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Inner-Product Axioms (axiom)

Mon, 21 Sep 2026 15:22:00 +0900

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Attention is built on a quantity that looks like a similarity but is defined by three axioms: an inner product is symmetric, linear in each argument, and positive definite. Those three properties are what allow a score to be read as “how much one vector points along another”.

Kolmogorov Axioms for a Token Distribution (axiom)

Mon, 21 Sep 2026 13:32:00 +0900

An axiom is an assumption taken as given, and the ones that hold up a language model are Kolmogorov’s three: probabilities are non-negative, the whole space has probability one, and disjoint events add. Everything else about token distributions is derived from them rather than assumed.