# Embedding Space Interpolation Beyond Mini-Batch, Beyond Pairs and Beyond Examples

arXiv: https://arxiv.org/abs/2311.05538 · HTML: https://mlsanity.com/paper/2311.05538/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 73 references that are in the map.
- First posted on arXiv 9 Nov 2023.

## Builds on (most cited first, 30 of 59)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Random Erasing Data Augmentation](https://mlsanity.com/paper/1708.04896/) (2017)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [SimMIM: A Simple Framework for Masked Image Modeling](https://mlsanity.com/paper/2111.09886/) (2021)
- [iBOT: Image BERT Pre-Training with Online Tokenizer](https://mlsanity.com/paper/2111.07832/) (2021)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [AutoAugment: Learning Augmentation Policies from Data](https://mlsanity.com/paper/1805.09501/) (2018)
- [Dense Contrastive Learning for Self-Supervised Visual Pre-Training](https://mlsanity.com/paper/2011.09157/) (2020)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [Multi-Similarity Loss with General Pair Weighting for Deep Metric Learning](https://mlsanity.com/paper/1904.06627/) (2019)

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

- [Mixture of Mixups for Multi-label Classification of Rare Anuran Sounds](https://mlsanity.com/paper/2403.09598/) (2024)
- [Acoustic Feature Mixup for Balanced Multi-aspect Pronunciation Assessment](https://mlsanity.com/paper/2406.15723/) (2024)
- [PowMix: A Versatile Regularizer for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2312.12334/) (2023)
- [MS-Mix: Sentiment-Guided Adaptive Augmentation for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2510.11579/) (2025)

## Abstract (arXiv)

Mixup refers to interpolation-based data augmentation, originally motivated as a way to go beyond empirical risk minimization (ERM). Its extensions mostly focus on the definition of interpolation and the space (input or feature) where it takes place, while the augmentation process itself is less studied. In most methods, the number of generated examples is limited to the mini-batch size and the number of examples being interpolated is limited to two (pairs), in the input space. We make progress in this direction by introducing MultiMix, which generates an arbitrarily large number of interpolated examples beyond the mini-batch size and interpolates the entire mini-batch in the embedding space. Effectively, we sample on the entire convex hull of the mini-batch rather than along linear segments between pairs of examples. On sequence data, we further extend to Dense MultiMix. We densely interpolate features and target labels at each spatial location and also apply the loss densely. To mitigate the lack of dense labels, we inherit labels from examples and weight interpolation factors by attention as a measure of confidence. Overall, we increase the number of loss terms per mini-batch by orders of magnitude at little additional cost. This is only possible because of interpolating in the embedding space. We empirically show that our solutions yield significant improvement over state-of-the-art mixup methods on four different benchmarks, despite interpolation being only linear. By analyzing the embedding space, we show that the classes are more tightly clustered and uniformly spread over the embedding space, thereby explaining the improved behavior.