Deep Learning Through the Lens of Example Difficulty

TL;DR

This paper introduces a new measure called prediction depth to analyze how individual examples influence deep learning models, revealing relationships with uncertainty, confidence, and learning speed, and categorizing difficult examples to improve accuracy.

Contribution

It proposes the prediction depth measure and categorizes difficult examples, providing new insights into model behavior and improving prediction accuracy.

Findings

Prediction depth correlates with model uncertainty and confidence.

Difficult examples can be grouped into three interpretable categories.

Understanding example difficulty explains phenomena like layer specialization and learning order.

Abstract

Existing work on understanding deep learning often employs measures that compress all data-dependent information into a few numbers. In this work, we adopt a perspective based on the role of individual examples. We introduce a measure of the computational difficulty of making a prediction for a given input: the (effective) prediction depth. Our extensive investigation reveals surprising yet simple relationships between the prediction depth of a given input and the model's uncertainty, confidence, accuracy and speed of learning for that data point. We further categorize difficult examples into three interpretable groups, demonstrate how these groups are processed differently inside deep models and showcase how this understanding allows us to improve prediction accuracy. Insights from our study lead to a coherent view of a number of separately reported phenomena in the literature: early layers generalize while later layers memorize; early layers converge faster and networks learn easy data and simple functions first.