Affective Tagging as Metric Deformation in Cognitive Maps: A Variational Model

Current computational models of cognitive maps and grid-like representations successfully describe the geometry of state spaces, yet remain largely affect-neutral. In existing models, emotional salience functions as an external modulatory signal. Here, affective salience is formalized as emotional tag weight: an internal variable that deforms the effective metric of the cognitive map. We propose a mechanistic variational model based on this variable. Tag weight is a scalar quantity aggregating valence, intensity, novelty, prediction error, goal relevance, and bodily/interoceptive cost. Within the proposed mechanism, the episodic weight is distributed across the associative nodes of the cognitive map and can be expressed as a salience field V_τ(s), linking local node weights to deformation of the effective metric. At the geometric level, this field acts as a metric-deformation operator: effective distances to states with high tag weight contract relative to competing alternatives, changing node energies and transition probabilities. The model yields three testable predictions. First, a change in interoceptive or bodily state (e.g., fatigue, physiological arousal, or recovery) should reorder preferences among associative nodes under unchanged external task conditions. Second, the dynamics of tag weight dissociate into a fast reactive component and a slow consolidating component, which should appear as distinct time constants in behavioral and physiological correlates. Third, the same external event under different internal states should yield different generalization boundaries due to metric deformation, predicting reconfiguration of categorical errors. This work presents a mechanistic theoretical model requiring empirical validation.