{"slug": "when-do-conservation-laws-survive-learned-representations-certified-horizons-for", "title": "When Do Conservation Laws Survive Learned Representations? Certified Horizons for Latent World Models", "summary": "Researchers at arXiv propose a method to certify conservation laws in learned latent world models by decoding physical invariants from latent states. They derive shell-horizon certificates that decompose into representation, readout, and latent-dynamics defects, and test them on conservative systems. The approach shows that conservation certificates can survive learned representations, but geometric priors like symplectic structure do not transfer across learned charts, while soft Lipschitz-aligned invariants perform better.", "body_md": "arXiv:2606.24945v1 Announce Type: new\nAbstract: We ask a representation-learning question about physical world models: when does a conservation law remain certifiable after a model learns a latent representation? A certified horizon bounds -- in advance, from measurable model defects -- how many steps a rollout provably stays on a physical invariant's level set. The key design choice is what is certified: not a learned latent Hamiltonian or a learned scalar witness (a model can conserve either while drifting in true energy), but the decoded physical invariant obtained by decoding the latent state and evaluating the known invariant. Around this object we derive shell-horizon certificates whose budget decomposes into representation, readout, and latent-dynamics defects, with a monotone alignment bridge through which a soft learned witness yields a certified horizon for the decoded invariant, and test them across state, learned-lift, and pixel observations on conservative systems. Conservation certificates can survive learned representation, but not all geometric priors survive equally: hard canonical symplectic structure yields the longest horizons in known phase coordinates yet does not cross a learned chart, whereas a controlled-Lipschitz-aligned soft invariant survives in the learned-representation settings we test; pixel certification is recovered on a readout-stable sub-tube; and the Kepler problem exposes a geometric boundary. The central object is therefore not a latent Hamiltonian, but a decoded physical invariant whose robustness to representation learning can be measured, certified, and falsified.", "url": "https://wpnews.pro/news/when-do-conservation-laws-survive-learned-representations-certified-horizons-for", "canonical_source": "https://arxiv.org/abs/2606.24945", "published_at": "2026-06-25 04:00:00+00:00", "updated_at": "2026-06-25 04:25:31.953764+00:00", "lang": "en", "topics": ["machine-learning", "ai-research", "ai-safety"], "entities": ["arXiv"], "alternates": {"html": "https://wpnews.pro/news/when-do-conservation-laws-survive-learned-representations-certified-horizons-for", "markdown": "https://wpnews.pro/news/when-do-conservation-laws-survive-learned-representations-certified-horizons-for.md", "text": "https://wpnews.pro/news/when-do-conservation-laws-survive-learned-representations-certified-horizons-for.txt", "jsonld": "https://wpnews.pro/news/when-do-conservation-laws-survive-learned-representations-certified-horizons-for.jsonld"}}