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The Yun-Sra-Jadbabaie SS-RS-GD Inequalities

Algorithms & optimization · posed by Chulhee Yun, Suvrit Sra, Ali Jadbabaie, 2021 · solved

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Statement

Yun, Sra and Jadbabaie posed as a COLT 2021 open question whether, for well-conditioned symmetric matrices, the operators encoding the expected iterate of single-shuffle SGD, random-reshuffle SGD and gradient descent on a quadratic finite sum satisfy ∥Wss∥≤∥Wrs∥≤∥Wgd∥\|W_{ss}\| \le \|W_{rs}\| \le \|W_{gd}\|. They do.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    GPT-5.5 Pro (extended), with Binghui Peng

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

    AI involvement
    ai discovered
    — the result was found by a model.

    The paper states the proof was found via GPT-5.5 Pro prompted by the author, and a footnote says the proof idea was completely generated by the model, linking the shared conversation. The write-up was assembled by the author.

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