Mathematical formalism of Ze
DOI:
https://doi.org/10.65649/kzj86888Keywords:
Cognitive Architecture, Variational Inference, Model Conflict, Active Inference, ZeAbstract
This article introduces and formalizes Ze, a novel theoretical framework for cognitive architecture and autonomous systems. Ze posits that advanced intelligence requires the maintenance of two distinct, asymmetric generative models of the same environment: a causal (forward) model MA\mathcal{M}_AMA and a counterfactual (inverse) model MB\mathcal{M}_BMB. Each model minimizes its own variational free energy FA\mathcal{F}_AFA, FB\mathcal{F}_BFB, and their interaction dynamics define core cognitive processes. A key emergent quantity is the model conflict ΔF=∣FA−FB∣\Delta \mathcal{F} = |\mathcal{F}_A - \mathcal{F}_B|ΔF=∣FA−FB∣, which regulates a phase transition between two fundamental regimes: an interference regime (characterized by low posterior divergence I≈0\mathcal{I} \approx 0I≈0 where model outputs are constructively fused), and a localization regime (ΔF>θ\Delta \mathcal{F} > \thetaΔF>θ) where the system commits to a single resolved interpretation s^\hat{s}s^. The framework is extended to include active action selection from model-specific policies, a mechanism for representational growth via "which-path" information, and a "quantum eraser" operator for strategic simplification. We demonstrate that this architecture establishes a strict formal isomorphism with quantum measurement phenomena, notably the double-slit experiment, but is grounded entirely in classical variational inference. The theory reinterprets cognitive "collapse" not as a postulate but as an optimization-driven phase transition and yields the key testable prediction that active, alternating intervention accelerates localization compared to passive observation.
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