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        "description": "Inherits RPROP and 1-bit SGD. Rates concern stationarity under lower-bound/smoothness/variance and growing-batch settings; majority-vote speedup adds symmetric unimodal noise assumptions. Not convergence for every unbiased gradient distribution or global optimality. Companion error-feedback work gives explicit failure examples, retained as separate corrective theory rather than erased by the original abstract's broad wording.",
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      "statement": "# signSGD and Signum: sign updates and distributed majority aggregation\n\nAnalyzed sign-only stochastic updates and sign-of-momentum variants, with majority-vote worker aggregation for bidirectional low-bit communication.\n\n## Scientific scope\n\nInherits RPROP and 1-bit SGD. Rates concern stationarity under lower-bound/smoothness/variance and growing-batch settings; majority-vote speedup adds symmetric unimodal noise assumptions. Not convergence for every unbiased gradient distribution or global optimality. Companion error-feedback work gives explicit failure examples, retained as separate corrective theory rather than erased by the original abstract's broad wording.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nJeremy Bernstein; Yu-Xiang Wang; Kamyar Azizzadenesheli; Anima Anandkumar\n\nSource-listed authors or explicitly credited technical contributors for the cited versions. Family entries retain source-specific attribution; a combined list is not one original-paper byline or equal individual work. Names alone do not establish resolved identities.\n\n\n\n## Original sources\n\n- [signSGD: compressed optimisation for non-convex problems](https://arxiv.org/abs/1802.04434v1)\n",
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