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I have been coming across function calls that use arguments that are not in the function definition. I would like to know how that works (i.e. how the compiler interprets this).

For example, this function call:

 interp.plot_confusion_matrix(figsize=(12,12), dpi=60)

uses the variables "figsize" and "dpi", but neither of them turn up in the definition of plot_confusion_matrix: help(interp.plot_confusion_matrix) gives:

plot_confusion_matrix(normalize: bool = False, title: str = 'Confusion matrix', 
cmap: Any = 'Blues', norm_dec: int = 2, slice_size: int = None, **kwargs) -> None 
method of fastai.vision.learner.ClassificationInterpretation instance
    Plot the confusion matrix, with `title` and using `cmap`.

Why is it not an error to use "figsize" and "dpi" in the function call if they are not arguments of the function? How does this work in python?

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Those parameters are taken care of by **kwargs in the function definition. You can look how this is dealt with by the code in the fastai repo and looking for **kwargs in the function definition.
Some explanations about how this works can be found on SO: https://stackoverflow.com/questions/3394835/use-of-args-and-kwargs.

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