# Rethinking InfoNCE: How Many Negative Samples Do You Need?

arXiv: https://arxiv.org/abs/2105.13003 · HTML: https://mlsanity.com/paper/2105.13003/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 29 references that are in the map.
- First posted on arXiv 27 May 2021.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [BERT4Rec: Sequential Recommendation with Bidirectional Encoder Representations from Transformer](https://mlsanity.com/paper/1904.06690/) (2019)
- [Contrastive Learning with Hard Negative Samples](https://mlsanity.com/paper/2010.04592/) (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)
- [Debiased Contrastive Learning](https://mlsanity.com/paper/2007.00224/) (2020)
- [Self-supervised Graph Learning for Recommendation](https://mlsanity.com/paper/2010.10783/) (2020)
- [InfoXLM: An Information-Theoretic Framework for Cross-Lingual Language Model Pre-Training](https://mlsanity.com/paper/2007.07834/) (2020)
- [Pre-training Tasks for Embedding-based Large-scale Retrieval](https://mlsanity.com/paper/2002.03932/) (2020)
- [A Mutual Information Maximization Perspective of Language Representation Learning](https://mlsanity.com/paper/1910.08350/) (2019)
- [NPA: Neural News Recommendation with Personalized Attention](https://mlsanity.com/paper/1907.05559/) (2019)
- [Neural News Recommendation with Attentive Multi-View Learning](https://mlsanity.com/paper/1907.05576/) (2019)
- [Contrastive Distillation on Intermediate Representations for Language Model Compression](https://mlsanity.com/paper/2009.14167/) (2020)
- [Unsupervised Video Representation Learning by Bidirectional Feature Prediction](https://mlsanity.com/paper/2011.06037/) (2020)
- [Temporal Context Aggregation for Video Retrieval with Contrastive Learning](https://mlsanity.com/paper/2008.01334/) (2020)

## Built on by (most cited first, 19 of 19)

- [Learning Temporal Distances: Contrastive Successor Features Can Provide a Metric Structure for Decision-Making](https://mlsanity.com/paper/2406.17098/) (2024)
- [Breaking the False Sense of Security in Backdoor Defense through Re-Activation Attack](https://mlsanity.com/paper/2405.16134/) (2024)
- [DiME: Maximizing Mutual Information by a Difference of Matrix-Based Entropies](https://mlsanity.com/paper/2301.08164/) (2023)
- [Does Negative Sampling Matter? A Review with Insights into its Theory and Applications](https://mlsanity.com/paper/2402.17238/) (2024)
- [Exploring Facial Expression Recognition through Semi-Supervised Pretraining and Temporal Modeling](https://mlsanity.com/paper/2403.11942/) (2024)
- [CrossAligner & Co: Zero-Shot Transfer Methods for Task-Oriented Cross-lingual Natural Language Understanding](https://mlsanity.com/paper/2203.09982/) (2022)
- [Exploring Large-scale Unlabeled Faces to Enhance Facial Expression Recognition](https://mlsanity.com/paper/2303.08617/) (2023)
- [CLCE: An Approach to Refining Cross-Entropy and Contrastive Learning for Optimized Learning Fusion](https://mlsanity.com/paper/2402.14551/) (2024)
- [RocqStar: Leveraging Similarity-driven Retrieval and Agentic Systems for Rocq generation](https://mlsanity.com/paper/2505.22846/) (2025)
- [SupCLAP: Controlling Optimization Trajectory Drift in Audio-Text Contrastive Learning with Support Vector Regularization](https://mlsanity.com/paper/2509.21033/) (2025)
- [Graph is a Natural Regularization: Revisiting Vector Quantization for Graph Representation Learning](https://mlsanity.com/paper/2508.06588/) (2025)
- [SC-GIR: Goal-oriented Semantic Communication via Invariant Representation Learning](https://mlsanity.com/paper/2509.01119/) (2025)
- [Gaussian Joint Embeddings For Self-Supervised Representation Learning](https://mlsanity.com/paper/2603.26799/) (2026)
- [A Novel Information-Theoretic Objective to Disentangle Representations for Fair Classification](https://mlsanity.com/paper/2310.13990/) (2023)
- [Model-enhanced Contrastive Reinforcement Learning for Sequential Recommendation](https://mlsanity.com/paper/2310.16566/) (2023)
- [Curriculum Recommendations Using Transformer Base Model with InfoNCE Loss And Language Switching Method](https://mlsanity.com/paper/2401.09699/) (2024)
- [Stack Trace Deduplication: Faster, More Accurately, and in More Realistic Scenarios](https://mlsanity.com/paper/2412.14802/) (2024)
- [Progressive Domain Adaptation with Contrastive Learning for Object Detection in the Satellite Imagery](https://mlsanity.com/paper/2209.02564/) (2022)
- [From "What-If" to "What-Is": Counterfactual Thinking-Inspired Semantic Alignment for Visual Brain Decoding](https://mlsanity.com/paper/2608.15163/) (2026)

## Abstract (arXiv)

InfoNCE loss is a widely used loss function for contrastive model training. It aims to estimate the mutual information between a pair of variables by discriminating between each positive pair and its associated K negative pairs. It is proved that when the sample labels are clean, the lower bound of mutual information estimation is tighter when more negative samples are incorporated, which usually yields better model performance. However, in many real-world tasks the labels often contain noise, and incorporating too many noisy negative samples for model training may be suboptimal. In this paper, we study how many negative samples are optimal for InfoNCE in different scenarios via a semi-quantitative theoretical framework. More specifically, we first propose a probabilistic model to analyze the influence of the negative sampling ratio K on training sample informativeness. Then, we design a training effectiveness function to measure the overall influence of training samples on model learning based on their informativeness. We estimate the optimal negative sampling ratio using the K value that maximizes the training effectiveness function. Based on our framework, we further propose an adaptive negative sampling method that can dynamically adjust the negative sampling ratio to improve InfoNCE based model training. Extensive experiments on different real-world datasets show our framework can accurately predict the optimal negative sampling ratio in different tasks, and our proposed adaptive negative sampling method can achieve better performance than the commonly used fixed negative sampling ratio strategy.