记忆是有益还是有害？先验信息设定阈值
Is Memorization Helpful or Harmful? Prior Information Sets the Threshold
AI总结：
在过参数化线性模型和贝叶斯框架下，研究先验分布如何决定训练误差与泛化误差的关系，给出记忆必要或过拟合有害的条件。
摘要：
我们研究了任意估计过程中训练误差与泛化误差之间的联系，在贝叶斯设置下，基于一般先验的过参数化线性模型中进行工作。我们发现了先验分布$π$固有的决定因素，给出了最优泛化需要训练误差(i)接近插值（相对于噪声大小，即记忆是必要的），或(ii)接近噪声水平（即过拟合是有害的）的显式条件。值得注意的是，当噪声达到由Fisher信息和先验$π$的方差参数决定的阈值时，这些现象会发生。
英文摘要：
We examine the connection between training error and generalization error for arbitrary estimating procedures, working in an overparameterized linear model under general priors in a Bayesian setup. We find determining factors inherent to the prior distribution $π$, giving explicit conditions under which optimal generalization necessitates that the training error be (i) near interpolating relative to the noise size (i.e., memorization is necessary), or (ii) close to the noise level (i.e., overfitting is harmful). Remarkably, these phenomena occur when the noise reaches thresholds determined by the Fisher information and the variance parameters of the prior $π$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
