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Physical Transformer

Digital AI systems spanning large language models, vision models, and generative architectures that operate primarily in symbolic, linguistic, or pixel domains. They have achieved striking progress, but almost all of this progress lives in virtual spaces. These systems transform embeddings and tokens, yet do not themselves touch the world and rarely admit a physical interpretation. In this work we propose a physical transformer that couples modern transformer style computation with geometric representation and physical dynamics. At the micro level, attention heads, and feed-forward blocks are modeled as interacting spins governed by effective Hamiltonians plus non-Hamiltonian bath terms. At the meso level, their aggregated state evolves on a learned Neural Differential Manifold (NDM) under Hamiltonian flows and Hamilton, Jacobi, Bellman (HJB) optimal control, discretized by symplectic layers that approximately preserve geometric and energetic invariants. At the macro level, the model maintains a generative semantic workspace and a two-dimensional information-phase portrait that tracks uncertainty and information gain over a reasoning trajectory. Within this hierarchy, reasoning tas