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https://github.com/ZIYU-DEEP/Awesome-Information-Bottleneck

This is a curated list for Information Bottleneck Principle, in memory of Professor Naftali Tishby.
https://github.com/ZIYU-DEEP/Awesome-Information-Bottleneck

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This is a curated list for Information Bottleneck Principle, in memory of Professor Naftali Tishby.

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# Awesome Information Bottleneck Paper List [![Awesome](https://awesome.re/badge-flat2.svg)](https://awesome.re) [![PRs Welcome](https://img.shields.io/badge/PRs-welcome-brightgreen.svg?style=flat-square)](http://makeapullrequest.com)



*In memory of Professor Naftali Tishby.*\

*Last updated on October, 2022.*





## 0. Introduction

![illustration](./illustration.png)

**To learn, you must forget**. This may probably be one of the most intuitive lessons we have from Naftali Tishby's Information Bottleneck (IB) methods, which grew out of the fundamental tradeoff (rate *v.s.* distortion) from Claude Shannon's information theory, and later creatively explained the learning behaviors of deep neural networks by the fitting & compression framework.



It has been four years since the dazzling talk on [Opening the Black Box of Deep Neural Networks](https://www.youtube.com/watch?v=FSfN2K3tnJU), and more than twenty years since the [first paper](https://arxiv.org/abs/physics/0004057) on the Information Bottleneck method. It is time for us to take a look back, to celebrate what has been established, and to prepare for a future.



This repository is organized as follows:

- [Classics](#1-classics)

- [Reviews](#2-reviews)

- [Theories](#3-theories)

- [Models](#4-models)

- [Applications (General)](#5-applications-general)

- [Applications (RL)](#6-applications-rl)

- [Methods for Mutual Information Estimation](#7-methods-for-mutual-information-estimation) (😣 MI is notoriously hard to estimate! )

- [Other Information Theory Driven Work](#8-other-information-theory-driven-work) (verbose)

- [Citation](#9-citation)



All papers are selected and sorted by topic/conference/year/importance. Please send a pull request if you would like to add any paper.



We also made [slides on theory, applications and controversy](https://github.com/ZIYU-DEEP/Awesome-Information-Bottleneck/blob/main/IB-Intro-Ye.pdf) for the initial Information Bottleneck principle in deep learning (*p.s.*, some controversy has been addressed by recent publications, *e.g.*, [Lorenzen et al., 2021](http://arxiv.org/abs/2106.12912v1)).



## 1. Classics

**Agglomerative Information Bottleneck** [[link](https://papers.nips.cc/paper/1999/file/be3e9d3f7d70537357c67bb3f4086846-Paper.pdf)] \

Noam Slonim, Naftali Tishby\

*NIPS, 1999*





🐤 **The Information Bottleneck Method** [[link](https://arxiv.org/abs/physics/0004057)] \

Naftali Tishby, Fernando C. Pereira, William Bialek\

*Preprint, 2000*





**Predictability, complexity and learning** [[link](https://pubmed.ncbi.nlm.nih.gov/11674845/)] \

William Bialek, Ilya Nemenman, Naftali Tishby\

*Neural Computation, 2001*





**Sufficient Dimensionality Reduction: A novel analysis principle** [[link](https://www.cs.huji.ac.il/labs/learning/Papers/sdr_ICML.pdf)] \

Amir Globerson, Naftali Tishby\

*ICML, 2002*





**The information bottleneck: Theory and applications** [[link](http://www.yaroslavvb.com/papers/slonim-information.pdf)] \

Noam Slonim\

*PhD Thesis, 2002*





**An Information Theoretic Tradeoff between Complexity and Accuarcy** [[link](https://www.cs.huji.ac.il/labs/learning/Papers/ib_theory.pdf)] \

Ran Gilad-Bachrach, Amir Navot, Naftali Tishby\

*COLT, 2003*





**Information Bottleneck for Gaussian Variables** [[link](https://www.cs.huji.ac.il/labs/learning/Papers/GIB_JMLR2004.pdf)] \

Gal Chechik, Amir Globerson, Naftali Tishby, Yair Weiss\

*NIPS, 2003*





**Information and Fitness** [[link](https://www.cs.huji.ac.il/labs/learning/Papers/info+fitness.pdf)] \

Samuel F. Taylor, Naftali Tishby and William Bialek\

*Preprint, 2007*





**Efficient representation as a design principle for neural coding and computation** [[link](https://arxiv.org/abs/0712.4381)] \

William Bialek, Rob R. de Ruyter van Steveninck, and Naftali Tishby\

*Preprint, 2007*





**The Information Bottleneck Revisited or How to Choose a Good Distortion Measure** [[link](https://www.cs.huji.ac.il/labs/learning/Papers/flaske2.pdf)] \

Peter Harremoes and Naftali Tishby\

*ISIT, 2007*





🐤 **Learning and Generalization with the Information Bottleneck** [[link](https://www.cs.huji.ac.il/labs/learning/Papers/ibgen_full.pdf)] \

Ohad Shamir, Sivan Sabato, Naftali Tishby\

*Journal of Theoretical Computer Science, 2009*





🐤 **Information-Theoretic Bounded Rationality** [[link](https://arxiv.org/abs/1512.06789)] \

Pedro A. Ortega, Daniel A. Braun, Justin Dyer, Kee-Eung Kim, Naftali Tishby\

*Preprint, 2015*





🐤 **Opening the Black Box of Deep Neural Networks via Information** [[link](https://arxiv.org/abs/1703.00810)] \

Ravid Shwartz-Ziv, Naftali Tishby\

*ICRI, 2017*





## 2. Reviews

**Information Bottleneck and its Applications in Deep Learning** [[link](https://arxiv.org/abs/1904.03743)] \

Hassan Hafez-Kolahi, Shohreh Kasaei\

*Preprint, 2019*





**The Information Bottleneck Problem and Its Applications in Machine Learning** [[link](https://arxiv.org/abs/2004.14941)] \

Ziv Goldfeld, Yury Polyanskiy\

*Preprint, 2020*





**On the Information Bottleneck Problems: Models, Connections, Applications and Information Theoretic Views** [[link](https://www.mdpi.com/1099-4300/22/2/151)] \

Abdellatif Zaidi, Iñaki Estella-Aguerri, Shlomo Shamai\

*Entropy, 2020*





**Information Bottleneck: Theory and Applications in Deep Learning** [[link](https://www.mdpi.com/1099-4300/22/12/1408)] \

Bernhard C. Geiger, Gernot Kubin\

*Entropy, 2020*





**On Information Plane Analyses of Neural Network Classifiers – A Review** [[link](https://arxiv.org/abs/2003.09671)] \

Bernhard C. Geiger\

*Preprint, 2021*

> Table 1 (p.2) gives a nice summary on the effect of different architectures & MI estimators on the existence of the compression phases and causal links between compression and generalizations.



**A Critical Review of Information Bottleneck Theory and its Applications to Deep Learning** [[link](https://arxiv.org/abs/2105.04405v1)] \

Mohammad Ali Alomrani\

*Preprint, 2021*





**Information Flow in Deep Neural Networks** [[link](https://arxiv.org/abs/2202.06749)] \

Ravid Shwartz-Ziv\

*PhD Thesis, 2022*





## 3. Theories

**Gaussian Lower Bound for the Information Bottleneck Limit** [[link](https://www.jmlr.org/papers/volume18/17-398/17-398.pdf)] \

Amichai Painsky, Naftali Tishby\

*JMLR, 2017*





**Information-theoretic analysis of generalization capability of learning algorithms** [[link](https://arxiv.org/pdf/1705.07809.pdf)] \

Aolin Xu, Maxim Raginsky\

*NeurIPS, 2017*





**Caveats for information bottleneck in deterministic scenarios** [[link](https://arxiv.org/abs/1808.07593)] [[ICLR version](https://openreview.net/forum?id=rke4HiAcY7)]\

Artemy Kolchinsky, Brendan D. Tracey, Steven Van Kuyk\

*UAI, 2018*





🐤🔥 **Emergence of Invariance and Disentanglement in Deep Representations** [[link](https://arxiv.org/abs/1706.01350)] \

Alessandro Achille, Stefano Soatto\

*JMLR, 2018*

> - This paper is a gem. On a high-level, it shows the relationship of generalization and **information bottleneck in weights** (IIW).

