Not All Samples Are Created Equal: Deep Learning with Importance Sampling

TL;DR

This paper introduces an importance sampling method for deep learning training that focuses on informative examples to reduce gradient variance, leading to faster convergence and improved accuracy.

Contribution

It derives a practical upper bound for per-sample gradient norms and an estimator for variance reduction, enabling efficient importance sampling in standard SGD.

Findings

Up to 10x reduction in training loss within fixed time.

Test error improvements between 5% and 17%.

Applicable with minimal code changes.

Abstract

Deep neural network training spends most of the computation on examples that are properly handled, and could be ignored. We propose to mitigate this phenomenon with a principled importance sampling scheme that focuses computation on "informative" examples, and reduces the variance of the stochastic gradients during training. Our contribution is twofold: first, we derive a tractable upper bound to the per-sample gradient norm, and second we derive an estimator of the variance reduction achieved with importance sampling, which enables us to switch it on when it will result in an actual speedup. The resulting scheme can be used by changing a few lines of code in a standard SGD procedure, and we demonstrate experimentally, on image classification, CNN fine-tuning, and RNN training, that for a fixed wall-clock time budget, it provides a reduction of the train losses of up to an order of magnitude and a relative improvement of test errors between 5% and 17%.