Abstract: A technique executes a client machine-trained model (“client model”) on a client device. In operation, the client device submits a description of a task to be performed by the client device to a network-accessible main system. The main system uses a main-system machine-trained model (“main-system model”) to produce a task prompt based on the task description. The client device subsequently uses the task prompt to process queries pertaining to the task. The main-system is trained to increase the accuracy of responses produced by the client model, while reducing the sizes of task prompts produced by the main system. The training process is performed by holding weights of the client model constant.