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.

The cyclic perceptron update procedure

Definition

Input a finite ordered sample $((x_{i}, y_{i}))_{i = 1}^{n}$ with $n \geq 1$ , $x_{i} \in R^{d}$ , and $y_{i} \in {- 1, + 1}$ . Put ${\tilde{x}}_{i} = (x_{i}, 1) \in R^{d + 1}$ and initialize $w = 0$ . In each pass, visit $i = 1, \dots, n$ in the fixed order. Whenever $y_{i} w^{T} {\tilde{x}}_{i} \leq 0$ , replace $w$ by $w + y_{i} {\tilde{x}}_{i}$ and count one update. After a full pass with no updates, stop and return $w$ . The associated classifier returns $+ 1$ when $w^{T} (x, 1) > 0$ and $- 1$ when $w^{T} (x, 1) \leq 0$ , so a score tie is assigned to $- 1$ . The procedure has no iteration limit; if its stop condition never holds, it continues with further passes.

Definition references

Hastie, Tibshirani, and Friedman, ESL, §4.5.1, update (4.44)

Stanford CS229 Spring 2022 lecture notes, §2.2

Used by

Dependency tree · 0 levels

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

Sources

Hastie, Tibshirani, and Friedman, The Elements of Statistical Learning, 2nd ed., corrected 12th printing (standard reference, not scraped)
Stanford CS229 Spring 2022 lecture notes (standard reference, not scraped)