# A Relational Macrostate Theory Guides Artificial Intelligence to Learn Macro and Design Micro

arXiv: https://arxiv.org/abs/2210.07374 · HTML: https://mlsanity.com/paper/2210.07374/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 21 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 8 of 8)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Contrastive Learning of Structured World Models](https://mlsanity.com/paper/1911.12247/) (2019)
- [AI Poincar'e: Machine Learning Conservation Laws from Trajectories](https://mlsanity.com/paper/2011.04698/) (2020)
- [When the map is better than the territory](https://mlsanity.com/paper/1612.09592/) (2016)
- [Discovering State Variables Hidden in Experimental Data](https://mlsanity.com/paper/2112.10755/) (2021)

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

- [Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studies](https://mlsanity.com/paper/2312.16815/) (2023)

## Abstract (arXiv)

The high-dimesionality, non-linearity and emergent properties of complex systems pose a challenge to identifying general laws in the same manner that has been so successful in simpler physical systems. In Anderson's seminal work on why "more is different" he pointed to how emergent, macroscale patterns break symmetries of the underlying microscale laws. Yet, less recognized is that these large-scale, emergent patterns must also retain some symmetries of the microscale rules. Here we introduce a new, relational macrostate theory (RMT) that defines macrostates in terms of symmetries between two mutually predictive observations, and develop a machine learning architecture, MacroNet, that identifies macrostates. Using this framework, we show how macrostates can be identifed across systems ranging in complexity from the simplicity of the simple harmonic oscillator to the much more complex spatial patterning characteristic of Turing instabilities. Furthermore, we show how our framework can be used for the inverse design of microstates consistent with a given macroscopic property -- in Turing patterns this allows us to design underlying rule with a given specification of spatial patterning, and to identify which rule parameters most control these patterns. By demonstrating a general theory for how macroscopic properties emerge from conservation of symmetries in the mapping between observations, we provide a machine learning framework that allows a unified approach to identifying macrostates in systems from the simple to complex, and allows the design of new examples consistent with a given macroscopic property.