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 an embedding 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.

Deep neural networks are representation learning techniques. During training, a deep net is capable of generating a descriptive language of unprecedented size and detail in machine learning. Extracting the descriptive language coded within a trained CNN model (in the case of image data), and reusing it for other purposes is a field of interest, as it provides access to the visual descriptors previously learnt by the CNN after processing millions of images, without requiring an expensive training phase. Contributions to this field (commonly known as feature representation transfer or transfer learning) have been purely empirical so far, extracting all CNN features from a single layer close to the output and testing their performance by feeding them to a classifier. This approach has provided consistent results, although its relevance is limited to classification tasks. In a completely different approach, in this paper we statistically measure the discriminative power of every single feature found within a deep CNN, when used for characterizing every class of 11 datasets. We seek to provide new insights into the behavior of CNN features, particularly the ones from convolutional layers, as this can be relevant for their application to knowledge representation and reasoning. Our results confirm that low and middle level features may behave differently to high level features, but only under certain conditions. We find that all CNN features can be used for knowledge representation purposes both by their presence or by their absence, doubling the information a single CNN feature may provide. We also study how much noise these features may include, and propose a thresholding approach to discard most of it. All these insights have a direct application to the generation of CNN embedding spaces.