>   - Be aware how this differs from Tishby's original definition on information bottleneck in representation).

> - Specifically, if we approximate SGD by stochastic differential equations, we can see that SGD naturally leads to minimization in IIW.

> - The authors argue that *an* optimal representation should have 4 properties: *sufficiency*, *minimality*, *invariance*, and *disentanglement*. Notably, the last two properties can naturally emerge with the minimization in mutual information between the datasets and network weights, or IIW.







**On the Information Bottleneck Theory of Deep Learning** [[link](https://openreview.net/forum?id=ry_WPG-A-)] \

Andrew Michael Saxe, Yamini Bansal, Joel Dapello, Madhu Advani, Artemy Kolchinsky, Brendan Daniel Tracey, David Daniel Cox\

*ICLR, 2018*





**The Dual Information Bottleneck** [[link](https://arxiv.org/abs/2006.04641v1)] \

Zoe Piran, Ravid Shwartz-Ziv, Naftali Tishby\

*Preprint, 2019*





🐤 **Learnability for the Information Bottleneck** [[link](https://arxiv.org/abs/1907.07331)] [[slides](https://docs.google.com/presentation/d/1sBYA6V-mL6cwYxEWxA5oMDOKYEq1FIjvZ3jOoXDlVD8/edit?usp=sharing)] [[poster](https://docs.google.com/presentation/d/1jkMxI7j8YXTxtUdy9PAtRfYRaLvFdT7hI1qP9m-qDbE/edit?usp=sharing)] [[journal version](https://www.mdpi.com/1099-4300/21/10/924)] [[workshop version](https://openreview.net/forum?id=SJePKo5HdV)] \

Tailin Wu, Ian Fischer, Isaac L. Chuang, Max Tegmark\

*UAI, 2019*





🐤 **Phase Transitions for the Information Bottleneck in Representation Learning** [[link](https://openreview.net/forum?id=HJloElBYvB)] [[video](https://media.mis.mpg.de/mml/2021-02-04)] \

Tailin Wu, Ian Fischer\

*ICLR, 2020*





**Bottleneck Problems: Information and Estimation-Theoretic View** [[link](http://arxiv.org/abs/2011.06208v1)] \

Shahab Asoodeh, Flavio Calmon\

*Preprint, 2020*





**Information Bottleneck: Exact Analysis of (Quantized) Neural Networks** [[link](http://arxiv.org/abs/2106.12912v1)] \

Stephan Sloth Lorenzen, Christian Igel, Mads Nielsen\

*Preprint, 2021*

> - This paper shows that **different ways of binning** when **computing the mutual information** leads to qualitatively different results.

> - It then confirms then original IB paper's results of the **fitting & compression** phase using quantized nets with exact computation for mutual information.







**Perturbation Theory for the Information Bottleneck** [[link](http://arxiv.org/abs/2105.13977v1)] \

Vudtiwat Ngampruetikorn, David J. Schwab\

*Preprint, 2021*





**PAC-Bayes Information Bottleneck** [[link](https://openreview.net/forum?id=iLHOIDsPv1P)] \

Zifeng Wang, Shao-Lun Huang, Ercan Engin Kuruoglu, Jimeng Sun, Xi Chen, Yefeng Zheng\

*ICLR, 2022*

> - This paper discusses using $I(w, S)$ instead to $I(T, X)$ as the information bottleneck.

> - However, ***activations*** should in effect play a crucial role in network's generalization, but they are not explicitly captured by $I(w, S)$.







## 4. Models

**Deep Variational Information Bottleneck** [[link](https://openreview.net/forum?id=HyxQzBceg)] \

Alexander A. Alemi, Ian Fischer, Joshua V. Dillon, Kevin Murphy\

*ICLR, 2017*





**The Deterministic Information Bottleneck** [[link](https://direct.mit.edu/neco/article/29/6/1611/8273/The-Deterministic-Information-Bottleneck)] [[UAI Version](https://www.auai.org/uai2016/proceedings/papers/319.pdf)] \

DJ Strouse, David J. Schwab\

*Neural Computation, 2017*

> This replaces the mutual information term with entropy in the original IB objective.







**Learning Sparse Latent Representations with the Deep Copula Information Bottleneck** [[link](https://openreview.net/forum?id=Hk0wHx-RW)] \

Aleksander Wieczorek, Mario Wieser, Damian Murezzan, Volker Roth \

*ICLR, 2018*





**Generalization in Reinforcement Learning with Selective Noise Injection and Information Bottleneck** [[link](https://papers.nips.cc/paper/2019/hash/e2ccf95a7f2e1878fcafc8376649b6e8-Abstract.html)] \

Maximilian Igl, Kamil Ciosek, Yingzhen Li, Sebastian Tschiatschek, Cheng Zhang, Sam Devlin, Katja Hofmann\

*NeurIPS, 2019*





**Information bottleneck through variational glasses** [[link](http://bayesiandeeplearning.org/2019/papers/75.pdf)]\

Slava Voloshynovskiy, Mouad Kondah, Shideh Rezaeifar, Olga Taran, Taras Holotyak, Danilo Jimenez Rezende\

*NeurIPS Bayesian Deep Learning Workshop, 2019*





🐤 **Variational Discriminator Bottleneck** [[link](https://openreview.net/forum?id=HyxPx3R9tm)] \

Xue Bin Peng, Angjoo Kanazawa, Sam Toyer, Pieter Abbeel, Sergey Levine\

*ICLR, 2019*





**Nonlinear Information Bottleneck** [[link](https://www.mdpi.com/1099-4300/21/12/1181)] \

Artemy Kolchinsky, Brendan Tracey, David Wolpert\

*Entropy, 2019*

> This formuation shows better performance than VIB.







**General Information Bottleneck Objectives and their Applications to Machine Learning** [[link](https://arxiv.org/pdf/1912.06248.pdf)] \

Sayandev Mukherjee\

*Preprint, 2019*

> This paper synthesize IB and Predictive IB, and provides a new variational bound.







🐤 **Graph Information Bottleneck** [[link](https://arxiv.org/abs/2010.12811)] [[code](https://github.com/snap-stanford/GIB)] [[slides](https://docs.google.com/presentation/d/1yGs6kfaFHKlZdu0REuSpZTN4Pqt7b0bAnh2y8lvYm3A/edit)] \

Tailin Wu, Hongyu Ren, Pan Li, Jure Leskovec,\

*NeurIPS, 2020*





🐤 **Learning Optimal Representations with the Decodable Information Bottleneck** [[link](https://papers.nips.cc/paper/2020/hash/d8ea5f53c1b1eb087ac2e356253395d8-Abstract.html)] \

Yann Dubois, Douwe Kiela, David J. Schwab, Ramakrishna Vedantam\

*NeurIPS, 2020*





🐤 **Concept Bottleneck Models** [[link](https://arxiv.org/abs/2007.04612v3)] \

Pang Wei Koh, Thao Nguyen, Yew Siang Tang, Stephen Mussmann, Emma Pierson, Been Kim, Percy Liang\

*ICML, 2020*





**Disentangled Representations for Sequence Data using Information Bottleneck Principle** [[link](http://proceedings.mlr.press/v129/yamada20a.html)] [[talk](https://papertalk.org/papertalks/13911)] \

Masanori Yamada, Heecheol Kim, Kosuke Miyoshi, Tomoharu Iwata, Hiroshi Yamakawa\

*ICML, 2020*





🐤 **IBA: Restricting the Flow: Information Bottlenecks for Attribution** [[link](https://openreview.net/forum?id=S1xWh1rYwB)] [[code](https://github.com/BioroboticsLab/IBA)] \

Karl Schulz, Leon Sixt, Federico Tombari, Tim Landgraf\

*ICLR, 2020*





**On the Difference between the Information Bottleneck and the Deep Information Bottleneck** [[link](https://www.mdpi.com/1099-4300/22/2/131)] \

Aleksander Wieczorek, Volker Roth\

*Entropy, 2020*





**The Convex Information Bottleneck Lagrangian** [[link](http://arxiv.org/abs/1911.11000v2)] \

Borja Rodríguez Gálvez, Ragnar Thobaben, Mikael Skoglund\

*Preprint, 2020*





**The HSIC Bottleneck: Deep Learning without Back-Propagation** [[link](https://arxiv.org/abs/1908.01580)] [[code](https://github.com/choasma/HSIC-bottleneck)] \

Wan-Duo Kurt Ma, J.P. Lewis, W. Bastiaan Kleijn

*AAAI, 2020*

> - This paper uses Hilbert-Schmidt independence criterion (HSIC) as a surrogate to compute mutual information in IB objective.

