Lesson 1 · Learning as function fitting

Guess the Function

Welcome to the machine learning track. Strip away the acronyms and essentially all of supervised machine learning — from a line through points to a trillion-parameter language model — is one move with three choices in it:

  1. Choose a function family (the hypothesis space): the set of functions you’re willing to consider. All straight lines f(x) = ax + b. All depth-6 decision trees. All transformers of a certain shape. This choice quietly encodes your assumptions about the world.
  2. Choose a loss: a number measuring how wrong a candidate function is on your examples — squared error, misclassification rate, cross-entropy. The loss defines what “good” means.
  3. Search the family for a member with low loss: closed-form algebra for lines, greedy splitting for trees, gradient descent for neural nets. “Training” is this search; a “model” is the member you settled on.

That’s the whole game: examples in, function out — where the function’s behavior was induced from data rather than spelled out by a programmer. The learning happens precisely where a human didn’t write the rule.

The question above gives you four computations. Three of them are this move — examples, a scored family, a search. One is something else entirely, and saying precisely why it doesn’t fit the frame is the point of the exercise. (Hint: it’s not about difficulty, and quicksort certainly involves a function.)

Which of these is NOT an instance of learning-as-function-fitting?