PhaseBrain: A Torus-Based Semantic Dynamics Model for Multimodal Structure, Probabilistic Angular Prediction, and Phase Cohesion

We present PhaseBrain, a torus-based semantic dynamics model that represents perception, structure, and prediction through the evolution of angular states on a multidimensional torus. Unlike models operating in unconstrained Euclidean latent spaces, PhaseBrain encodes all modalities—text, code, audio, images, and time series—as trajectories of phases and amplitudes, enabling a single probabilistic law of angular dynamics shared across channels.

The model introduces:
(1) a toroidal latent geometry where semantic factors (e.g., token identity, syntactic role, block depth, class labels) become circular coordinates;
(2) probabilistic angular dynamics parameterized by von Mises distributions, with concentration κ functioning as a calibrated measure of epistemic confidence;
(3) semantic phase cohesion via cross-channel phase-locking metrics (PLV), providing interpretable structure and modality-agnostic diagnostics.

We further propose the Phase Interchange Framework (PIF), a unified modality frontend mapping heterogeneous data into phase–amplitude sequences on the torus.

Experiments show that PhaseBrain improves structural consistency in synthetic grammars, supports phase-based linting and controlled decoding, learns abstract role automata, performs latent phase classification for simple images, and exposes calibrated angular uncertainty via ensemble and diffusion analyses.

These results position torus-based semantic dynamics as a promising paradigm for interpretable, probabilistic, and multimodal structural modeling.