> - It shows an alternative way to learn a neural network without backpropagation, inspired by the IB principle.



**Disentangled Information Bottleneck** [[link](https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwjhjduUk_vyAhVZ6XMBHQlpBPoQFnoECAQQAQ&url=https%3A%2F%2Fojs.aaai.org%2Findex.php%2FAAAI%2Farticle%2Fview%2F17120%2F16927&usg=AOvVaw1yu4FBl7RBV1xGUgh21VmY)] [[code](https://github.com/PanZiqiAI/disentangled-information-bottleneck)] \

Ziqi Pan, Li Niu, Jianfu Zhang, Liqing Zhang\

*AAAI, 2021*





🐤 **IB-GAN: Disentangled Representation Learning** [[link](https://ojs.aaai.org/index.php/AAAI/article/view/16967)] [[code](https://github.com/insuj3on/IB-GAN)][[talk](https://papertalk.org/papertalks/30379)]\

Insu Jeon, Wonkwang Lee, Myeongjang Pyeon, Gunhee Kim\

*AAAI, 2021*

> This model add additional IB constraint based on InfoGAN.







**Deciding What to Learn: A Rate-Distortion Approach** [[link](https://arxiv.org/abs/2101.06197v3)] \

Dilip Arumugam, Benjamin Van Roy\

*ICML, 2021*





🐤 **Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization** [[link](http://arxiv.org/abs/2106.06607v1)] \

Kartik Ahuja, Ethan Caballero, Dinghuai Zhang, Yoshua Bengio, Ioannis Mitliagkas, Irina Rish\

*Preprint, 2021*





**Multi-Task Variational Information Bottleneck** [[link](http://arxiv.org/abs/2007.00339v4)] \

Weizhu Qian, Bowei Chen, Yichao Zhang, Guanghui Wen, Franck Gechter\

*Preprint, 2021*





## 5. Applications (General)

🐤 **Analyzing neural codes using the information bottleneck method** [[link](https://www.cs.huji.ac.il/labs/learning/Papers/nips01_sub.pdf)] \

Elad Schneidman, Noam Slonim, Naftali Tishby, Rob R. deRuyter van Steveninck, William Bialek\

*NIPS, 2001*





**Past-future information bottleneck in dynamical systems** [[link](https://journals.aps.org/pre/abstract/10.1103/PhysRevE.79.041925)] \

Felix Creutzig, Amir Globerson, Naftali Tishby\

*Physical Review, 2009*





**Compressing Neural Networks using the Variational Information Bottleneck** [[link](http://proceedings.mlr.press/v80/dai18d.html)] \

Bin Dai, Chen Zhu, Baining Guo, David Wipf \

*ICML, 2018*





🐤 **InfoMask: Masked Variational Latent Representation to Localize Chest Disease** [[link](https://arxiv.org/abs/1903.11741)] \

Saeid Asgari Taghanaki, Mohammad Havaei, Tess Berthier, Francis Dutil, Lisa Di Jorio, Ghassan Hamarneh, Yoshua Bengio\

*MICCAI, 2019*

> Be aware how this differs from the [IBA](https://openreview.net/forum?id=S1xWh1rYwB) paper.







**Past–future information bottleneck for sampling molecular reaction coordinate simultaneously with thermodynamics and kinetics** [[link](https://www.nature.com/articles/s41467-019-11405-4)] \

Yihang Wang, João Marcelo Lamim Ribeiro, Pratyush Tiwary\

*Nature Communications, 2019*





**Kernelized information bottleneck leads to biologically plausible 3-factor Hebbian learning in deep networks** [[link](https://papers.nips.cc/paper/2020/hash/517f24c02e620d5a4dac1db388664a63-Abstract.html)] \

Roman Pogodin, Peter Latham\

*NeurIPS, 2020*





**Training Normalizing Flows with the Information Bottleneck for Competitive Generative Classification** [[link](https://papers.nips.cc/paper/2020/hash/593906af0d138e69f49d251d3e7cbed0-Abstract.html)] \

Lynton Ardizzone, Radek Mackowiak, Carsten Rother, Ullrich Köthe\

*NeurIPS, 2020*





**Unsupervised Speech Decomposition via Triple Information Bottleneck** [[link](https://proceedings.mlr.press/v119/qian20a.html)] [[code](https://github.com/auspicious3000/SpeechSplit)] \

Kaizhi Qian, Yang Zhang, Shiyu Chang, Mark Hasegawa-Johnson, David Cox\

*ICML, 2020*





**Learning Efficient Multi-agent Communication: An Information Bottleneck Approach** [[link](https://proceedings.mlr.press/v119/wang20i.html)] \

Rundong Wang, Xu He, Runsheng Yu, Wei Qiu, Bo An, Zinovi Rabinovich\

*ICML, 2020*





🐤 **Inserting Information Bottlenecks for Attribution in Transformers** [[link](https://arxiv.org/abs/2012.13838v2)] \

Zhiying Jiang, Raphael Tang, Ji Xin, Jimmy Lin\

*EMNLP, 2020*





**Information Bottleneck for Estimating Treatment Effects with Systematically Missing Covariates** [[link](https://www.mdpi.com/1099-4300/22/4/389)] \

Sonali Parbhoo, Mario Wieser, Aleksander Wieczorek, and Volker Roth\

*Entropy, 2020*





**Variational Information Bottleneck for Unsupervised Clustering: Deep Gaussian Mixture Embedding** [[link](http://arxiv.org/abs/1905.11741v3)] \

Yigit Ugur, George Arvanitakis, Abdellatif Zaidi\

*Entropy, 2020*





**Learning to Learn with Variational Information Bottleneck for Domain Generalization** [[link](http://arxiv.org/abs/2007.07645v1)] \

Yingjun Du, Jun Xu, Huan Xiong, Qiang Qiu, Xiantong Zhen, Cees G. M. Snoek, Ling Shao\

*ECCV, 2020*





**The information bottleneck and geometric clustering** [[link](http://arxiv.org/abs/1712.09657v2)] \

DJ Strouse, David J Schwab\

*Preprint, 2020*





**Causal learning with sufficient statistics: an information bottleneck approach** [[link](http://arxiv.org/abs/2010.05375v1)] \

Daniel Chicharro, Michel Besserve, Stefano Panzeri\

*Preprint, 2020*





**Learning Robust Representations via Multi-View Information Bottleneck** [[link](http://arxiv.org/abs/2002.07017v2)] \

Marco Federici, Anjan Dutta, Patrick Forré, Nate Kushman, Zeynep Akata\

*Preprint, 2020*





🐤 **Information Bottleneck Disentanglement for Identity Swapping** [[link](https://openaccess.thecvf.com/content/CVPR2021/html/Gao_Information_Bottleneck_Disentanglement_for_Identity_Swapping_CVPR_2021_paper.html)] \

Gege Gao, Huaibo Huang, Chaoyou Fu, Zhaoyang Li, Ran He\

*CVPR, 2021*





**A Variational Information Bottleneck Based Method to Compress Sequential Networks for Human Action Recognition** [[link](https://openaccess.thecvf.com/content/WACV2021/papers/Srivastava_A_Variational_Information_Bottleneck_Based_Method_to_Compress_Sequential_Networks_WACV_2021_paper.pdf)] \

Ayush Srivastava, Oshin Dutta, Jigyasa Gupta, Sumeet Agarwal, Prathosh AP\

*WACV, 2021*





**The Variational Bandwidth Bottleneck: Stochastic Evaluation on an Information Budget** [[link](https://openreview.net/forum?id=Hye1kTVFDS)] \

