AlgorithmAlgorithm: Literature-sourcedProof: Not applicablePipeline-generatedjudge 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.

Class-weighted mean classifier

Definition

Input: an integer $n \geq 1$ , an integer $d \geq 1$ , and an ordered labeled sample $((x_{1}, y_{1}), \dots, (x_{n}, y_{n}))$ with $x_{i} \in R^{d}$ and $y_{i} \in {- 1, + 1}$ . Compute $w = \frac{1}{n} \sum_{i = 1}^{n} y_{i} x_{i} .$ Output the vector $w$ and the binary linear classifier $f_{w} : R^{d} \to {- 1, + 1}$ defined by $f_{w} (x) = + 1$ when $⟨ w, x ⟩ \geq 0$ and $f_{w} (x) = - 1$ when $⟨ w, x ⟩ < 0$ . The zero-score tie is assigned to $+ 1$ .

Definition references

Schmidt et al., class-weighted sample mean in Theorem 5 and normalized direction in Theorem 21.

Used by

Robust sample upper bound in the Gaussian model Theorem

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Ludwig Schmidt, Shibani Santurkar, Dimitris Tsipras, Kunal Talwar, and Aleksander Madry, Adversarially Robust Generalization Requires More Data, arXiv:1804.11285v2, Theorems 5 and 21 (standard reference, not scraped)