Learning About Growing Neural Cellular Automata

Neural cellular automata have been proven effective in simulating morphogenetic processes. Developing such automata has been applied in 2D and 3D processes related to creating and regenerating complex structures and enabling their behaviors. However, neural cellular automata are inherently uncontrollable after the training process. Starting from a neural cellular automaton trained to generate a given shape from one living cell, this paper aims to gain insight into the behavior of the automaton, and to analyze the influence of the different image characteristics on the training and stabilization process and its shortcomings in different scenarios. For each considered shape, the automaton is trained on one RGB image of size
$72 \times 72$
pixels containing the shape on an uniform white background, in which each pixel represents a cell. The evolution of the automaton starts from one living cell, employing a shallow neural network for the update rule, followed by backpropagation after a variable number of evolutionary steps. We studied the behavior of the automaton and the way in which different components like symmetry, orientation and colours of the shape influence its growth and alteration after a number of epochs and discussed this thoroughly in the experimental section of the paper. We further discuss a pooling strategy, used to stabilize the model and illustrate the influence of this pooling on the training process. The benefits of this strategy are compared to the original model and the behavior of the automaton during its evolution is studied in detail. Finally, we compare the results of models using different filters in the first stage of feature selection. The main results of our study are the insights gained into how the neural cellular automaton works, what it is actually learning, and what influence this learning, as there are observable result differences depending on the characteristics of the input images and the filters used in the model.