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Ananke: Contractive Torus Attractor Networks

arXiv · AI, language, vision and robotics · article · Sep 21, 2026 · UTC

We introduce Ananke, a representation-learning framework that scaffolds latent representations onto a structured product-torus prior, and its flagship visual backbone realization, Contractive Torus Attractor Networks (CTAN). By factorizing high-dimensional latent spaces into an orthogonal direct sum of two-dimensional phase planes ($\bigoplus_{k=1}^K \R^2$), Ananke coordinates feature updates via a decoupled dual-phase continuous flow: skew-symmetric Hamiltonian transport moves features tangentially along energy level sets to preserve semantic phase invariants, while signed gradient dissipatio

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