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Open source machine learning (ML) libraries enable developers to integrate advanced ML functionality into their own applications. However, popular ML libraries, such as TensorFlow, are not available natively in all programming languages and software package ecosystems. Hence, developers who wish to use an ML library which is not available in their programming language or ecosystem of choice, may need to resort to using a so-called binding library (or binding). Bindings provide support across programming languages and package ecosystems for reusing a host library. For example, the Keras .NET binding provides support for the Keras library in the NuGet (.NET) ecosystem even though the Keras library was written in Python. In this paper, we collect 2,436 cross-ecosystem bindings for 546 ML libraries across 13 software package ecosystems by using an approach called BindFind, which can automatically identify bindings and link them to their host libraries. Furthermore, we conduct an in-depth study of 133 cross-ecosystem bindings and their development for 40 popular open source ML libraries. Our findings reveal that the majority of ML library bindings are maintained by the community, with npm being the most popular ecosystem for these bindings. Our study also indicates that most bindings cover only a limited range of the host library's releases, often experience considerable delays in supporting new releases, and have widespread technical lag. Our findings highlight key factors to consider for developers integrating bindings for ML libraries and open avenues for researchers to further investigate bindings in software package ecosystems.