoders (VAEs), Generative Adversarial Networks (GANs), and diffusion-based models. Despite their differences, many methods rely on over-parameterized input features and auxiliary losses to improve empirical results. These strategies should not be strictly necessary for diffusion models to match the human motion distribution. We show that on par with state-of-the-art results in unconditional human motion generation are achievable with a score-based diffusion model using only careful feature-space normalization and analytically derived weightings for the standard L2 score-matching loss, while generating both motion and shape directly, thereby avoiding slow post hoc shape recovery from joints. We build the method step by step, with a clear theoretical motivation for each component, and provide targeted ablations demonstrating the effectiveness of each proposed addition in isolation.

In other words, they form a Simplex Equiangular Tight Frame (ETF).

We empirically investigate the camera bias of person re-identification (ReID) models. Previously, camera-aware methods have been proposed to address this issue, but they are largely confined to training domains of the models. We measure the camera bias of ReID models on unseen domains and reveal that camera bias becomes more pronounced under data distribution shifts. As a debiasing method for unseen domain data, we revisit feature normalization on embedding vectors. While the normalization has been used as a straightforward solution, its underlying causes and broader applicability remain unexplored. We analyze why this simple method is effective at reducing bias and show that it can be applied to detailed bias factors such as low-level image properties and body angle. In addition, we explore the inherent risk of camera bias in unsupervised learning of ReID models. The unsupervised models remain highly biased towards camera labels even for seen domain data, indicating substantial room for improvement. Based on observations of the negative impact of camera-biased pseudo labels on training, we suggest simple training strategies to mitigate the bias. By applying these strategies to existing unsupervised learning algorithms, we show that significant performance improvements can be achieved with minor modifications. Person re-identification (ReID) is a process of retrieving images of a query identity from gallery images. With recent advances in deep learning, a wide range of challenging ReID scenarios have been covered, including object occlusion (Miao et al., 2019; Somers et al., 2023), change of appearance (Jin et al., 2022), and infrared images (Wu et al., 2017; Wu & Ye, 2023). In general, the inter-camera sample matching is not trivial since the shared information among images from the same camera can mislead a model easily.

When training overparameterized deep networks for classification tasks, it has been widely observed that the learned features exhibit a so-called "neural collapse'" phenomenon. More specifically, for the output features of the penultimate layer, for each class the within-class features converge to their means, and the means of different classes exhibit a certain tight frame structure, which is also aligned with the last layer's classifier. As feature normalization in the last layer becomes a common practice in modern representation learning, in this work we theoretically justify the neural collapse phenomenon under normalized features. Based on an unconstrained feature model, we simplify the empirical loss function in a multi-class classification task into a nonconvex optimization problem over the Riemannian manifold by constraining all features and classifiers over the sphere. In this context, we analyze the nonconvex landscape of the Riemannian optimization problem over the product of spheres, showing a benign global landscape in the sense that the only global minimizers are the neural collapse solutions while all other critical points are strict saddle points with negative curvature.

The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of these activities and respective aspects. The selection of an appropriate normalization method needs to take into account the type and characteristics of the involved features, the methods to be used subsequently for the just mentioned data processing, as well as the specific questions being considered. After briefly considering how normalization constitutes one of the many interrelated parts typically involved in data analysis and modeling, the present work addressed the important issue of feature normalization from the perspective of uniform and proportional (right skewed) features and comparison operations. More general right skewed features are also considered in an approximated manner. Several concepts, properties, and results are described and discussed, including the description of a duality relationship between uniform and proportional feature spaces and respective comparisons, specifying conditions for consistency between comparisons in each of the two domains. Two normalization possibilities based on non-centralized dispersion of features are also presented, and also described is a modified version of the Jaccard similarity index which incorporates intrinsically normalization. Preliminary experiments are presented in order to illustrate the developed concepts and methods.