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This paper introduces causal-fate dynamics to model how influence in a system can persist beyond its immediate realization, proposing a finite-transport representation for specified maps. By examining a C. elegans neural model and Internet routing, the authors demonstrate that unresolved influence can retain future relevance. They then construct a Transformer architecture that explicitly manages and realizes latent contextual influence, maintaining language modeling performance.
Latent contextual influence can be explicitly transported and selectively realized in Transformers, enabling models to retain predictive information beyond immediate state.
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.