Parallel Function Calling vs Routing to Functions Yourself

Is parallel function calling a black box implementation of building a classifier with LLMs? Given that when you use parallel function calling the model chooses the function based on how you have described the schema, it seems like under the hood it is basically taking the inputs and approximating which function seems best used.

In implementations where you want to control which function is used, you may use a classification model or an LLM as a classification model to route the inputs to the correct function. In that case are these functionally equivalent? Either somewhat transparent (rolling your own classifier / LLM classifier) vs completely untunable (parallel function calling)?

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