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            "content": "测验：牛顿法与优化进阶"
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            "content": "共 30 题",
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            "content": "1. 优化问题里，牛顿法本质上是在求什么的根？\nA.  \\( f(x)=0 \\) \nB.  \\( f'(x)=0 \\) \nC.  \\( f''(x)=0 \\) \nD. 积分=0",
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            "content": "2. 一维优化牛顿法的迭代公式是?\nA.  \\( x_{n+1}=x_{n}-f(x_{n})/f'(x_{n}) \\) \nB.  \\( x_{n+1}=x_{n}-f'(x_{n})/f''(x_{n}) \\) \nC.  \\( x_{n+1}=x_{n}-\\eta f'(x_{n}) \\) \nD.  \\( x_{n+1}=x_{n}+f'(x_{n})/f''(x_{n}) \\)",
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            "content": "3. 多维优化牛顿法写作 \\(x \\leftarrow x - H^{-1} \\cdot\\) 梯度，\\(H\\) 是什么？A. 雅可比矩阵B. Hessian（二阶偏导矩阵）C. 协方差矩阵D. 单位矩阵",
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            "content": "4. 对二次函数 \\( f(x) = (x - 3)^2 + 1 \\)，从 \\( x_0 = 0 \\) 出发，牛顿法几步到最小值？A. 1步B. 约20步C. 不收敛D. 取决于学习率",
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            "content": "5. 梯度下降是一阶方法，牛顿法是？\nA. 零阶（只用 f）\nB. 一阶\nC. 二阶（用到 Hessian）\nD. 三阶",
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            "content": "6. 牛顿法在根（或非退化极小）附近的局部收敛速度是？A. 线性B. 二阶（误差近似平方）",
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            "content": "C. 永不收敛  \nD. 与 \\(\\eta\\) 相同",
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            "content": "7. Hessian 正定，对应驻点的几何是？\nA. 局部极小（碗）\nB. 局部极大（倒碗）\nC. 鞍点（马鞍）\nD. 无法判断",
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            "content": "8. Hessian 有正有负特征值时，驻点是？\nA. 全局最小\nB. 鞍点\nC. 一定发散\nD. 一定是极大",
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            "content": "9. \\(f(x, y) = x^{2} - y^{2}\\) 在原点处，牛顿法一步会到哪里？A. 某个极小值B. 原点（鞍点）C. 无穷远D. 随机",
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