# Information Theory in Open-world Machine Learning Foundations, Frameworks, and Future Direction

arXiv: https://arxiv.org/abs/2510.15422 · HTML: https://mlsanity.com/paper/2510.15422/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 104 of its 144 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 30 of 104)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Towards Open Set Deep Networks](https://mlsanity.com/paper/1511.06233/) (2015)
- [Continual Test-Time Domain Adaptation](https://mlsanity.com/paper/2203.13591/) (2022)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Planning to Explore via Self-Supervised World Models](https://mlsanity.com/paper/2005.05960/) (2020)
- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [Open-Set Recognition: a Good Closed-Set Classifier is All You Need?](https://mlsanity.com/paper/2110.06207/) (2021)
- [Recent Advances in Open Set Recognition: A Survey](https://mlsanity.com/paper/1811.08581/) (2018)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Learning to Discover Novel Visual Categories via Deep Transfer Clustering](https://mlsanity.com/paper/1908.09884/) (2019)
- [Learning Robust Representations via Multi-View Information Bottleneck](https://mlsanity.com/paper/2002.07017/) (2020)
- [Understanding the Role of Training Regimes in Continual Learning](https://mlsanity.com/paper/2006.06958/) (2020)
- [A Fine-Grained Analysis on Distribution Shift](https://mlsanity.com/paper/2110.11328/) (2021)
- [Reducing Network Agnostophobia](https://mlsanity.com/paper/1811.04110/) (2018)
- [Open-World Semi-Supervised Learning](https://mlsanity.com/paper/2102.03526/) (2021)

## Abstract (arXiv)

Open world Machine Learning (OWML) aims to develop intelligent systems capable of recognizing known categories, rejecting unknown samples, and continually learning from novel information. Despite significant progress in open set recognition, novelty detection, and continual learning, the field still lacks a unified theoretical foundation that can quantify uncertainty, characterize information transfer, and explain learning adaptability in dynamic, nonstationary environments. This paper presents a comprehensive review of information theoretic approaches in open world machine learning, emphasizing how core concepts such as entropy, mutual information, and Kullback Leibler divergence provide a mathematical language for describing knowledge acquisition, uncertainty suppression, and risk control under open world conditions. We synthesize recent studies into three major research axes: information theoretic open set recognition enabling safe rejection of unknowns, information driven novelty discovery guiding new concept formation, and information retentive continual learning ensuring stable long term adaptation. Furthermore, we discuss theoretical connections between information theory and provable learning frameworks, including PAC Bayes bounds, open-space risk theory, and causal information flow, to establish a pathway toward provable and trustworthy open world intelligence. Finally, the review identifies key open problems and future research directions, such as the quantification of information risk, development of dynamic mutual information bounds, multimodal information fusion, and integration of information theory with causal reasoning and world model learning.