Neural Field Turing Machine: A Differentiable Spatial Computer
This provides a unified computational substrate bridging discrete algorithms and continuous field dynamics for researchers in AI and computational modeling, though it appears incremental as it builds on existing concepts like Turing machines and neural fields.
The paper tackles the problem of unifying symbolic computation, physical simulation, and perceptual inference by introducing the Neural Field Turing Machine (NFTM), a differentiable architecture that achieves linear O(N) scaling and Turing completeness under bounded error, demonstrated through applications like cellular automata simulation, PDE solving, and image inpainting with stable long-horizon rollouts.
We introduce the Neural Field Turing Machine (NFTM), a differentiable architecture that unifies symbolic computation, physical simulation, and perceptual inference within continuous spatial fields. NFTM combines a neural controller, continuous memory field, and movable read/write heads that perform local updates. At each timestep, the controller reads local patches, computes updates via learned rules, and writes them back while updating head positions. This design achieves linear O(N) scaling through fixed-radius neighborhoods while maintaining Turing completeness under bounded error. We demonstrate three example instantiations of NFTM: cellular automata simulation (Rule 110), physics-informed PDE solvers (2D heat equation), and iterative image refinement (CIFAR-10 inpainting). These instantiations learn local update rules that compose into global dynamics, exhibit stable long-horizon rollouts, and generalize beyond training horizons. NFTM provides a unified computational substrate bridging discrete algorithms and continuous field dynamics within a single differentiable framework.