Conserved active information
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908972547571712 |
|---|---|
| author | Chen, Yanchen Díaz-Pachón, Daniel Andrés |
| author_facet | Chen, Yanchen Díaz-Pachón, Daniel Andrés |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21834 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conserved active information Chen, Yanchen Díaz-Pachón, Daniel Andrés Neural and Evolutionary Computing Computational Complexity Human-Computer Interaction Information Theory 94A15 (primary), 94A17 (primary), 60A05 (secondary), 62A01 (secondary), 68Q07 (secondary), 68Q15 (secondary) F.1.3; F.2.3; H.1.1 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. |
| title | Conserved active information |
| topic | Neural and Evolutionary Computing Computational Complexity Human-Computer Interaction Information Theory 94A15 (primary), 94A17 (primary), 60A05 (secondary), 62A01 (secondary), 68Q07 (secondary), 68Q15 (secondary) F.1.3; F.2.3; H.1.1 |
| url | https://arxiv.org/abs/2512.21834 |