Neural Cellular Automata Manifold

Very recently, a deep Neural Cellular Automata (NCA)[1] has been proposed to simulate the complex morphogenesis process with deep networks. This model learns to grow an image starting from a fixed single pixel. In this paper, we move a step further and propose a new model that extends the expressive power of NCA from a single image to an manifold of images. 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 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. The proposed model also extends the capabilities of the NCA to a general purpose network, which can be used in a broad range of problems. We thoroughly evaluate our approach in a dataset of synthetic emojis and also in real images of CIFAR-10.