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act III

The Instruments

There is no universally best learner. Every strength is paid for with an assumption.

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No Free Lunch

before this →Why Memorizing Fails

A troubling theorem sits at the foundation of learning: averaged over all possible problems, every learning algorithm performs exactly as well as random guessing. The no free lunch theorem.

So why does machine learning work at all? Because the real world is not all possible problems. It has structure — locality, smoothness, repetition — and we build models whose assumptions match it.

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no free lunch: for every problem an algorithm wins, another one loses

Inductive bias: the assumption you cannot avoid

Every model brings an inductive bias — a built-in preference for some patterns over others. A convolutional network assumes nearby pixels matter together. A recurrent network assumes order matters. A transformer assumes anything can attend to anything. Choosing an architecture is choosing which assumptions to bet on.

Occam’s razor is the practical version: among models that fit equally well, prefer the simpler. Simplicity is not an aesthetic — a simpler model has fewer ways to accidentally fit noise, which is why it usually generalizes better.

Capacity is a dial

how much a model can memorize

Capacity is roughly how many patterns a model can fit. Too little and it cannot represent the truth; too much and it can memorize nonsense. Modern deep learning loves huge capacity — and then uses regularization and huge data to keep it honest.

the practical lessonDo not ask “what is the best model?” Ask “what assumptions does this task have, and which model encodes them?”
STRUCTUREreal tasks are not random
INDUCTIVE BIASassumptions we bake into the model
GENERALIZATIONassumptions match the world → it works
end of the instrumentsWe now have the full toolkit: information, beliefs, geometry, gradients, and generalization. Time to build the machines that use it.
introduces →inductive biasno free lunchOccam's razorcapacity
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