Anirudh Goyal, Yoshua Bengio, Matthew Botvinick, Sergey Levine\

*ICLR, 2020*





**Variational Information Bottleneck for Effective Low-Resource Fine-Tuning** [[link](https://openreview.net/forum?id=kvhzKz-_DMF)] \

 Rabeeh Karimi mahabadi, Yonatan Belinkov, James Henderson \

*ICLR, 2021*





**Dynamic Bottleneck for Robust Self-Supervised Exploration** [[link](https://proceedings.neurips.cc/paper/2021/hash/8d3369c4c086f236fabf61d614a32818-Abstract.html)] \

Chenjia Bai, Lingxiao Wang, Lei Han, Animesh Garg, Jianye Hao, Peng Liu, Zhaoran Wang\

*NeurIPS, 2021*





**Distilling Robust and Non-Robust Features in Adversarial Examples by Information Bottleneck** [[link](https://openreview.net/forum?id=90M-91IZ0JC)] [[talk](https://papertalk.org/papertalks/35620)] \

Junho Kim, Byung-Kwan Lee, Yong Man Ro

*NeurIPS, 2021*





**Revisiting Hilbert-Schmidt Information Bottleneck for Adversarial Robustness** [[link](https://proceedings.neurips.cc/paper/2021/file/055e31fa43e652cb4ab6c0ee845c8d36-Paper.pdf)] [[talk](https://papertalk.org/papertalks/36111)] \

Zifeng Wang, Tong Jian, Aria Masoomi, Stratis Ioannidis, Jennifer Dy\

*NeurIPS, 2021*





**A Variational Information Bottleneck Approach to Multi-Omics Data Integration** [[link](http://arxiv.org/abs/2102.03014v2)] \

Changhee Lee, Mihaela van der Schaar\

*AISTATS, 2021*





**Information Bottleneck Approach to Spatial Attention Learning** [[link](http://arxiv.org/abs/2108.03418v1)] \

Qiuxia Lai, Yu Li, Ailing Zeng, Minhao Liu, Hanqiu Sun, Qiang Xu\

*IJCAI, 2021*





**Unsupervised Hashing with Contrastive Information Bottleneck** [[link](http://arxiv.org/abs/2105.06138v2)] \

Zexuan Qiu, Qinliang Su, Zijing Ou, Jianxing Yu, Changyou Chen\

*IJCAI, 2021*





**Neuron Campaign for Initialization Guided by Information Bottleneck Theory** [[link](http://arxiv.org/abs/2108.06530v1)] \

Haitao Mao, Xu Chen, Qiang Fu, Lun Du, Shi Han, Dongmei Zhang\

*CIKM, 2021*





**Information Theoretic Meta Learning with Gaussian Processes** [[link](https://arxiv.org/pdf/2009.03228.pdf)] \

Michalis K. Titsias, Francisco J. R. Ruiz, Sotirios Nikoloutsopoulos, Alexandre Galashov\

*UAI, 2021*





**A Closer Look at the Adversarial Robustness of Information Bottleneck Models** [[link](http://arxiv.org/abs/2107.05712v1)] \

Iryna Korshunova, David Stutz, Alexander A. Alemi, Olivia Wiles, Sven Gowal\

*ICML Workshop on A Blessing in Disguise, 2021*





**Information Bottleneck Attribution for Visual Explanations of Diagnosis and Prognosis** [[link](http://arxiv.org/abs/2104.02869v2)] \

Ugur Demir, Ismail Irmakci, Elif Keles, Ahmet Topcu, Ziyue Xu, Concetto Spampinato, Sachin Jambawalikar, Evrim Turkbey, Baris Turkbey, Ulas Bagci\

*Preprint, 2021*





**State Predictive Information Bottleneck** [[link](https://arxiv.org/abs/2011.10127)] [[code](https://github.com/tiwarylab/State-Predictive-Information-Bottleneck)] \

Dedi Wang, Pratyush Tiwary\

*Preprint, 2021*





**Disentangled Variational Information Bottleneck for Multiview Representation Learning** [[link](http://arxiv.org/abs/2105.07599v1)] [[code](https://github.com/feng-bao-ucsf/DVIB)] \

Feng Bao\

*Preprint, 2021*





**Invariant Information Bottleneck for Domain Generalization** [[link](http://arxiv.org/abs/2106.06333v2)] \

Bo Li, Yifei Shen, Yezhen Wang, Wenzhen Zhu, Colorado J. Reed, Jun Zhang, Dongsheng Li, Kurt Keutzer, Han Zhao\

*Preprint, 2021*





**Information-Bottleneck-Based Behavior Representation Learning for Multi-agent Reinforcement learning** [[link](https://arxiv.org/abs/2109.14188)] \

Yue Jin, Shuangqing Wei, Jian Yuan, Xudong Zhang\

*Preprint, 2021*





**Generalization in Quantum Machine Learning: a Quantum Information Perspective** [[link](http://arxiv.org/abs/2102.08991)] \

Leonardo Banchi, Jason Pereira, Stefano Pirandola\

*Preprint, 2021*





**Causal Effect Estimation using Variational Information Bottleneck** [[link](https://arxiv.org/abs/2110.13705)] \

Zhenyu Lu, Yurong Cheng, Mingjun Zhong, George Stoian, Ye Yuan, Guoren Wang\

*Preprint, 2021*





**A Closer Look at the Adversarial Robustness of Information Bottleneck Models** [[link](https://arxiv.org/abs/2107.05712)] \

Iryna Korshunova, David Stutz, Alexander A. Alemi, Olivia Wiles, Sven Gowal\

*ICML Workshop on A Blessing in Disguise, 2021*





🐤 **Neuron Campaign for Initialization Guided by Information Bottleneck Theory** [[link](https://arxiv.org/abs/2108.06530)] \

Haitao Mao, Xu Chen, Qiang Fu, Lun Du, Shi Han, Dongmei Zhang\

*CIKM, 2021*





**Improving Subgraph Recognition with Variational Graph Information Bottleneck** [[link](https://arxiv.org/abs/2112.09899)] \

Junchi Yu, Jie Cao, Ran He\

*CVPR, 2022*





**Graph Structure Learning with Variational Information Bottleneck** [[link](https://arxiv.org/abs/2112.08903)] \

Qingyun Sun, Jianxin Li, Hao Peng, Jia Wu, Xingcheng Fu, Cheng Ji, Philip S. Yu\

*AAAI, 2022*





**Renyi Fair Information Bottleneck for Image Classification** [[link](https://arxiv.org/abs/2203.04950)] \

Adam Gronowski, William Paul, Fady Alajaji, Bahman Gharesifard, Philippe Burlina\

*Preprint, 2022*





**The Distributed Information Bottleneck reveals the explanatory structure of complex systems** [[link](https://arxiv.org/abs/2204.07576)] \

Kieran A. Murphy, Dani S. Bassett\

*Preprint, 2021*





**Sparsity-Inducing Categorical Prior Improves Robustness of the Information Bottleneck** [[link](https://arxiv.org/abs/2203.02592)] \

Anirban Samaddar, Sandeep Madireddy, Prasanna Balaprakash\

*Preprint, 2022*





**Pareto-optimal clustering with the primal deterministic information bottleneck** [[link](https://arxiv.org/abs/2204.02489)] \

Andrew K. Tan, Max Tegmark, Isaac L. Chuang\

*Preprint, 2022*





**Information-Theoretic Odometry Learning** [[link](https://arxiv.org/abs/2203.05724)] \

Sen Zhang, Jing Zhang, Dacheng Tao\

*Preprint, 2022*





**Causal Effect Estimation using Variational Information Bottleneck** [[link](https://arxiv.org/abs/2110.13705)] \

Zhenyu Lu, Yurong Cheng, Mingjun Zhong, George Stoian, Ye Yuan, Guoren Wang\

*Preprint, 2022*





## 6. Applications (RL)

**InfoBot: Transfer and Exploration via the Information Bottleneck** [[paper](https://openreview.net/forum?id=rJg8yhAqKm)] [[code](https://github.com/maximecb/gym-minigrid)]\

Anirudh Goyal, Riashat Islam, DJ Strouse, Zafarali Ahmed, Hugo Larochelle, Matthew Botvinick, Yoshua Bengio, Sergey Levine\

*ICLR, 2019*

> The idea is simply to constrain the dependence on a certain goal, so that the agent can learn a *default behavior*.







