Title: Neural Cellular Automata Manifold. Abstract: Very recently, the Neural Cellular Automata (NCA) has been proposed to simulate the morphogenesis process with deep networks. NCA learns to grow an image starting from a fixed single pixel. 
In this work, we show that the neural network (NN) architecture of the NCA can be encapsulated in a larger NN. This allows us to propose a new model that encodes a manifold of NCA, each of them capable of generating a distinct image. Therefore, we are effectively learning a representation space of CA, which shows generalization capabilities. We accomplish this by introducing dynamic convolutions inside an Auto-Encoder architecture, for the first time used to join two different sources of information, the encoding and cell's environment information.
In biological terms, our approach would play the role of the transcription factors, modulating the mapping of genes into specific proteins that drive cellular differentiation, which occurs right before the morphogenesis.
We thoroughly evaluate our approach in a dataset of synthetic emojis and also in real images of CIFAR-10.
Our model introduces a general-purpose network, which can be used in a broad range of problems beyond image generation. 