# Power-law statistics and universal scaling in the absence of criticality

arXiv: https://arxiv.org/abs/1503.08033 · HTML: https://mlsanity.com/paper/1503.08033/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2015.

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

- [Optimal input representation in neural systems at the edge of chaos](https://mlsanity.com/paper/2107.05709/) (2021)
- [Turing's cascade instability supports the coordination of the mind, brain, and behavior](https://mlsanity.com/paper/2204.07904/) (2022)
- [The Universe Learning Itself: On the Evolution of Dynamics from the Big Bang to Machine Intelligence](https://mlsanity.com/paper/2512.16515/) (2025)
- [Training and Inference Dynamics of PLDR-LLMs: Row-Map Collapse, Renormalization, and Predictive Reduction](https://mlsanity.com/paper/2609.34130/) (2026)

## Abstract (arXiv)

Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates, and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.