Abstract
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.
Abstract (translated)
我们介绍了一种新的架构——神经场图灵机（Neural Field Turing Machine，NFTM），这是一种可微分的架构，它将符号计算、物理仿真和感知推理统一在连续的空间场中。NFTM结合了神经控制器、连续记忆场以及能够执行局部更新并可在空间上移动的读写头。在每个时间步长内，控制器会读取局部区域的信息，通过学习到的规则进行计算，并将结果写回到记忆场的同时调整读写头的位置。这种设计实现了线性 O(N) 的扩展能力，在保持图灵完备性的前提下使用了固定半径的邻域范围。 我们演示了 NFTM 的三种具体实现：细胞自动机模拟（Rule 110）、物理信息偏微分方程求解器（二维热传导方程）以及迭代图像细化（CIFAR-10 图像修复）。这些实例展示了通过学习局部更新规则，如何组合成全局动态过程，并且在长时间尺度内保持稳定性和泛化能力，超越了训练时间范围。 NFTM 提供了一种统一的计算框架，在单一可微分架构中将离散算法和连续场动力学连接起来。
URL
https://arxiv.org/abs/2509.03370