**Generalization in Reinforcement Learning with Selective Noise Injection and Information Bottleneck** [[link](https://arxiv.org/abs/1910.12911)] [[code](https://github.com/microsoft/IBAC-SNI)] [[talk](https://www.youtube.com/watch?v=tWtM4Dq05ZA)]\

Maximilian Igl, Kamil Ciosek, Yingzhen Li, Sebastian Tschiatschek, Cheng Zhang, Sam Devlin, Katja Hofmann\

*NeurIPS, 2019*





**Learning Task-Driven Control Policies via Information Bottlenecks** [[link](https://arxiv.org/abs/2002.01428)] [[spotlight talk](https://www.youtube.com/watch?v=nzLyRHON24E)]\

Vincent Pacelli, Anirudha Majumdar\

*RSS, 2020*





🐤 **The Bottleneck Simulator: A Model-based Deep Reinforcement Learning Approach** [[journal '20](https://www.jair.org/index.php/jair/article/view/12463/26616)] [[arxiv '18](https://arxiv.org/abs/1807.04723)]

Iulian Vlad Serban, Chinnadhurai Sankar, Michael Pieper, Joelle Pineau, Yoshua Bengio\

*Journal of Artificial Intelligence Research (JAIR), 2020*





**Learning Robust Representations via Multi-View Information Bottleneck** [[link](https://openreview.net/forum?id=B1xwcyHFDr)] [[code](https://github.com/mfederici/Multi-View-Information-Bottleneck)] [[talk](https://iclr.cc/virtual_2020/poster_B1xwcyHFDr.html)]\

Marco Federici, Anjan Dutta, Patrick Forré, Nate Kushman, Zeynep Akata\

*ICLR, 2020*





**DRIBO: Robust Deep Reinforcement Learning via Multi-View Information Bottleneck** [[paper](https://openreview.net/forum?id=Py8WbvKH_wv)] [[code](https://github.com/JmfanBU/DRIBO)]\

Jiameng Fan, Wenchao Li\

*ICML, 2022*





**Learning Representations in Reinforcement Learning: an Information Bottleneck Approach** [[link](https://openreview.net/forum?id=Syl-xpNtwS)] [[code](https://github.com/AnonymousSubmittedCode/SVIB)]\

Yingjun Pei, Xinwen Hou\

*Rejected by ICLR, 2020*





**Dynamics Generalization via Information Bottleneck in Deep Reinforcement Learning** [[link](https://arxiv.org/abs/2008.00614)]\

Xingyu Lu, Kimin Lee, Pieter Abbeel, Stas Tiomkin\

*ArXiv, 2020*





**Dynamic Bottleneck for Robust Self-Supervised Exploration** [[paper](https://openreview.net/forum?id=-t6TeG3A6Do)] [[code](https://github.com/Baichenjia/DB)]\

Chenjia Bai, Lingxiao Wang, Lei Han, Animesh Garg, Jianye HAO, Peng Liu, Zhaoran Wang\

*NeurIPS, 2021*





**Regret Bounds for Information-Directed Reinforcement Learning** [[paper](https://arxiv.org/abs/2206.04640)]\

Botao Hao, Tor Lattimore\

*ArXiv, 2022*





## 7. Methods for Mutual Information Estimation

> 😣😣😣 Mutual information is notoriously hard to estimate!



🐤 **Benchmarking Mutual Information** [[link](https://arxiv.org/pdf/2306.11078.pdf)] [[code](https://github.com/cbg-ethz/bmi)] [[doc](https://cbg-ethz.github.io/bmi/#getting-started)] \

Paweł Czyż, Frederic Grabowski, Julia E. Vogt, Niko Beerenwinkel, Alexander Marx\

*NeurIPS, 2023*





**Variational f-Divergence and Derangements for Discriminative Mutual Information Estimation** [[link](https://arxiv.org/abs/2305.20025)] [[code](https://github.com/tonellolab/fDIME)] \

Nunzio A. Letizia, Nicola Novello, Andrea M. Tonello\

*ArXiv, 2023*





**Estimating Mutual Information** [[link](https://arxiv.org/abs/cond-mat/0305641)] [[code](https://github.com/ravidziv/IDNNs)] \

Alexander Kraskov, Harald Stoegbauer, Peter Grassberger\

*Physical Review, 2004*





**Efficient Estimation of Mutual Information for Strongly Dependent Variables** [[link](https://arxiv.org/abs/1411.2003)] [[code](https://github.com/ravidziv/IDNNs)] \

Shuyang Gao, Greg Ver Steeg, Aram Galstyan\

*AISTATS, 2015*

> - This shows that KNN-based estimators requires number of samples which scales *exponentially* with the true MI; that is, they become inaccurate as MI gets large.

> - Thus, as the relationship become more dependent, the MI estimation becomes more inaccurate. Or in other words, KNN-based estimators are only good at *detecting independence of variables*.







🐤 **`MINE`: Mutual Information Neural Estimation** [[link](https://arxiv.org/abs/1801.04062)] [[code](https://github.com/gtegner/mine-pytorch)] \

Mohamed Ishmael Belghazi, Aristide Baratin, Sai Rajeswar, Sherjil Ozair, Yoshua Bengio, Aaron Courville, R Devon Hjelm\

*ICML, 2018*





**Evaluating Capability of Deep Neural Networks for Image Classification via Information Plane** [[link](https://openaccess.thecvf.com/content_ECCV_2018/html/Hao_Cheng_Evaluating_Capability_of_ECCV_2018_paper.html)] [[code](https://github.com/haochenglouis/ib_cnn)] \

Hao Cheng, Dongze Lian, Shenghua Gao, Yanlin Geng\

*ECCV, 2018*





🐤 **`InfoMax`: Learning Deep representations by Mutual Information Estimation and Maximization** [[link](https://arxiv.org/abs/1808.06670)] [[code](https://github.com/rdevon/DIM)] \

R Devon Hjelm, Alex Fedorov, Samuel Lavoie-Marchildon, Karan Grewal, Phil Bachman, Adam Trischler, Yoshua Bengio\

*ICLR, 2019 (Oral)*



🐤 **On Variational Bounds of Mutual Information** [[link](https://arxiv.org/pdf/1905.06922.pdf)] [[PyTorch](https://github.com/arashabzd/milib)] \

Ben Poole, Sherjil Ozair, Aaron van den Oord, Alexander A. Alemi, George Tucker\

*ICML, 2019*





🐤 **Estimating Information Flow in Deep Neural Networks** [[link](https://arxiv.org/abs/1810.05728)] [[PyTorch](https://github.com/ankithmo/estimateMI)] \

Ziv Goldfeld, Ewout van den Berg, Kristjan Greenewald, Igor Melnyk, Nam Nguyen, Brian Kingsbury, Yury Polyanskiy\

*ICML, 2019*





**Neural Estimators for Conditional Mutual Information Using Nearest Neighbors Sampling** [[link](https://arxiv.org/abs/2006.07225v3)] [[code](https://github.com/smolavipour/CMI_Neural_Estimator)] \

Sina Molavipour, Germán Bassi, Mikael Skoglund\

*Preprint, 2020*





**`CCMI`: Classifier based Conditional Mutual Information Estimation** [[link](https://arxiv.org/abs/1906.01824)] [[code](https://github.com/sudiptodip15/CCMI)] \

Sudipto Mukherjee, Himanshu Asnani, Sreeram Kannan\

*UAI, 2020*



**`MIGE`: Mutual Information Gradient Estimation for Representation Learning** [[link](https://arxiv.org/abs/2005.01123)] [[code](https://github.com/zhouyiji/MIGE)] \

Liangjian Wen, Yiji Zhou, Lirong He, Mingyuan Zhou, Zenglin Xu\

*ICLR, 2020*





🐤 **Information Bottleneck: Exact Analysis of (Quantized) Neural Networks** [[link](https://arxiv.org/abs/2106.12912v1)]\

Stephan Sloth Lorenzen, Christian Igel, Mads Nielsen\

*Preprint, 2021*

> - This paper shows that different ways of binning when computing the mutual information leads to qualitatively different results.

