# Test Sample Accuracy Scales with Training Sample Density in Neural Networks Source: [Test Sample Accuracy Scales with Training Sample Density in Neural Networks]() Collection index: [llms.txt]() Data updated: 2025-10-27T06:16:31.054Z Authors: Xu Ji, Razvan Pascanu, Devon Hjelm, Balaji Lakshminarayanan, Andrea Vedaldi Published: 2021-06-15T18:34:41.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()