Attention Field Theory: Riemannian Geometry of Free-Energy-Driven Attention Dynamics

Attention Field Theory (AFT) presents a geometric account of subjective experience in which attention is modeled as a continuous density field on a manifold of attendable distinctions. Each point in this model space carries a radial coordinate that tracks subjective degree of belief, distinguishing fully real experience from latent possibilities such as memory, imagination, and prediction. A scalar salience potential, built from prediction error and precision weighting, drives attention down its gradient while diffusion captures intrinsic variability.

The paper shows that, under a single forward prediction assumption on the evidence surface that plays the role of a Markov blanket, these dynamics become mathematically equivalent to the perceptual component of continuous time, Gaussian Active Inference. Attention flow appears as a natural gradient descent of variational free energy in the Fisher information geometry, while coupled stochastic differential equations describe precision plasticity and slow remodeling of the experiential metric. This yields a three timescale picture: fast attentional drift and diffusion, intermediate adaptation of sensory gain, and gradual warping of representational geometry under sustained practice and expertise.

Beyond the formal results, AFT links these structures to phenomenology and experiment. Simple field configurations recover familiar attentional states such as focused perception, imagination, meditation-like scanning, and mind wandering. The theory generates concrete neural, behavioural, and autonomic predictions, including signatures in gamma-band gain, reaction time variability, representational distances, and pupil-linked arousal. In doing so, AFT offers a principled bridge between lived attention, predictive brain theories, and empirical protocols in neuroscience, psychology, and contemplative science.