> - It then confirms then original IB paper's results of the fitting & compression phase using quantized nets with exact computation for mutual information.







🐤 **Tight Mutual Information Estimation With Contrastive Fenchel-Legendre Optimization** [[link](https://arxiv.org/abs/2107.01131)] [[code](https://github.com/qingguo666/FLO)]\

Qing Guo, Junya Chen, Dong Wang, Yuewei Yang, Xinwei Deng, Lawrence Carin, Fan Li, Chenyang Tao\

*Preprint, 2021*





**Entropy and mutual information in models of deep neural networks** [[link](https://arxiv.org/abs/1805.09785)] \

Marylou Gabrié, Andre Manoel, Clément Luneau, Jean Barbier, Nicolas Macris, Florent Krzakala, Lenka Zdeborová\

*NeurIPS, 2018*





🐤 **Understanding the Limitations of Variational Mutual Information Estimators** [[link](https://iclr.cc/virtual_2020/poster_B1x62TNtDS.html)] [[PyTorch](https://github.com/ermongroup/smile-mi-estimator)] \

Jiaming Song, Stefano Ermon \

*ICLR, 2020*

> - This implementation includes `InfoNCE`, `NWJ`, `NWJ-JS`, `MINE`, and their own method `SMILE`.

> - Basically, they show that the *variance* of traditional MI estimation can grow exponentially with true MI. In other words, just as KNN estimators, the more dependent (the higher MI), the less accurate.

> - Also, those estimators ***does not satisfy*** some important self-consistency properties, such as *data processing inequality*.

> - They propose SMILE which aims to reduce the variance issue.







🐤🐤 **Sliced Mutual Information: A Scalable Measure of Statistical Dependence** [[link](https://openreview.net/forum?id=27qon5Ut4PSl)] \

Ziv Goldfeld, Kristjan Greenewald\

*NeurIPS, 2021  (**spotlight**)*





🐤 **TImproving Mutual Information Estimation with Annealed and Energy-Based Bounds** [[link](https://openreview.net/forum?id=T0B9AoM_bFg)]\

Qing Guo, Junya Chen, Dong Wang, Yuewei Yang, Xinwei Deng, Lawrence Carin, Fan Li, Chenyang Tao\

*ICLR, 2022*





**Assessing Neural Network Representations During Training Using Noise-Resilient `Diffusion Spectral Entropy`** [[link](https://arxiv.org/abs/2312.04823)] [[code](https://github.com/ChenLiu-1996/DiffusionSpectralEntropy)]\

Danqi Liao*, Chen Liu*, Benjamin W Christensen, Alexander Tong, Guillaume Huguet, Guy Wolf, Maximilian Nickel, Ian Adelstein, Smita Krishnaswamy\

*ICML Workshop, 2023*

> This paper leverages diffusion geometry to estimate Entropy and MI in high dimensional representations of modern neural networks.





## 8. Other Information Theory Driven Work

**f-GANs in an Information Geometric Nutshell** [[link](https://papers.nips.cc/paper/2017/hash/2f2b265625d76a6704b08093c652fd79-Abstract.html)] \

Richard Nock, Zac Cranko, Aditya K. Menon, Lizhen Qu, Robert C. Williamson\

*NeurIPS, 2017*





**Fully Decentralized Policies for Multi-Agent Systems: An Information Theoretic Approach** [[link](https://papers.nips.cc/paper/2017/hash/8bb88f80d334b1869781beb89f7b73be-Abstract.html)] \

Roel Dobbe, David Fridovich-Keil, Claire Tomlin\

*NeurIPS, 2017*





**Information Theoretic Properties of Markov Random Fields, and their Algorithmic Applications** [[link](https://papers.nips.cc/paper/2017/hash/8fb5f8be2aa9d6c64a04e3ab9f63feee-Abstract.html)] \

Linus Hamilton, Frederic Koehler, Ankur Moitra\

*NeurIPS, 2017*





**Information-theoretic analysis of generalization capability of learning algorithms** [[link](https://papers.nips.cc/paper/2017/hash/ad71c82b22f4f65b9398f76d8be4c615-Abstract.html)] \

Aolin Xu, Maxim Raginsky\

*NeurIPS, 2017*





**Learning Discrete Representations via Information Maximizing Self-Augmented Training** [[link](https://proceedings.mlr.press/v70/hu17b.html)] \

Weihua Hu, Takeru Miyato, Seiya Tokui, Eiichi Matsumoto, Masashi Sugiyama\

*ICML, 2017*





🐣 **Nonparanormal Information Estimation** [[link](https://proceedings.mlr.press/v70/singh17a.html)] \

Shashank Singh, Barnabás Póczos\

*ICML, 2017*

> This paper shows how to robustly estimate mutual information using i.i.d. samples from unknown distribution.







**Entropy and mutual information in models of deep neural networks** [[link](https://papers.nips.cc/paper/2018/hash/6d0f846348a856321729a2f36734d1a7-Abstract.html)] \

Marylou Gabrié, Andre Manoel, Clément Luneau, jean barbier, Nicolas Macris, Florent Krzakala, Lenka Zdeborová\

*NeurIPS, 2018*





**Chaining Mutual Information and Tightening Generalization Bounds** [[link](https://papers.nips.cc/paper/2018/hash/8d7628dd7a710c8638dbd22d4421ee46-Abstract.html)] \

Amir Asadi, Emmanuel Abbe, Sergio Verdu\

*NeurIPS, 2018*





**Information Constraints on Auto-Encoding Variational Bayes** [[link](https://papers.nips.cc/paper/2018/hash/9a96a2c73c0d477ff2a6da3bf538f4f4-Abstract.html)] \

Romain Lopez, Jeffrey Regier, Michael I. Jordan, Nir Yosef\

*NeurIPS, 2018*





**Adaptive Learning with Unknown Information Flows** [[link](https://papers.nips.cc/paper/2018/hash/9e740b84bb48a64dde25061566299467-Abstract.html)] \

Yonatan Gur, Ahmadreza Momeni\

*NeurIPS, 2018*





**Information-based Adaptive Stimulus Selection to Optimize Communication Efficiency in Brain-Computer Interfaces** [[link](https://papers.nips.cc/paper/2018/hash/a3eb043e7bf775de87763e9f8121c953-Abstract.html)] \

Boyla Mainsah, Dmitry Kalika, Leslie Collins, Siyuan Liu, Chandra Throckmorton\

*NeurIPS, 2018*





**Information Theoretic Guarantees for Empirical Risk Minimization with Applications to Model Selection and Large-Scale Optimization** [[link](https://proceedings.mlr.press/v80/alabdulmohsin18a.html)] \

Ibrahim Alabdulmohsin\

*ICML, 2018*





**Mutual Information Neural Estimation** [[link](https://proceedings.mlr.press/v80/belghazi18a.html)] \

Mohamed Ishmael Belghazi, Aristide Baratin, Sai Rajeshwar, Sherjil Ozair, Yoshua Bengio, Aaron Courville, Devon Hjelm\

*ICML, 2018*





**Learning to Explain: An Information-Theoretic Perspective on Model Interpretation** [[link](https://proceedings.mlr.press/v80/chen18j.html)]\

Jianbo Chen, Le Song, Martin Wainwright, Michael Jordan\

*ICML, 2018*





**Fast Information-theoretic Bayesian Optimisation** [[link](https://proceedings.mlr.press/v80/ru18a.html)] \

Binxin Ru, Michael A. Osborne, Mark Mcleod, Diego Granziol\

*ICML, 2018*





**Locality-Sensitive Hashing for f-Divergences: Mutual Information Loss and Beyond** [[link](https://papers.nips.cc/paper/2019/hash/21b29648a47a45ad16bb0da0c004dfba-Abstract.html)] \

