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Deep learning becomes the driving force behind many contemporary technologies and has been successfully applied in many fields. Through software dependencies, a multi-layer supply chain (SC) with a deep learning framework as the core and substantial down-stream projects as the periphery has gradually formed and is constantly developing. However, basic knowledge about the structure and characteristics of the SC is lacking, which hinders effective support for its sustainable development. Previous studies on software SC usually focus on the packages in different registries without paying attention to the SCs derived from a single project. We present an empirical study on two deep learning SCs: TensorFlow and PyTorch SCs. By constructing and analyzing their SCs, we aim to understand their structure, application domains, and evolutionary factors. We find that both SCs exhibit a short and sparse hierarchy …