ExampleConstruction: AI-generatedVerification: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

AdaBoost stops at a perfect round

Example

On the two-observation sample $(x_{1}, y_{1}) = (0, + 1)$ and $(x_{2}, y_{2}) = (1, - 1)$ , let the first base classifier return $h_{1} (x_{1}) = + 1$ and $h_{1} (x_{2}) = - 1$ . Its weighted error is $e_{1} = 0$ , so AdaBoost stops and returns $h_{1}$ with zero training error; no coefficient is formed.

Facts & Assumptions

Given: The stated sample, labels, and classifier outputs.

[F1]

Finite-sample AdaBoost.M1 with half-log coefficients: When $e_{m} = 0$ , the algorithm halts and returns $h_{m}$ itself as a perfect classifier without forming a coefficient.

Verification

1.1givenalgebra

Both predictions equal their labels, so the number of training mistakes is $0$ and $e_{1} = 0$ for the initial uniform weights.

2.1F1step 1.1∎

By [F1], the algorithm stops at this round and returns $h_{1}$ ; since both predictions match, its training error is $0$ and no logarithmic coefficient is evaluated.

Depends on

Finite-sample AdaBoost.M1 with half-log coefficients

Used by

Nothing in the library uses this result yet.

Dependency tree · one level

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