{"ID":2824912,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.21834","arxiv_id":"2512.21834","title":"Conserved active information","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2512.21834","url_pdf":"https://arxiv.org/pdf/2512.21834v2","authors":"[\"Yanchen Chen\",\"Daniel Andrés Díaz-Pachón\"]","published":"2025-12-26T02:38:14Z","proceeding":"cs.NE","tasks":"[\"cs.NE\",\"cs.CC\",\"cs.HC\",\"cs.IT\"]","methods":"[]","has_code":false}