On-device recommender systems recently have garnered increasing attention due to their advantages of providing prompt response and securing privacy. To stay current with evolving user interests, cloud-based recommender systems are periodically updated with new interaction data. However, on-device models struggle to retrain themselves because of limited onboard computing resources. As a solution, we consider the scenario where the model retraining occurs on the server side and then the updated parameters are transferred to edge devices via network communication. While this eliminates the need for local retraining, it incurs a regular transfer of parameters that significantly taxes network bandwidth. To mitigate this issue, we develop an efficient approach based on compositional codes to compress the model update. This approach ensures the on-device model is updated flexibly with minimal additional parameters whilst utilizing previous knowledge. The extensive experiments conducted on multiple session-based recommendation models with distinctive architectures demonstrate that the on-device model can achieve comparable accuracy to the retrained server-side counterpart through transferring an update 60x smaller in size. The codes are available at \url{https://github.com/xiaxin1998/ODUpdate}.
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