angular margin loss

This paper addresses the positive-unlabeled (PU) learning problem by proposing AngularPU, a novel PU learning framework grounded in hyperspherical geometry. Instead of explicitly modeling negative examples, AngularPU defines the positive class via learnable prototype vectors and performs classification using cosine similarity and angular margins. It further introduces angular regularization to encourage uniform dispersion of unlabeled samples on the unit hypersphere, thereby enhancing inter-class separability. Theoretically, AngularPU is proven to achieve Bayes-optimality and prototype consistency under mild assumptions. Empirically, AngularPU outperforms or matches state-of-the-art methods across multiple benchmark datasets—particularly excelling in settings with sparse positive examples and high-dimensional embeddings. The framework offers strong geometric interpretability, robust generalization, and favorable scalability, making it both principled and practical for real-world PU learning tasks.

Existing deep constrained clustering (DCC) methods suffer from anchor dependency or insufficient discriminability of Euclidean embeddings, limiting scalability and practical applicability. To address these issues, we propose SpherePair—a spherical-geometric angle-constrained embedding framework that models pairwise constraints as angular relationships on the unit hypersphere, thereby decoupling representation learning from clustering. Its core is the SpherePair Loss, a theoretically grounded contrastive loss defined on the sphere: it requires no pre-specified number of clusters, ensures constraint consistency, supports incremental sample generalization, enables rapid cluster-number inference, and guarantees convergence. Jointly optimized with deep neural networks, SpherePair achieves state-of-the-art performance across multiple benchmark datasets. The method delivers superior clustering accuracy, strong scalability to large-scale data, and robustness for real-world deployment.

This work addresses the challenge of learning normalized embedding representations that are both intra-class compact and inter-class angularly separable while preserving neural network expressiveness and accelerating convergence. To this end, the authors propose the CoCo loss function, which uniquely unifies intra-class representation collapse and inter-class contrast within a single objective. Operating in the normalized embedding space, CoCo guides the network toward a geometrically optimal configuration, offering both optimization flexibility and strong clustering dynamics. Theoretical analysis and gradient characterization demonstrate its compatibility with diverse architectures. Empirical evaluation shows that CoCo matches or surpasses kernel SVMs, random forests, and cross-entropy baselines across multiple tabular datasets from OpenML-CC18, while significantly improving convergence speed and intra-class compactness.

In open-set face recognition, noisy samples degrade the performance of margin-based softmax losses (e.g., ArcFace). To address this, we propose Exponential Angular Margin Loss (ExpFace). Our method introduces a dynamic angular margin in the cosine similarity space, formulated exponentially to adaptively strengthen penalty near class centers and attenuate it near decision boundaries—thereby jointly optimizing intra-class compactness and inter-class separability. By modeling similarity curves and optimizing gradient flow, ExpFace ensures monotonic and stable decision boundary learning. Extensive experiments demonstrate that ExpFace consistently outperforms SphereFace, CosFace, and ArcFace across multiple benchmark datasets. It exhibits improved training stability, superior generalization, and notably enhanced robustness to label noise—achieving state-of-the-art accuracy under realistic open-set conditions.

Hard negative sampling in contrastive learning critically influences representation geometry, yet its precise roles in mitigating dimensional collapse (DC) and inducing neural collapse (NC) remain poorly understood. Method: We develop a generalized contrastive loss framework, integrating equiangular tight frame (ETF) geometric modeling and unit-sphere normalization analysis. Contribution/Results: We provide the first rigorous proof that, under both supervised and unsupervised hard contrastive learning (HSCL/HUCL), any global optimum necessarily exhibits NC—i.e., class means form an ETF and intra-class features collapse to identical points. Crucially, we extend this result to generic losses including InfoNCE without assuming class-conditional independence. Theory and experiments jointly demonstrate that NC emerges stably *only* when hard negative sampling is synergistically combined with feature normalization under Adam-based batch optimization; otherwise, DC prevails. Our code is publicly available.

This work addresses the instability in speaker verification training caused by the exploding gradients of the arccos function in Angular Margin loss, which also hinders effective optimization on hard samples. To mitigate this issue, the authors propose ChebyAAM, a novel loss function that, for the first time, incorporates Chebyshev polynomials into angular margin design to accurately approximate the arccos operation. This approximation effectively alleviates gradient explosion and enhances discriminative learning for challenging samples. Extensive experiments on three benchmark datasets—VoxCeleb, SITW, and CN-Celeb—demonstrate significant performance improvements, confirming the superiority and stability of the proposed approximation strategy.

This work addresses the challenge of limited feature generalizability in respiratory sound classification caused by variations in recording quality and class imbalance. To this end, the authors propose QLung, a novel framework that introduces, for the first time, a no-reference audio quality assessment metric based on spectral entropy and root-mean-square energy. This metric dynamically adjusts the angular margin in a normalized angular classifier and is combined with a log-scaling strategy to enhance intra-class compactness and inter-class separability, thereby stabilizing training. Evaluated on the ICBHI dataset, QLung achieves a 2.46% improvement over the cross-entropy baseline and demonstrates state-of-the-art out-of-distribution generalization performance on the SPRSound dataset.

This work addresses the hard-margin support vector machine (SVM) problem on linearly separable datasets by proposing a geometrically motivated iterative optimization method. Starting from an arbitrary initial separating hyperplane, the algorithm employs an active-set strategy that leverages only local sample information at each iteration to progressively reorient the hyperplane. This process monotonically increases the margin while preserving correct classification, ultimately converging to the global optimum. The key innovation lies in decomposing the original convex quadratic program into a sequence of small-scale subproblems, thereby circumventing the need to solve a large-scale optimization problem directly. Experimental results demonstrate that, given a feasible initial solution, the proposed method is competitive on large-scale datasets and outperforms mainstream solvers in certain scenarios.

Traditional loss functions in biometric verification struggle to simultaneously optimize intra-class compactness, inter-class separability, and angular margin. To address this, we propose two novel loss functions—Q-Margin and A3M—that jointly integrate α-divergence with angular margin mechanisms—the first such formulation. To mitigate training instability in A3M, we introduce a prototype re-initialization strategy. Our approach operates within the Softmax framework, unifying α-divergence optimization, angular margin constraints, and dynamic prototype calibration. Evaluated on IJB-B, IJB-C (face), and VoxCeleb (speaker) benchmarks, our method achieves significant performance gains under stringent false acceptance rate (FAR ≤ 1e−4) conditions—outperforming state-of-the-art baselines, especially in high-security applications like banking authentication. The core contribution is a theoretically grounded framework establishing compatibility between α-divergence and angular margin, empirically validated to yield substantial discriminative gains at ultra-low FAR thresholds.

Deep visual classifiers often exhibit poor calibration and weak robustness under distribution shifts, despite achieving high accuracy on clean data. To address this, this work proposes MaCS, a novel framework that unifies maximal class separation and local prediction stability within a single theoretical formulation. By introducing a hinge-squared margin penalty and a KL-divergence consistency regularizer in logit space, MaCS jointly optimizes calibration and robustness without requiring additional data or architectural modifications. Theoretical analysis yields provable bounds on generalization error and robustness radius. Extensive experiments demonstrate that MaCS significantly reduces expected calibration error (ECE) and negative log-likelihood (NLL), enhances robustness to common corruptions, and maintains or even improves top-1 accuracy across diverse image classification benchmarks and backbone architectures.