What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation
This work addresses a fundamental issue in deep learning for researchers and practitioners, offering empirical validation of a theoretical explanation for memorization, though it is incremental as it builds on prior theory.
The paper tackles the problem of why neural networks memorize training data, particularly outliers and mislabeled points, by testing a theory that memorization is necessary for optimal generalization in long-tailed data distributions. The results demonstrate significant benefits of memorization for generalization on standard benchmarks, providing quantitative evidence for the theory.
Deep learning algorithms are well-known to have a propensity for fitting the training data very well and often fit even outliers and mislabeled data points. Such fitting requires memorization of training data labels, a phenomenon that has attracted significant research interest but has not been given a compelling explanation so far. A recent work of Feldman (2019) proposes a theoretical explanation for this phenomenon based on a combination of two insights. First, natural image and data distributions are (informally) known to be long-tailed, that is have a significant fraction of rare and atypical examples. Second, in a simple theoretical model such memorization is necessary for achieving close-to-optimal generalization error when the data distribution is long-tailed. However, no direct empirical evidence for this explanation or even an approach for obtaining such evidence were given. In this work we design experiments to test the key ideas in this theory. The experiments require estimation of the influence of each training example on the accuracy at each test example as well as memorization values of training examples. Estimating these quantities directly is computationally prohibitive but we show that closely-related subsampled influence and memorization values can be estimated much more efficiently. Our experiments demonstrate the significant benefits of memorization for generalization on several standard benchmarks. They also provide quantitative and visually compelling evidence for the theory put forth in (Feldman, 2019).