# Conserved active information

arXiv: https://arxiv.org/abs/2512.21834 · HTML: https://mlsanity.com/paper/2512.21834/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Dec 2025.

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

- [PRIM-cipal components analysis](https://mlsanity.com/paper/2604.15538/) (2026)

## Abstract (arXiv)

We introduce conserved active information I^oplus, a symmetric extension of active information that quantifies net information gain/loss across the entire search space, respecting No-Free-Lunch conservation. Through Bernoulli and uniform-baseline examples, we show I^oplus reveals regimes hidden from KL divergence, such as when strong knowledge reduces global disorder. Such regimes are proven formally under uniform baseline, distinguishing disorder (increasing mild knowledge from order-imposing strong knowledge. We further illustrate these regimes with examples from Markov chains and cosmological fine-tuning. This resolves a longstanding critique of active information while enabling applications in search, optimization, and beyond.