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Supervised-contrastive loss (SCL) is an alternative to cross-entropy (CE) for classification tasks that makes use of similarities in the embedding space to allow for richer representations. In this work, we propose methods to engineer the…

Machine Learning · Computer Science 2023-10-03 Jaidev Gill , Vala Vakilian , Christos Thrampoulidis

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

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

The recently discovered Neural Collapse (NC) phenomenon occurs pervasively in today's deep net training paradigm of driving cross-entropy (CE) loss towards zero. During NC, last-layer features collapse to their class-means, both classifiers…

Machine Learning · Computer Science 2022-05-11 X. Y. Han , Vardan Papyan , David L. Donoho

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) 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

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

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

While cross entropy (CE) is the most commonly used loss to train deep neural networks for classification tasks, many alternative losses have been developed to obtain better empirical performance. Among them, which one is the best to use is…

Machine Learning · Computer Science 2022-10-11 Jinxin Zhou , Chong You , Xiao Li , Kangning Liu , Sheng Liu , Qing Qu , Zhihui Zhu

Recent findings reveal that over-parameterized deep neural networks, trained beyond zero training-error, exhibit a distinctive structural pattern at the final layer, termed as Neural-collapse (NC). These results indicate that the final…

Machine Learning · Computer Science 2024-03-01 Tina Behnia , Christos Thrampoulidis

Contrastive learning (CL) is one of the most successful paradigms for self-supervised learning (SSL). In a principled way, it considers two augmented "views" of the same image as positive to be pulled closer, and all other images as…

Machine Learning · Computer Science 2023-06-21 Chun-Hsiao Yeh , Cheng-Yao Hong , Yen-Chi Hsu , Tyng-Luh Liu , Yubei Chen , Yann LeCun

State-of-the-art pre-trained image models predominantly adopt a two-stage approach: initial unsupervised pre-training on large-scale datasets followed by task-specific fine-tuning using Cross-Entropy loss~(CE). However, it has been…

Computer Vision and Pattern Recognition · Computer Science 2024-11-18 Zijun Long , George Killick , Lipeng Zhuang , Gerardo Aragon-Camarasa , Zaiqiao Meng , Richard Mccreadie

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

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

The current paradigm of training deep neural networks for classification tasks includes minimizing the empirical risk that pushes the training loss value towards zero, even after the training error has been vanished. In this terminal phase…

Machine Learning · Computer Science 2024-06-07 Hien Dang , Tho Tran , Tan Nguyen , Nhat Ho

Learning good image representations that are beneficial to downstream tasks is a challenging task in computer vision. As such, a wide variety of self-supervised learning approaches have been proposed. Among them, contrastive learning has…

Computer Vision and Pattern Recognition · Computer Science 2023-02-06 Yun Yue , Fangzhou Lin , Kazunori D Yamada , Ziming Zhang

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

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural…

Machine Learning · Computer Science 2023-06-21 Hien Dang , Tho Tran , Stanley Osher , Hung Tran-The , Nhat Ho , Tan Nguyen
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