Abstract
Neural Cellular Automata (NCA) is a class of Cellular Automata where the update rule is parameterized by a neural network that can be trained using gradient descent. In this paper, we focus on NCA models used for texture synthesis, where the update rule is inspired by partial differential equations (PDEs) describing reaction-diffusion systems. To train the NCA model, the spatio-termporal domain is discretized, and Euler integration is used to numerically simulate the PDE. However, whether a trained NCA truly learns the continuous dynamic described by the corresponding PDE or merely overfits the discretization used in training remains an open question. We study NCA models at the limit where space-time discretization approaches continuity. We find that existing NCA models tend to overfit the training discretization, especially in the proximity of the initial condition, also called "seed". To address this, we propose a solution that utilizes uniform noise as the initial condition. We demonstrate the effectiveness of our approach in preserving the consistency of NCA dynamics across a wide range of spatio-temporal granularities. Our improved NCA model enables two new test-time interactions by allowing continuous control over the speed of pattern formation and the scale of the synthesized patterns. We demonstrate this new NCA feature in our interactive online demo. Our work reveals that NCA models can learn continuous dynamics and opens new venues for NCA research from a dynamical systems' perspective.
Abstract (translated)
神经元细胞自动机（NCA）是一种细胞自动机，其中更新规则通过一个可以利用梯度下降进行训练的神经网络进行参数化。在本文中，我们重点关注用于纹理合成的高NCA模型，其中更新规则受到描述反应扩散系统的部分微分方程（PDE）的启发。为了训练NCA模型，将空间时间离散化，并用欧拉积分进行数值求解PDE。然而，训练后的NCA是否真正学会了由相应PDE描述的连续动态，还是仅仅在训练中过度拟合使用的离散化，仍然是一个未解决的问题。我们研究了在空间时间离散化逼近连续的情况下NCA模型的极限。我们发现，现有的NCA模型往往在训练附近过度拟合训练离散化，尤其是在初始条件附近，也称为“种子”处。为了解决这个问题，我们提出了一个使用均匀噪声作为初始条件的解决方案。我们证明了我们的方法在保持NCA动态的一致性方面具有有效性。通过允许对图案形成速度和合成图案的大小进行连续控制，我们的改进NCA模型为NCA研究提供了新的途径。我们在交互式在线演示中展示了这一新的NCA特性。我们的研究揭示了NCA模型可以学习连续动态，并为NCA研究从动态系统的角度打开新的研究方向。
URL
https://arxiv.org/abs/2404.06279