Lin Chen, Hossein Esfandiari, Gang Fu, Vahab Mirrokni\

*NeurIPS, 2019*





**Information-Theoretic Confidence Bounds for Reinforcement Learning** [[link](https://papers.nips.cc/paper/2019/hash/411ae1bf081d1674ca6091f8c59a266f-Abstract.html)] \

Xiuyuan Lu, Benjamin Van Roy\

*NeurIPS, 2019*





**L-DMI: A Novel Information-theoretic Loss Function for Training Deep Nets Robust to Label Noise** [[link](https://papers.nips.cc/paper/2019/hash/8a1ee9f2b7abe6e88d1a479ab6a42c5e-Abstract.html)] \

Yilun Xu, Peng Cao, Yuqing Kong, Yizhou Wang\

*NeurIPS, 2019*





**Connections Between Mirror Descent, Thompson Sampling and the Information Ratio** [[link](https://papers.nips.cc/paper/2019/hash/92cf3f7ef90630755b955924254e6ec4-Abstract.html)] \

Julian Zimmert, Tor Lattimore\

*NeurIPS, 2019*





**Region Mutual Information Loss for Semantic Segmentation** [[link](https://papers.nips.cc/paper/2019/hash/a67c8c9a961b4182688768dd9ba015fe-Abstract.html)] \

Shuai Zhao, Yang Wang, Zheng Yang, Deng Cai\

*NeurIPS, 2019*





**Learning Representations by Maximizing Mutual Information Across Views** [[link](https://papers.nips.cc/paper/2019/hash/ddf354219aac374f1d40b7e760ee5bb7-Abstract.html)]\

Philip Bachman, R Devon Hjelm, William Buchwalter\

*NeurIPS, 2019*





**Icebreaker: Element-wise Efficient Information Acquisition with a Bayesian Deep Latent Gaussian Model** [[link](https://papers.nips.cc/paper/2019/hash/c055dcc749c2632fd4dd806301f05ba6-Abstract.html)] \

Wenbo Gong, Sebastian Tschiatschek, Sebastian Nowozin, Richard E. Turner, José Miguel Hernández-Lobato, Cheng Zhang\

*NeurIPS, 2019*





**Thompson Sampling with Information Relaxation Penalties** [[link](https://papers.nips.cc/paper/2019/hash/e5b294b70c9647dcf804d7baa1903918-Abstract.html)] \

Seungki Min, Costis Maglaras, Ciamac C. Moallemi\

*NeurIPS, 2019*





**InfoMax: Learning deep representations by mutual information estimation and maximization** [[link](https://openreview.net/forum?id=Bklr3j0cKX)][[code](https://github.com/rdevon/DIM)] \

R Devon Hjelm, Alex Fedorov, Samuel Lavoie-Marchildon, Karan Grewal, Phil Bachman, Adam Trischler, Yoshua Bengio\

*ICLR, 2019*





**Max-MIG: an Information Theoretic Approach for Joint Learning from Crowds** [[link](https://openreview.net/forum?id=BJg9DoR9t7)] \

Peng Cao, Yilun Xu, Yuqing Kong, Yizhou Wang\

*ICLR, 2019*





**Information-Directed Exploration for Deep Reinforcement Learning** [[link](https://openreview.net/forum?id=Byx83s09Km)] \

Nikolay Nikolov, Johannes Kirschner, Felix Berkenkamp, Andreas Krause\

*ICLR, 2019*





**Soft Q-Learning with Mutual-Information Regularization** [[link](https://openreview.net/forum?id=HyEtjoCqFX)] \

Jordi Grau-Moya, Felix Leibfried, Peter Vrancx\

*ICLR, 2019*





**Hierarchical Reinforcement Learning via Advantage-Weighted Information Maximization** [[link](https://openreview.net/forum?id=Hyl_vjC5KQ)] \

Takayuki Osa, Voot Tangkaratt, Masashi Sugiyama\

*ICLR, 2019*





**Information Asymmetry in KL-regularized RL** [[link](https://openreview.net/forum?id=S1lqMn05Ym)] \

Alexandre Galashov, Siddhant M. Jayakumar, Leonard Hasenclever, Dhruva Tirumala, Jonathan Schwarz, Guillaume Desjardins, Wojciech M. Czarnecki, Yee Whye Teh, Razvan Pascanu, Nicolas Heess\

*ICLR, 2019*





**Adaptive Estimators Show Information Compression in Deep Neural Networks** [[link](https://openreview.net/forum?id=SkeZisA5t7)] \

 Ivan Chelombiev, Conor Houghton, Cian O'Donnell\

*ICLR, 2019*





**Information Theoretic lower bounds on negative log likelihood** [[link](https://openreview.net/forum?id=rkemqsC9Fm)] \

Luis A. Lastras-Montaño\

*ICLR, 2019*





**New results on information theoretic clustering** [[link](https://proceedings.mlr.press/v97/cicalese19a.html)] [[code](https://github.com/lmurtinho/RatioGreedyClustering/tree/ICML_submission)] \

Ferdinando Cicalese, Eduardo Laber, Lucas Murtinho\

*ICML, 2019*





**Estimating Information Flow in Deep Neural Networks** [[link](https://proceedings.mlr.press/v97/goldfeld19a.html)] \

Ziv Goldfeld, Ewout Van Den Berg, Kristjan Greenewald, Igor Melnyk, Nam Nguyen, Brian Kingsbury, Yury Polyanskiy\

*ICML, 2019*





🐣 **The information-theoretic value of unlabeled data in semi-supervised learning** [[link](https://proceedings.mlr.press/v97/golovnev19a.html)] \

Alexander Golovnev, David Pal, Balazs Szorenyi\

*ICML, 2019*





**EMI: Exploration with Mutual Information** [[link](https://proceedings.mlr.press/v97/kim19a.html)] [[code](https://github.com/snu-mllab/EMI)] \

Hyoungseok Kim, Jaekyeom Kim, Yeonwoo Jeong, Sergey Levine, Hyun Oh Song\

*ICML, 2019*





🐣 **On Variational Bounds of Mutual Information** [[link](https://proceedings.mlr.press/v97/poole19a.html)] \

Ben Poole, Sherjil Ozair, Aaron Van Den Oord, Alex Alemi, George Tucker\

*ICML, 2019*





**Where is the Information in a Deep Neural Network?** [[link](https://arxiv.org/abs/1905.12213)] \

Alessandro Achille, Giovanni Paolini, Stefano Soatto\

*Preprint, 2020*





**Information Maximization for Few-Shot Learning** [[link](https://papers.nips.cc/paper/2020/hash/196f5641aa9dc87067da4ff90fd81e7b-Abstract.html)] \

Malik Boudiaf, Imtiaz Ziko, Jérôme Rony, Jose Dolz, Pablo Piantanida, Ismail Ben Ayed\

*NeurIPS, 2020*





**Belief-Dependent Macro-Action Discovery in POMDPs using the Value of Information** [[link](https://papers.nips.cc/paper/2020/hash/7f2be1b45d278ac18804b79207a24c53-Abstract.html)] \

Genevieve Flaspohler, Nicholas A. Roy, John W. Fisher III\

*NeurIPS, 2020*





**Predictive Information Accelerates Learning in RL** [[link](https://papers.nips.cc/paper/2020/hash/89b9e0a6f6d1505fe13dea0f18a2dcfa-Abstract.html)] \

Kuang-Huei Lee, Ian Fischer, Anthony Liu, Yijie Guo, Honglak Lee, John Canny, Sergio Guadarrama\

*NeurIPS, 2020*

> "The **predictive information** is the **mutual information** between the *past* and the *future*, $I(X_{\text{past}}; X_{\text{future}})$."







