Toward a Mathematical Formulation of the Unified Dynamic Model of the Mind (UDMM): Active Inference Guided by a Virtual Attractor

Author Note The original conceptual framework of the Unified Dynamic Model of the Mind (UDMM) was developed by the author. The mathematical formulation and computational concepts proposed in this paper were developed in inferential collaboration with the Gemini Large Language Model (Google), used as a tool to support the initial formulation of the mathematical and technical framework. Correspondence concerning this article should be addressed to Mohamed Ahmed Aidaros, Atbara, Sudan. [[email protected]]. Abstract Current computational neuroscience models often struggle to account for the continuous, value-oriented human drive that is not satisfied by achieving discrete goals. This paper introduces a new conceptual framework, the Unified Dynamic Model of the Mind (UDMM), which posits the mind as an inferential system proactively shaping its environment. Central to UDMM is the concept of a "saturated world," reconceptualized here not as an achievable goal-state but as a virtual attractor—a hypothetical probabilistic distribution that cannot be fully attained, yet serves as a consistent compass guiding system behavior. We propose an initial mathematical formulation grounded in the Free Energy Principle and Active Inference (Friston, 2010), where the agent does not simply minimize prediction error to reach a stable state. Instead, it continuously minimizes the Kullback-Leibler (KL) Divergence between its expected future state distribution and the ideal distribution representing the saturated world. This approach produces behavior resembling a stable orbit around higher values. The paper outlines a roadmap for developing computational models based on this principle and opens new avenues for modeling meaning, purpose, and mental disorders as dysfunctions in the dynamic relationship with this virtual attractor. Keywords: Unified Dynamic Model of the Mind (UDMM), Active Inference, Free Energy Principle, Control Theory, Computational Neuroscience, Dynamical Systems Theory, Values