Continuous limit of mass-conserving neural cellular automata (MaCE-NCA)

Establish the continuous-time-and-space limit of the dynamics of mass-conserving neural cellular automata (MaCE-NCA) by deriving a formal continuous description (e.g., limiting partial differential equation) of the MaCE-NCA update rule, analogous to continuous-limit analyses of neural cellular automata such as NoiseNCA.

Background

The authors adapt Neural Cellular Automata (NCA) to include mass conservation by applying MaCE to the RGB channels while leaving other channels updated by the neural network.

While MaCE’s continuous limit is developed earlier in the paper, the continuous limit for the MaCE-NCA variant remains to be formally analyzed, and the authors explicitly defer this task to future work, suggesting an analogy with recent continuous-limit studies of NCA (e.g., NoiseNCA).