# On the Mathematical Structure of Cascade Effects and Emergent Phenomena

arXiv: https://arxiv.org/abs/1911.10376 · HTML: https://mlsanity.com/paper/1911.10376/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2019.

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

- [A General Theory for Compositional Generalization](https://mlsanity.com/paper/2405.11743/) (2024)

## Abstract (arXiv)

We argue that the mathematical structure, enabling certain cascading and emergent phenomena to intuitively emerge, coincides with Galois connections. We introduce the notion of generative effects to formally capture such phenomena. We establish that these effects arise, via a notion of a veil, from either concealing mechanisms in a system or forgetting characteristics from it. The goal of the work is to initiate a mathematical base that enables us to further study such phenomena. In particular, generative effects can be further linked to a certain loss of exactness. Homological algebra, and related algebraic methods, may then be used to characterize the effects.