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Supervised classification has a theoretical optimum, Neural Collapse (NC), yet neither of its two dominant paradigms reaches it in practice. Cross entropy (CE) leaves radial degrees of freedom unconstrained and converges to a degenerate…

Machine Learning · Computer Science 2026-05-22 Panagiotis Koromilas , Theodoros Giannakopoulos , Mihalis A. Nicolaou , Yannis Panagakis

Most Neural Networks (NNs) for classification are trained using Cross-Entropy as a loss function. This approach requires the model to have an explicit classification layer. However, there exist alternative approaches, such as Contrastive…

Machine Learning · Computer Science 2026-04-27 Leonardo Arrighi , Julia Eva Belloni , Aurélie Gallet , Ivan Gentile , Matteo Lippi , Marco Zullich

State-of-the-art natural language understanding classification models follow two-stages: pre-training a large language model on an auxiliary task, and then fine-tuning the model on a task-specific labeled dataset using cross-entropy loss.…

Computation and Language · Computer Science 2021-04-06 Beliz Gunel , Jingfei Du , Alexis Conneau , Ves Stoyanov

Supervised contrastive loss (SCL) is a competitive and often superior alternative to the cross-entropy loss for classification. While prior studies have demonstrated that both losses yield symmetric training representations under balanced…

Machine Learning · Computer Science 2023-10-20 Ganesh Ramachandra Kini , Vala Vakilian , Tina Behnia , Jaidev Gill , Christos Thrampoulidis

Contrastive learning (CL) aims to preserve relational structure between samples by learning representations that reflect a similarity graph. Yet, the geometry of the resulting embeddings remains poorly understood. Here we show that weighted…

Machine Learning · Computer Science 2026-05-15 Raphael Vock , Edouard Duchesnay , Benoit Dufumier

For a widely-studied data model and general loss and sample-hardening functions we prove that the losses of Supervised Contrastive Learning (SCL), Hard-SCL (HSCL), and Unsupervised Contrastive Learning (UCL) are minimized by representations…

Machine Learning · Computer Science 2025-05-08 Ruijie Jiang , Thuan Nguyen , Shuchin Aeron , Prakash Ishwar

Contrastive learning, especially self-supervised contrastive learning (SSCL), has achieved great success in extracting powerful features from unlabeled data. In this work, we contribute to the theoretical understanding of SSCL and uncover…

Machine Learning · Computer Science 2023-06-05 Tianyang Hu , Zhili Liu , Fengwei Zhou , Wenjia Wang , Weiran Huang

Semi-supervised learning acts as an effective way to leverage massive unlabeled data. In this paper, we propose a novel training strategy, termed as Semi-supervised Contrastive Learning (SsCL), which combines the well-known contrastive loss…

Computer Vision and Pattern Recognition · Computer Science 2021-05-18 Yuhang Zhang , Xiaopeng Zhang , Robert. C. Qiu , Jie Li , Haohang Xu , Qi Tian

Contrastive learning has emerged as a powerful method in deep learning, excelling at learning effective representations through contrasting samples from different distributions. However, neural collapse, where embeddings converge into a…

Machine Learning · Computer Science 2024-10-08 Huanran Li , Manh Nguyen , Daniel Pimentel-Alarcón

Contrastive Self-supervised Learning (CSL) is a practical solution that learns meaningful visual representations from massive data in an unsupervised approach. The ordinary CSL embeds the features extracted from neural networks onto…

Computer Vision and Pattern Recognition · Computer Science 2022-08-19 Shentong Mo , Zhun Sun , Chao Li

Contrastive self-supervised learning (CSL) with a prototypical regularization has been introduced in learning meaningful representations for downstream tasks that require strong semantic information. However, to optimize CSL with a loss…

Computer Vision and Pattern Recognition · Computer Science 2022-10-20 Shentong Mo , Zhun Sun , Chao Li

Supervised contrastive learning (SupCL) has emerged as a prominent approach in representation learning, leveraging both supervised and self-supervised losses. However, achieving an optimal balance between these losses is challenging;…

Machine Learning · Computer Science 2025-03-12 Chungpa Lee , Jeongheon Oh , Kibok Lee , Jy-yong Sohn

Contrastive learning has emerged as a powerful method in deep learning, excelling at learning effective representations through contrasting samples from different distributions. However, dimensional collapse, where embeddings converge into…

Machine Learning · Computer Science 2025-12-10 Huanran Li , Manh Nguyen , Daniel Pimentel-Alarcón

Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can…

Machine Learning · Statistics 2023-03-03 Florian Graf , Christoph D. Hofer , Marc Niethammer , Roland Kwitt

Despite its empirical success, the theoretical foundations of self-supervised contrastive learning (CL) are not yet fully established. In this work, we address this gap by showing that standard CL objectives implicitly approximate a…

Machine Learning · Computer Science 2025-11-12 Achleshwar Luthra , Tianbao Yang , Tomer Galanti

Self-supervised contrastive learning (CL) has achieved remarkable empirical success, often producing representations that rival supervised pre-training on downstream tasks. Recent theory explains this by showing that the CL loss closely…

Machine Learning · Computer Science 2025-10-13 Achleshwar Luthra , Priyadarsi Mishra , Tomer Galanti

Contrastive learning (CL) is a predominant technique in image classification, but they showed limited performance with an imbalanced dataset. Recently, several supervised CL methods have been proposed to promote an ideal regular simplex…

Computer Vision and Pattern Recognition · Computer Science 2026-04-02 Sumin Roh , Harim Kim , Ho Yun Lee , Il Yong Chun

Graph contrastive learning (GCL) aligns node representations by classifying node pairs into positives and negatives using a selection process that typically relies on establishing correspondences within two augmented graphs. The…

Machine Learning · Computer Science 2024-11-27 Maysam Behmanesh , Maks Ovsjanikov

Self-supervised learning enables networks to learn discriminative features from massive data itself. Most state-of-the-art methods maximize the similarity between two augmentations of one image based on contrastive learning. By utilizing…

Computer Vision and Pattern Recognition · Computer Science 2023-07-05 Jidong Ge , Yuxiang Liu , Jie Gui , Lanting Fang , Ming Lin , James Tin-Yau Kwok , LiGuo Huang , Bin Luo

Learning generalizable self-supervised graph representations for downstream tasks is challenging. To this end, Contrastive Learning (CL) has emerged as a leading approach. The embeddings of CL are arranged on a hypersphere where similarity…

Machine Learning · Computer Science 2025-02-25 Yifei Zhang , Hao Zhu , Menglin Yang , Jiahong Liu , Rex Ying , Irwin King , Piotr Koniusz
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