# Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data

arXiv: https://arxiv.org/abs/2004.08220 · HTML: https://mlsanity.com/paper/2004.08220/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2020.

## Built on by (most cited first, 16 of 16)

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- [A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots](https://mlsanity.com/paper/2605.08550/) (2026)
- [Finding emergence in data by maximizing effective information](https://mlsanity.com/paper/2308.09952/) (2023)
- [Neural Information Squeezer for Causal Emergence](https://mlsanity.com/paper/2201.10154/) (2022)
- [Quantifying Semantic Emergence in Language Models](https://mlsanity.com/paper/2405.12617/) (2024)
- [Measuring Uncertainty in Transformer Circuits with Effective Information Consistency](https://mlsanity.com/paper/2509.07149/) (2025)
- [Inference of time-ordered multibody interactions](https://mlsanity.com/paper/2111.14611/) (2021)
- [The Reflexive Integrated Information Unit: A Differentiable Primitive for Artificial Consciousness](https://mlsanity.com/paper/2506.13825/) (2025)
- [Partial Effective Information Decomposition for Synergistic Causality](https://mlsanity.com/paper/2605.03267/) (2026)
- [Govern the Repository, Not the Agent: Measuring Ecosystem-Level Risk in AI-Native Software](https://mlsanity.com/paper/2606.28235/) (2026)
- [Emergent Generalization by Representation Learning in Artificial Neural Networks](https://mlsanity.com/paper/2607.10430/) (2026)
- [Perspective Latents as an Architectural Condition for Causal Emergence in Active Inference Agents](https://mlsanity.com/paper/2607.20708/) (2026)

## Abstract (arXiv)

The broad concept of emergence is instrumental in various of the most challenging open scientific questions -- yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces a formal theory of causal emergence in multivariate systems, which studies the relationship between the dynamics of parts of a system and macroscopic features of interest. Our theory provides a quantitative definition of downward causation, and introduces a complementary modality of emergent behaviour -- which we refer to as causal decoupling. Moreover, the theory allows practical criteria that can be efficiently calculated in large systems, making our framework applicable in a range of scenarios of practical interest. We illustrate our findings in a number of case studies, including Conway's Game of Life, Reynolds' flocking model, and neural activity as measured by electrocorticography.