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What is the definition of a "model" in the discussion of a neural network?

I need a canonical definition.

Can you please supply me with a definition along with a reference from any book or research article?

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When reading books and articles about machine learning or artificial intelligence in general, one can safely assume that the word "model" is used as an abbreviation for "Statistical model". Surprisingly many books skip the job of providing a definition for it, allegedly cause the authors consider it a sort of primitive concept, i.e. they leave the hot potato there hoping that the readers are already familiar with statistics and data science (special mention in this regard to Pattern Recognition and Machine Learning , big classic in which Bishop just use the word from the very beginning without any concern). But in general the closest entity associated with statistical model is just a mathematical function.

Here some references to point that out:

"Predictive modeling: the process of developing a mathematical tool or model that generates an accurate prediction" [page 2, Introduction]

"Broadly speaking, supervised statistical learning involves building a statistical model for predicting, or estimating, an output based on one or more inputs." [page 1 Introduction]

"The quintessential example of a deep learning model is the feedforward deep network, or multilayer perceptron (MLP). A multilayer perceptron is just a mathematical function mapping some set of input values to output values." [page 7 Introduction]

If you're not satisfied and you're looking for a dense, algebraic definition of statistical model, you can check What is a statistical model? by Peter McCullagh. I won't try to explain the definition in the answer cause honestly it's really though and it goes beyond my math skills.

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