arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1906.05271cs.LGstat.ML
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学习需要专业化吗?关于长尾的小故事

Does Learning Require Memorization? A Short Tale about a Long Tail

Apple(苹果公司);Simons Institute for the Theory of Computing(西蒙斯计算理论研究所);Google Research(谷歌研究院)

Vitaly Feldman

摘要:

图像识别任务的最先进的结果是使用过参数化的学习算法实现的,这些算法(几乎)完美地拟合训练集,并且即使是随机标签也能很好地拟合。这种记住训练数据的标签的倾向没有被现有的理论分析所解释。当训练数据包含敏感的个人信息时,训练数据的记忆也呈现显著的隐私风险,因此理解这种记忆对于准确学习是否是必要的是重要的。我们为这一现象提供了第一个概念解释和理论模型。具体来说,我们证明了自然数据分布的标签记忆是必要的,以实现接近最佳的泛化误差。至关重要的是,即使是异常值和噪声标签的标签也需要记住。该模型的动机和支持的结果,最近的几个实证工作。在我们的模型中,数据是从一个混合的子群体,我们的研究结果表明,记忆是必要的,每当分布的子群体的频率是长尾。图像和文本数据是长尾的,因此我们的研究结果建立了这些经验现象之间的正式联系。我们的研究结果可以量化的成本限制记忆的学习和解释的不同影响,隐私和模型压缩对不同的子群。

英文摘要:

State-of-the-art results on image recognition tasks are achieved using over-parameterized learning algorithms that (nearly) perfectly fit the training set and are known to fit well even random labels. This tendency to memorize the labels of the training data is not explained by existing theoretical analyses. Memorization of the training data also presents significant privacy risks when the training data contains sensitive personal information and thus it is important to understand whether such memorization is necessary for accurate learning. We provide the first conceptual explanation and a theoretical model for this phenomenon. Specifically, we demonstrate that for natural data distributions memorization of labels is necessary for achieving close-to-optimal generalization error. Crucially, even labels of outliers and noisy labels need to be memorized. The model is motivated and supported by the results of several recent empirical works. In our model, data is sampled from a mixture of subpopulations and our results show that memorization is necessary whenever the distribution of subpopulation frequencies is long-tailed. Image and text data is known to be long-tailed and therefore our results establish a formal link between these empirical phenomena. Our results allow to quantify the cost of limiting memorization in learning and explain the disparate effects that privacy and model compression have on different subgroups.

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。

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