**Information Theoretic Regret Bounds for Online Nonlinear Control** [[link](https://papers.nips.cc/paper/2020/hash/aee5620fa0432e528275b8668581d9a8-Abstract.html)] \

Sham Kakade, Akshay Krishnamurthy, Kendall Lowrey, Motoya Ohnishi, Wen Sun\

*NeurIPS, 2020*





**Conditioning and Processing: Techniques to Improve Information-Theoretic Generalization Bounds** [[link](https://papers.nips.cc/paper/2020/hash/befe5b0172188ad14d48c3ebe9cf76bf-Abstract.html)] \

Hassan Hafez-Kolahi, Zeinab Golgooni, Shohreh Kasaei, Mahdieh Soleymani\

*NeurIPS, 2020*





**Variational Interaction Information Maximization for Cross-domain Disentanglement** [[link](https://papers.nips.cc/paper/2020/hash/fe663a72b27bdc613873fbbb512f6f67-Abstract.html)] \

HyeongJoo Hwang, Geon-Hyeong Kim, Seunghoon Hong, Kee-Eung Kim\

*NeurIPS, 2020*





**Information theoretic limits of learning a sparse rule** [[link](https://papers.nips.cc/paper/2020/hash/713fd63d76c8a57b16fc433fb4ae718a-Abstract.html)] \

Clément Luneau, jean barbier, Nicolas Macris\

*NeurIPS, 2020*





**Understanding Approximate Fisher Information for Fast Convergence of Natural Gradient Descent in Wide Neural Networks** [[link](https://papers.nips.cc/paper/2020/hash/7b41bfa5085806dfa24b8c9de0ce567f-Abstract.html)] \

Ryo Karakida, Kazuki Osawa\

*NeurIPS, 2020*





🐣 **On Mutual Information Maximization for Representation Learning** [[link](https://openreview.net/forum?id=rkxoh24FPH)] \

Michael Tschannen, Josip Djolonga, Paul K. Rubenstein, Sylvain Gelly, Mario Lucic\

*ICLR, 2020*





🐣 **Understanding the Limitations of Variational Mutual Information Estimators** [[link](https://openreview.net/forum?id=B1x62TNtDS)] \

Jiaming Song, Stefano Ermon\

*ICLR, 2020*





**Expected Information Maximization: Using the I-Projection for Mixture Density Estimation** [[link](https://openreview.net/forum?id=ByglLlHFDS)] \

Philipp Becker, Oleg Arenz, Gerhard Neumann \

*ICLR, 2020*





**Mutual Information Gradient Estimation for Representation Learning** [[link](https://openreview.net/forum?id=ByxaUgrFvH)] \

 Liangjian Wen, Yiji Zhou, Lirong He, Mingyuan Zhou, Zenglin Xu\

*ICLR, 2020*





**InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization** [[link](https://openreview.net/forum?id=r1lfF2NYvH)] \

 Fan-Yun Sun, Jordan Hoffman, Vikas Verma, Jian Tang\

*ICLR, 2020*





**A Mutual Information Maximization Perspective of Language Representation Learning** [[link](https://openreview.net/forum?id=Syx79eBKwr)] \

 Lingpeng Kong, Cyprien de Masson d'Autume, Lei Yu, Wang Ling, Zihang Dai, Dani Yogatama\

*ICLR, 2020*





**CLUB: A Contrastive Log-ratio Upper Bound of Mutual Information** [[link](https://proceedings.mlr.press/v119/cheng20b.html)] [[code](https://github.com/Linear95/CLUB)] \

Pengyu Cheng, Weituo Hao, Shuyang Dai, Jiachang Liu, Zhe Gan, Lawrence Carin\

*ICML, 2020*





**Information Particle Filter Tree: An Online Algorithm for POMDPs with Belief-Based Rewards on Continuous Domains** [[link](https://proceedings.mlr.press/v119/fischer20a.html)] [[code](https://github.com/johannes-fischer/icml2020_ipft)] \

Johannes Fischer, Ömer Sahin Tas\

*ICML, 2020*





**Bayesian Experimental Design for Implicit Models by Mutual Information Neural Estimation** [[link](https://proceedings.mlr.press/v119/kleinegesse20a.html)] [[code](https://github.com/stevenkleinegesse/minebed)] \

Steven Kleinegesse, Michael U. Gutmann\

*ICML, 2020*





**FR-Train: A Mutual Information-Based Approach to Fair and Robust Training** [[link](https://proceedings.mlr.press/v119/roh20a.html)] [[code](https://github.com/yuji-roh/fr-train)] \

Yuji Roh, Kangwook Lee, Steven Whang, Changho Suh\

*ICML, 2020*





**Learning Discrete Structured Representations by Adversarially Maximizing Mutual Information** [[link](https://proceedings.mlr.press/v119/stratos20a.html)] [[code](https://github.com/karlstratos/ammi)] \

Karl Stratos, Sam Wiseman\

*ICML, 2020*





**Learning Structured Latent Factors from Dependent Data:A Generative Model Framework from Information-Theoretic Perspective** [[link](https://proceedings.mlr.press/v119/zhang20m.html)] \

Ruixiang Zhang, Masanori Koyama, Katsuhiko Ishiguro\

*ICML, 2020*





**Learning Adversarially Robust Representations via Worst-Case Mutual Information Maximization** [[link](https://proceedings.mlr.press/v119/zhu20e.html)] [[code](https://github.com/schzhu/learning-adversarially-robust-representations)] \

Sicheng Zhu, Xiao Zhang, David Evans\

*ICML, 2020*





**Usable Information and Evolution of Optimal Representations During Training** [[link](https://openreview.net/forum?id=p8agn6bmTbr)] \

 Michael Kleinman, Alessandro Achille, Daksh Idnani, Jonathan Kao\

*ICLR, 2021*





**Domain-Robust Visual Imitation Learning with Mutual Information Constraints** [[link](https://openreview.net/forum?id=QubpWYfdNry)] \

 Edoardo Cetin, Oya Celiktutan\

*ICLR, 2021*





**Multi-Class Uncertainty Calibration via Mutual Information Maximization-based Binning** [[link](https://openreview.net/forum?id=AICNpd8ke-m)] \

 Kanil Patel, William H. Beluch, Bin Yang, Michael Pfeiffer, Dan Zhang\

*ICLR, 2021*





**Graph Information Bottleneck for Subgraph Recognition** [[link](https://openreview.net/forum?id=bM4Iqfg8M2k)] \

Junchi Yu, Tingyang Xu, Yu Rong, Yatao Bian, Junzhou Huang, Ran He\

*ICLR, 2021*





**InfoBERT: Improving Robustness of Language Models from An Information Theoretic Perspective** [[link](https://openreview.net/forum?id=hpH98mK5Puk)]\

 Boxin Wang, Shuohang Wang, Yu Cheng, Zhe Gan, Ruoxi Jia, Bo Li, Jingjing Liu\

*ICLR, 2021*





**Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Information** [[link](https://icml.cc/Conferences/2021/Schedule?showEvent=10675)] [[slides](https://icml.cc/media/icml-2021/Slides/10675.pdf)] \

Willie Neiswanger, Ke Alexander Wang, Stefano Ermon\

*ICML, 2021*





**Decomposed Mutual Information Estimation for Contrastive Representation Learning** [[link](http://proceedings.mlr.press/v139/sordoni21a/sordoni21a.pdf)] \

Alessandro Sordoni, Nouha Dziri, Hannes Schulz, Geoff Gordon, Philip Bachman, Remi Tachet Des Combes\

*ICML, 2021*





**ReduNet: A White-box Deep Network from the Principle of Maximizing Rate Reduction** [[link](https://arxiv.org/abs/2105.10446)] [[code](https://github.com/ryanchankh/ReduNet)] \

Kwan Ho Ryan Chan, Yaodong Yu, Chong You, Haozhi Qi, John Wright, Yi Ma\

*Preprint, 2021*





**Intelligence, physics and information – the tradeoff between accuracy and simplicity in machine learning** [[link](https://arxiv.org/abs/2001.03780)] \

Tailin Wu\

*PhD Thesis, 2021*





**The Information Geometry of Unsupervised Reinforcement Learning** [[link](https://arxiv.org/abs/2110.02719v1)] \

Benjamin Eysenbach, Ruslan Salakhutdinov, Sergey Levine\

*Preprint, 2021*





## 9. Citation

If you would like to cite this repository 🐣:

```tex

@misc{git2022ib,

      title = {Awesome Information Bottleneck},

      author = {Ziyu Ye},

      howpublished = {\url{https://github.com/ZIYU-DEEP/Awesome-Information-Bottleneck}},

      year = 2022}

```