# Simpler, Faster, Stronger: Breaking The log-K Curse On Contrastive Learners With FlatNCE

arXiv: https://arxiv.org/abs/2107.01152 · HTML: https://mlsanity.com/paper/2107.01152/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 70 references that are in the map.
- First posted on arXiv 2 Jul 2021.

## Builds on (most cited first, 30 of 44)

- [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)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Self-Supervised Learning of Pretext-Invariant Representations](https://mlsanity.com/paper/1912.01991/) (2019)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [CURL: Contrastive Unsupervised Representations for Reinforcement Learning](https://mlsanity.com/paper/2004.04136/) (2020)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Data-Efficient Image Recognition with Contrastive Predictive Coding](https://mlsanity.com/paper/1905.09272/) (2019)
- [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 Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Hard Negative Mixing for Contrastive Learning](https://mlsanity.com/paper/2010.01028/) (2020)
- [Debiased Contrastive Learning](https://mlsanity.com/paper/2007.00224/) (2020)
- [Keystroke Dynamics as Part of Lifelogging](https://mlsanity.com/paper/2010.10144/) (2020)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)

## Built on by (most cited first, 22 of 22)

- [CLOOB: Modern Hopfield Networks with InfoLOOB Outperform CLIP](https://mlsanity.com/paper/2110.11316/) (2021)
- [Provable Stochastic Optimization for Global Contrastive Learning: Small Batch Does Not Harm Performance](https://mlsanity.com/paper/2202.12387/) (2022)
- [Exploring Patch-wise Semantic Relation for Contrastive Learning in Image-to-Image Translation Tasks](https://mlsanity.com/paper/2203.01532/) (2022)
- [Not All Semantics are Created Equal: Contrastive Self-supervised Learning with Automatic Temperature Individualization](https://mlsanity.com/paper/2305.11965/) (2023)
- [The Role of Entropy and Reconstruction in Multi-View Self-Supervised Learning](https://mlsanity.com/paper/2307.10907/) (2023)
- [Model-Aware Contrastive Learning: Towards Escaping the Dilemmas](https://mlsanity.com/paper/2207.07874/) (2022)
- [PUMA: Layer-Pruned Language Model for Efficient Unified Multimodal Retrieval with Modality-Adaptive Learning](https://mlsanity.com/paper/2507.08064/) (2025)
- [RenyiCL: Contrastive Representation Learning with Skew Renyi Divergence](https://mlsanity.com/paper/2208.06270/) (2022)
- [Evaluating Self-Supervised Learning via Risk Decomposition](https://mlsanity.com/paper/2302.03068/) (2023)
- [Statistically Efficient Bayesian Sequential Experiment Design via Reinforcement Learning with Cross-Entropy Estimators](https://mlsanity.com/paper/2305.18435/) (2023)
- [Variational Inference Failures Under Model Symmetries: Permutation Invariant Posteriors for Bayesian Neural Networks](https://mlsanity.com/paper/2408.05496/) (2024)
- [Supervised Fine-Tuning or Contrastive Learning? Towards Better Multimodal LLM Reranking](https://mlsanity.com/paper/2510.14824/) (2025)
- [COMICS: End-to-end Bi-grained Contrastive Learning for Multi-face Forgery Detection](https://mlsanity.com/paper/2308.01520/) (2023)
- [PLReMix: Combating Noisy Labels with Pseudo-Label Relaxed Contrastive Representation Learning](https://mlsanity.com/paper/2402.17589/) (2024)
- [Multi-Level Contrastive Learning for Cross-Lingual Alignment](https://mlsanity.com/paper/2202.13083/) (2022)
- [Variational Inference with Holder Bounds](https://mlsanity.com/paper/2111.02947/) (2021)
- [Unsupervised Synthetic Image Refinement via Contrastive Learning and Consistent Semantic-Structural Constraints](https://mlsanity.com/paper/2304.12591/) (2023)
- [Temporal Representations for Exploration: Learning Complex Exploratory Behavior without Extrinsic Rewards](https://mlsanity.com/paper/2603.02008/) (2026)
- [Skill-aware Mutual Information Optimisation for Generalisation in Reinforcement Learning](https://mlsanity.com/paper/2406.04815/) (2024)
- [Deploying self-supervised learning in the wild for hybrid automatic speech recognition](https://mlsanity.com/paper/2205.08598/) (2022)
- [SemST: Semantically Consistent Multi-Scale Image Translation via Structure-Texture Alignment](https://mlsanity.com/paper/2310.04995/) (2023)
- [HARMONY: Bridging the Personalization-Generalization Gap by Mitigating Representation Skew in Heterogeneous Split Federated Learning](https://mlsanity.com/paper/2605.07211/) (2026)

## Abstract (arXiv)

InfoNCE-based contrastive representation learners, such as SimCLR, have been tremendously successful in recent years. However, these contrastive schemes are notoriously resource demanding, as their effectiveness breaks down with small-batch training (i.e., the log-K curse, whereas K is the batch-size). In this work, we reveal mathematically why contrastive learners fail in the small-batch-size regime, and present a novel simple, non-trivial contrastive objective named FlatNCE, which fixes this issue. Unlike InfoNCE, our FlatNCE no longer explicitly appeals to a discriminative classification goal for contrastive learning. Theoretically, we show FlatNCE is the mathematical dual formulation of InfoNCE, thus bridging the classical literature on energy modeling; and empirically, we demonstrate that, with minimal modification of code, FlatNCE enables immediate performance boost independent of the subject-matter engineering efforts. The significance of this work is furthered by the powerful generalization of contrastive learning techniques, and the introduction of new tools to monitor and diagnose contrastive training. We substantiate our claims with empirical evidence on CIFAR10, ImageNet, and other datasets, where FlatNCE consistently outperforms InfoNCE.