Title: The Role of Learning Regime, Architecture and Dataset Structure on Systematic Generalization in Simple Neural Networks. Abstract: Humans often systematically generalize in situations where standard deep neural networks do not. Empirical studies have shown that the learning procedure and network architecture can influence systematicity in deep networks, but the underlying reasons for this influence remain unclear. Here we theoretically study the acquisition of systematic knowledge by simple neural networks. We introduce a minimal space of datasets with systematic and non-systematic features in both the input and output. For shallow and deep linear networks, we derive learning trajectories for all datasets in this space. The solutions reveal that both shallow and deep networks rely on non-systematic inputs to the same extent throughout learning, such that even with early stopping, no networks learn a fully systematic mapping. Turning to the impact of architecture, we show that modularity improves extraction of systematic structure, but only achieves perfect systematicity in the trivial setting where systematic mappings are fully segregated from non-systematic information. Finally, we analyze iterated learning, a procedure in which generations of networks learn from languages generated by earlier learners. Here we find that networks with output modularity successfully converge over generations to a fully systematic `language’ starting from any dataset in our space. Our results contribute to clarifying the role of learning regime, architecture, and dataset structure in promoting systematic generalization, and provide theoretical support for empirical observations that iterated learning can improve systematicity.