What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation

TL;DR

This paper investigates why neural networks memorize training data, especially in long-tailed distributions, by empirically testing a recent theory and demonstrating how memorization benefits generalization.

Contribution

The authors design efficient influence estimation methods to empirically validate a theory linking memorization to long-tailed data distributions in neural networks.

Findings

Memorization significantly improves generalization on benchmarks.

Empirical evidence supports the theory that long-tailed data necessitates memorization.

Efficient influence estimation methods enable analysis of training example impacts.

Abstract

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).