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.

Coordinatewise threshold preprocessing

Definition

Input: an integer $d \geq 1$ and a vector $x \in R^{d}$ . Output $T (x) \in {- 1, + 1}^{d}$ with $T (x)_{i} = {\begin{cases} + 1, & x_{i} \geq 0, \\ - 1, & x_{i} < 0 \end{cases} (1 \leq i \leq d) .$

Definition references

Schmidt et al., thresholding operation and Theorem 10.

Kolter–Madry, Chapter 2, binary linear classifiers.

Used by

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, Theorem 10 (standard reference, not scraped)
Zico Kolter and Aleksander Madry, Adversarial Robustness: Theory and Practice, NeurIPS 2018 tutorial notes, Chapter 2 (standard reference, not scraped)