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Would a deployed or deployment-ready (i.e., already-trained) supervised learning model have a 100% accuracy rate for predictions on the training data (if you were to run the training data through it again)?

[Note: I don't know if it is possible for such models to incorporate "memory" such that the model would retrieve an output variable for a given training data point (containing various input variables) from memory (having seen it before during training), instead of retrieving it by plugging the data point's input variables into the equation that is the predictive model (obviously a unique, unknown equation created during the training process, with millions of parameters, which no human knows the precise nature of). If it is possible for such models to have "memory", then for the purposes of my question, please assume it is not.]

What I would like to know is: are SL predictive models perfectly parameterized for the training data, such that feeding any training data point in to the completed model will 100% of the time yield the correct output for that data point (note: I am aware that, in general, testing a deployment-ready model on its training data is not a very useful test), or are such models imperfect predictors even if run (when already-trained) on their training data?

I know people talk about overfitting and the bias-variance tradeoff. That would seem to indicate the latter to be the case, but I want to be sure.

Thank you for any answers you can offer!

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