# Finding emergence in data by maximizing effective information

arXiv: https://arxiv.org/abs/2308.09952 · HTML: https://mlsanity.com/paper/2308.09952/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 69 references that are in the map.
- First posted on arXiv 19 Aug 2023.

## Builds on (most cited first, 21 of 21)

- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Invariant Causal Prediction for Block MDPs](https://mlsanity.com/paper/2003.06016/) (2020)
- [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020)
- [Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximators](https://mlsanity.com/paper/2006.11469/) (2020)
- [Multi-Scale Spatial Temporal Graph Convolutional Network for Skeleton-Based Action Recognition](https://mlsanity.com/paper/2206.13028/) (2022)
- [Machine Learning for Neuroimaging with Scikit-Learn](https://mlsanity.com/paper/1412.3919/) (2014)
- [Data-driven discovery of intrinsic dynamics](https://mlsanity.com/paper/2108.05928/) (2021)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [Universal Approximation Property of Neural Ordinary Differential Equations](https://mlsanity.com/paper/2012.02414/) (2020)
- [When the map is better than the territory](https://mlsanity.com/paper/1612.09592/) (2016)
- [Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data](https://mlsanity.com/paper/2004.08220/) (2020)
- [The emergence of informative higher scales in complex networks](https://mlsanity.com/paper/1907.03902/) (2019)
- [Finding the right scale of a network: Efficient identification of causal emergence through spectral clustering](https://mlsanity.com/paper/1908.07565/) (2019)
- [Examining the causal structures of deep neural networks using information theory](https://mlsanity.com/paper/2010.13871/) (2020)
- [Neural Information Squeezer for Causal Emergence](https://mlsanity.com/paper/2201.10154/) (2022)
- [Independent Gaussian Distributions Minimize the Kullback-Leibler (KL) Divergence from Independent Gaussian Distributions](https://mlsanity.com/paper/2011.02560/) (2020)

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

- [Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studies](https://mlsanity.com/paper/2312.16815/) (2023)
- [Data driven modeling for self-similar dynamics](https://mlsanity.com/paper/2310.08282/) (2023)
- [A Framework for Analyzing Abnormal Emergence in Service Ecosystems Through LLM-based Agent Intention Mining](https://mlsanity.com/paper/2507.15770/) (2025)
- [Partial Effective Information Decomposition for Synergistic Causality](https://mlsanity.com/paper/2605.03267/) (2026)

## Abstract (arXiv)

Quantifying emergence and modeling emergent dynamics in a data-driven manner for complex dynamical systems is challenging due to the lack of direct observations at the micro-level. Thus, it's crucial to develop a framework to identify emergent phenomena and capture emergent dynamics at the macro-level using available data. Inspired by the theory of causal emergence (CE), this paper introduces a machine learning framework to learn macro-dynamics in an emergent latent space and quantify the degree of CE. The framework maximizes effective information, resulting in a macro-dynamics model with enhanced causal effects. Experimental results on simulated and real data demonstrate the effectiveness of the proposed framework. It quantifies degrees of CE effectively under various conditions and reveals distinct influences of different noise types. It can learn a one-dimensional coarse-grained macro-state from fMRI data, to represent complex neural activities during movie clip viewing. Furthermore, improved generalization to different test environments is observed across all simulation data.