# When Softmax Fails at the Top: Extreme Value Corrections for InfoNCE

arXiv: https://arxiv.org/abs/2606.00262 · HTML: https://mlsanity.com/paper/2606.00262/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 16 of 16)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [What Makes for Good Views for Contrastive Learning?](https://mlsanity.com/paper/2005.10243/) (2020)
- [Contrastive Learning with Hard Negative Samples](https://mlsanity.com/paper/2010.04592/) (2020)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [A Survey on Contrastive Self-supervised Learning](https://mlsanity.com/paper/2011.00362/) (2020)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Hard Negative Mixing for Contrastive Learning](https://mlsanity.com/paper/2010.01028/) (2020)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasets](https://mlsanity.com/paper/1707.08819/) (2017)
- [Keystroke Dynamics as Part of Lifelogging](https://mlsanity.com/paper/2010.10144/) (2020)
- [I-Con: A Unifying Framework for Representation Learning](https://mlsanity.com/paper/2504.16929/) (2025)
- [f-MICL: Understanding and Generalizing InfoNCE-based Contrastive Learning](https://mlsanity.com/paper/2402.10150/) (2024)
- [Contrastive Predictive Coding Done Right for Mutual Information Estimation](https://mlsanity.com/paper/2510.25983/) (2025)

## Abstract (arXiv)

InfoNCE is the standard contrastive learning objective, but its softmax form is not only a computational convenience: it also encodes a statistical assumption about how the top-scoring example is selected. Using extreme value theory, we show that this assumption is often misaligned with the normalized embedding setting used in modern contrastive learning. Motivated by this mismatch, we propose textscWEINCE, a simple modification of InfoNCE that uses anchor-wise online batch statistics to blend the usual softmax logits with an endpoint shortfall correction, adding no trainable parameters. Across five vision benchmarks, textscWEINCE yields consistent improvements in frozen-feature evaluation. These results show that a more faithful statistical treatment of hard negatives can improve contrastive objectives.