Deep learning (DL) frameworks have been extensively designed, implemented, and used in software projects across many domains. However, due to the lack of knowledge or information, time pressure, complex context, etc., various uncertainties emerge during the development, leading to assumptions made in DL frameworks. Though not all the assumptions are negative to the frameworks, being unaware of certain assumptions can result in critical problems (e.g., system vulnerability and failures). As the first step of addressing the critical problems, there is a need to explore and understand the assumptions made in DL frameworks. To this end, we conducted an exploratory study to understand self-claimed assumptions (SCAs) about their distribution, classification, and impacts using code comments from nine popular DL framework projects on GitHub. The results are that: (1) 3,084 SCAs are scattered across 1,775 files in the nine DL frameworks, ranging from 1,460 (TensorFlow) to 8 (Keras) SCAs. (2) There are four types of validity of SCAs: Valid SCA, Invalid SCA, Conditional SCA, and Unknown SCA, and four types of SCAs based on their content: Configuration and Context SCA, Design SCA, Tensor and Variable SCA, and Miscellaneous SCA. (3) Both valid and invalid SCAs may have an impact within a specific scope (e.g., in a function) on the DL frameworks. Certain technical debt is induced when making SCAs. There are source code written and decisions made based on SCAs. This is the first study on investigating SCAs in DL frameworks, which helps researchers and practitioners to get a comprehensive understanding on the assumptions made. We also provide the first dataset of SCAs for further research and practice in this area.