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Predicting materials properties from composition or structure is of greatinterest to the materials science community. Deep learning has recentlygarnered considerable interest in materials predictive tasks with low modelerrors when dealing with large materials data. However, deep learning modelssuffer in the small data regime that is common in materials science. Here weleverage the transfer learning concept and the graph network deep learningframework and develop the AtomSets machine learning framework for consistenthigh model accuracy at both small and large materials data. The AtomSets modelscan work with both compositional and structural materials data. By combiningwith transfer learned features from graph networks, they can achievestate-of-the-art accuracy from using small compositional data (<400) to largestructural data (>130,000). The AtomSets models show much lower errors than thestate-of-the-art graph network models at small data limits and the classicalmachine learning models at large data limits. They also transfer better in thesimulated materials discovery process where the targeted materials haveproperty values out of the training data limits. The models require minimaldomain knowledge inputs and are free from feature engineering. The presentedAtomSets model framework opens new routes for machine learning-assistedmaterials design and discovery.

AtomSets -- A Hierarchical Transfer Learning Framework for Small and Large Materials Datasets