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||c w|| = c ||w||; the normalized geometric margin of the linear classifier is invariant.", "source_wording_preserved": true, "notes": { "en": "Editorial correction: In this article’s linear classification example, positive rescaling of the parameters scales their norm by the same factor. It is the normalized margin that remains invariant. The source sentence’s ‘norm invariance’ wording is incorrect; the original wording is retained alongside this correction.", "zh": "编者勘正：在本文的线性分类示例中，参数按正比例缩放时，范数也按相同比例缩放；保持不变的是归一化间隔。原文“范数不变”的措辞有误，本阅读版保留原句并在此更正。", "es": "Corrección editorial: en el ejemplo de clasificación lineal de este artículo, al reescalar los parámetros por un factor positivo, su norma cambia por el mismo factor. Lo que permanece invariante es el margen normalizado. La expresión «invariancia de la norma» del original es incorrecta; se conserva la redacción original junto con esta corrección.", "ja": "編集上の訂正：本稿の線形分類の例では、パラメータを正の係数で拡大・縮小すると、そのノルムも同じ係数で変化します。不変なのは正規化マージンです。原文の「ノルムの不変性」という表現は誤りであり、本閲覧版では原文を保持したうえで、ここに訂正を示します。", "ar": "تصحيح تحريري: في المثال الخطي للتصنيف في هذا المقال، عند إعادة تحجيم المعاملات بعامل موجب، يتغير معيارها بالعامل نفسه؛ وما يبقى ثابتًا هو الهامش المُطبَّع. تعبير «ثبات المعيار» في النص الأصلي غير صحيح. تحتفظ هذه النسخة بصياغة الأصل مع إظهار هذا التصحيح." } } ] }, { "slug": "normalization-geometry", "source_slug": "normalization-geometry", "title": "Normalization Changes the Geometry of Learning", "url": "/guides/normalization-geometry/v5/", "localized_urls": { "en": "/guides/normalization-geometry/v5/en/", "zh": "/guides/normalization-geometry/v5/zh/", "es": "/guides/normalization-geometry/v5/es/", "ja": "/guides/normalization-geometry/v5/ja/", "ar": "/guides/normalization-geometry/v5/ar/" }, "previous_version": 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Its probability is a lower bound on joint-failure probability and limits overall availability from above. The source wording “a lower bound on benefits” is imprecise; the original sentence is retained alongside this correction. This is a model identity, not a measured ecological result.", "zh": "编者勘正：在本文的简化模型中，共同冲击使所有服务者同时不可用；该冲击的概率构成联合失效概率的下限，并给整体可用率设定上限。原文“收益有下限”的表述不准确，本阅读版保留原句并在此更正。这是模型中的概率关系，不是生态实测结果。", "es": "Corrección editorial: en el modelo simplificado de este artículo, una perturbación común deja indisponibles a todos los proveedores. Su probabilidad constituye un límite inferior para la probabilidad de fallo conjunto e impone un límite superior a la disponibilidad global. La expresión original «un límite inferior para los beneficios» es imprecisa; se conserva la frase original junto con esta corrección. 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