Day 73 asked what a clustering score is a number of. Day 74 asked which fairness equalities can hold at once. Both were about the number at the end of a run.
This is about the number people put in front of one: the promise that a model which did well on the data it was fitted to will do well on data it has not seen.
There is a whole theory of those promises. It is correct. This page measures what it is worth.
See it: https://dev48.infy.uk/ml/day75-generalization-bounds.html
Nothing here is sampled
- every labelling of every point set is enumerated
- every sign pattern is summed over
- the learner's true error is available in closed form
So "loose" is a factor, not an impression.
Capacity, counted rather than bounded
The growth function — how many distinct labellings a model class can produce on n points — is counted directly, and it matches its closed form at every size tried, for every class where one exists. The VC dimension is then read off the count rather than quoted from a table.
That matters because the usual practitioner substitute is parameter count, and the page shows exactly where that substitute and the real capacity part company.
Then the bound meets the thing it guarantees
With the true error known exactly, the bound can be held against it directly. The gap is the finding, and it is a multiple rather than a rounding.
That is not an argument against the theory. A bound that holds for every distribution has to pay for that generality, and the price is visible here as a number instead of a vibe. The practical reading: a generalization bound tells you a class cannot overfit past a point. It does not tell you how your model will do, and the distance between those two statements is measurable.
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