Causal-fate dynamics of unrealized influence

Abstract:Many dynamical systems generate influences whose consequences are not fully exhausted in the realized trajectory at the moment they arise. Such consequences are often treated as absent, delayed or statically stored, leaving unclear how unrealized influence retains future relevance as the system evolves. Here we formulate causal-fate dynamics, in which generated influence may be realized, remain latent, or be transformed by subsequent dynamics, and give an exact finite-transport representation when the relevant maps are specified. A connectome-constrained Caenorhabditis elegans model first motivates the biological hypothesis that unresolved inter-neuronal influence may persist and contribute to later propagation; it does not establish such a mechanism in living animals. We next examine operational Internet routing, where a dynamically updated cross-observer history retains predictive information beyond the current local route state. We then use the representation to construct a Transformer architecture that explicitly transports and selectively realizes latent contextual influence while retaining language-modeling function. The three studies distinguish a model-motivated scientific hypothesis, an observational phenomenon compatible with future-relevant history and an executable construction for carrying unrealized influence through subsequent computation.

39 pages (20-page main text and 19-page Supplementary Information), 6 figures, 14 supplementary tables. Code: this https URL

Systems and Control (eess.SY); Machine Learning (cs.LG)

arXiv:2610.11422 [eess.SY]

(or arXiv:2610.11422v1 [eess.SY] for this version)

https://doi.org/10.48550/arXiv.2610.11422 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

supplementary_data/ablation_results.csv

supplementary_data/anchor_peers.csv

supplementary_data/case_catalog.csv

supplementary_data/front_group_results.csv

supplementary_data/gain_ci.csv

supplementary_data/matched_witnesses.csv

supplementary_data/per_horizon_results.csv

supplementary_data/sample_counts.csv

supplementary_data/seed_robustness.csv

supplementary_data/selected_prefixes.csv

(5 additional files not shown) You must enabled JavaScript to view entire file list.

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.