TOWARDS GEOMETRO-DYNAMICAL INTELLIGENCE

This paper proposes the theory of geometric-dynamical intelligence and establishes an intelligence hierarchy based on homology groups $H_k$. Using discrete Hodge theory, this paper demonstrates that the Transformer architecture struggles to achieve $H_2$-level intelligence, and constructs a novel artificial intelligence algorithmic framework. This framework incorporates various new algorithms, including ternary algebraic networks for high-order interactions and attractor dynamics to address the spectral bias problem.