Error Correction Codes for Robust Classification with Neural Networks Under Sparse Noise

We consider the problem of designing neural network classifiers that are robust when their inputs are corrupted by sparse noise. We report on a series of experiments on the MNIST image dataset where we test the performance of neural network classifiers on images with a small number of corrupted pixels. We find that neural network classifiers are highly vulnerable to sparsely corrupted inputs, and this vulnerability remains even when substantial amounts of redundancy is added to the inputs. We show that this vulnerability can be effectively fixed by designing a real-numbered error correction code and using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{1}$</tex> minimization procedure to clean up the corrupted inputs.