# Signatures of Infinity: Nonergodicity and Resource Scaling in Prediction, Complexity, and Learning

arXiv: https://arxiv.org/abs/1504.00386 · HTML: https://mlsanity.com/paper/1504.00386/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2015.

## Built on by (most cited first, 3 of 3)

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## Abstract (arXiv)

We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes. Such processes are familiar from the well known multi-arm Bandit problem. We contrast our analysis with computation-theoretic and statistical inference approaches to understanding their complexity. The result is an alternative view of the relationship between predictability, complexity, and learning that highlights the distinct ways in which informational and correlational divergences arise in complex ergodic and nonergodic processes. We draw out consequences for the resource divergences that delineate the structural hierarchy of ergodic processes and for processes that are themselves hierarchical.