Test Sample Accuracy Scales with Training Sample Density in Neural Networks

TL;DR

This paper demonstrates that test sample accuracy in neural networks correlates with training sample density in representation space, and proposes a method to improve accuracy by discarding high-error-bound samples, especially out-of-distribution ones.

Contribution

It introduces a bound on empirical training error that scales inversely with training sample density and shows its effectiveness in predicting and improving test accuracy.

Findings

Error bound predicts test sample inaccuracy

Discarding high-error-bound samples improves accuracy by up to 20%

Density-based sampling enhances out-of-distribution detection

Abstract

Intuitively, one would expect accuracy of a trained neural network's prediction on test samples to correlate with how densely the samples are surrounded by seen training samples in representation space. We find that a bound on empirical training error smoothed across linear activation regions scales inversely with training sample density in representation space. Empirically, we verify this bound is a strong predictor of the inaccuracy of the network's prediction on test samples. For unseen test sets, including those with out-of-distribution samples, ranking test samples by their local region's error bound and discarding samples with the highest bounds raises prediction accuracy by up to 20% in absolute terms for image classification datasets, on average over thresholds.