# The NT-Xent loss upper bound

arXiv: https://arxiv.org/abs/2205.03169 · HTML: https://mlsanity.com/paper/2205.03169/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 7 references that are in the map.
- First posted on arXiv 6 May 2022.

## Builds on (most cited first, 7 of 7)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Intriguing Properties of Contrastive Losses](https://mlsanity.com/paper/2011.02803/) (2020)

## Built on by (most cited first, 4 of 4)

- [Guidelines for Augmentation Selection in Contrastive Learning for Time Series Classification](https://mlsanity.com/paper/2407.09336/) (2024)
- [Enhancing Hyperspectral Image Prediction with Contrastive Learning in Low-Label Regime](https://mlsanity.com/paper/2410.07790/) (2024)
- [Context-Enriched Contrastive Loss: Enhancing Presentation of Inherent Sample Connections in Contrastive Learning Framework](https://mlsanity.com/paper/2512.02152/) (2025)
- [SamaVaani: Auditing and Debiasing Multilingual Clinical ASR for Indian Languages](https://mlsanity.com/paper/2606.26901/) (2026)

## Abstract (arXiv)

Self-supervised learning is a growing paradigm in deep representation learning, showing great generalization capabilities and competitive performance in low-labeled data regimes. The SimCLR framework proposes the NT-Xent loss for contrastive representation learning. The objective of the loss function is to maximize agreement, similarity, between sampled positive pairs. This short paper derives and proposes an upper bound for the loss and average similarity. An analysis of the implications is however not provided, but we strongly encourage anyone in the field to conduct this.