# MIO : Mutual Information Optimization using Self-Supervised Binary Contrastive Learning

arXiv: https://arxiv.org/abs/2111.12664 · HTML: https://mlsanity.com/paper/2111.12664/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 55 references that are in the map.
- First posted on arXiv 24 Nov 2021.

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [Unsupervised Visual Representation Learning by Context Prediction](https://mlsanity.com/paper/1505.05192/) (2015)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Large Batch Training of Convolutional Networks](https://mlsanity.com/paper/1708.03888/) (2017)
- [An Investigation into Neural Net Optimization via Hessian Eigenvalue Density](https://mlsanity.com/paper/1901.10159/) (2019)
- [Empirical Analysis of the Hessian of Over-Parametrized Neural Networks](https://mlsanity.com/paper/1706.04454/) (2017)
- [Gradient Descent Happens in a Tiny Subspace](https://mlsanity.com/paper/1812.04754/) (2018)
- [Formal Limitations on the Measurement of Mutual Information](https://mlsanity.com/paper/1811.04251/) (2018)
- [Decoupled Contrastive Learning](https://mlsanity.com/paper/2110.06848/) (2021)
- [Self-supervised Video Representation Learning by Pace Prediction](https://mlsanity.com/paper/2008.05861/) (2020)
- [Traces of Class/Cross-Class Structure Pervade Deep Learning Spectra](https://mlsanity.com/paper/2008.11865/) (2020)
- [Self-Supervised Spatiotemporal Feature Learning via Video Rotation Prediction](https://mlsanity.com/paper/1811.11387/) (2018)
- [Learning Image Representations by Completing Damaged Jigsaw Puzzles](https://mlsanity.com/paper/1802.01880/) (2018)

## Built on by (most cited first, 1 of 1)

- [Understanding Self-supervised Contrastive Learning through Supervised Objectives](https://mlsanity.com/paper/2510.10572/) (2025)

## Abstract (arXiv)

Self-supervised contrastive learning frameworks have progressed rapidly over the last few years. In this paper, we propose a novel loss function for contrastive learning. We model our pre-training task as a binary classification problem to induce an implicit contrastive effect. We further improve the n"aive loss function after removing the effect of the positive-positive repulsion and incorporating the upper bound of the negative pair repulsion. Unlike existing methods, the proposed loss function optimizes the mutual information in positive and negative pairs. We also present a closed-form expression for the parameter gradient flow and compare the behaviour of self-supervised contrastive frameworks using Hessian eigenspectrum to analytically study their convergence. The proposed method outperforms SOTA self-supervised contrastive frameworks on benchmark datasets such as CIFAR-10, CIFAR-100, STL-10, and Tiny-ImageNet. After 200 pretraining epochs with ResNet-18 as the backbone, the proposed model achieves an accuracy of 86.36%, 58.18%, 80.50%, and 30.87% on the CIFAR-10, CIFAR-100, STL-10, and Tiny-ImageNet datasets, respectively, and surpasses the SOTA contrastive baseline by 1.93%, 3.57%, 4.85%, and 0.33%, respectively. The proposed framework also achieves a state-of-the-art accuracy of 78.4% (200 epochs) and 65.22% (100 epochs) Top-1 Linear Evaluation accuracy on ImageNet100 and ImageNet1K datasets, respectively.