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This study tackles the issue of neural network pruning that inaccurategradients exist when computing the empirical Fisher Information Matrix (FIM).We introduce an entropic Wasserstein regression (EWR) formulation, capitalizingon the geometric attributes of the optimal transport (OT) problem. This isanalytically showcased to excel in noise mitigation by adopting neighborhoodinterpolation across data points. The unique strength of the Wassersteindistance is its intrinsic ability to strike a balance between noise reductionand covariance information preservation. Extensive experiments performed onvarious networks show comparable performance of the proposed method withstate-of-the-art (SoTA) network pruning algorithms. Our proposed methodoutperforms the SoTA when the network size or the target sparsity is large, thegain is even larger with the existence of noisy gradients, possibly from noisydata, analog memory, or adversarial attacks. Notably, our proposed methodachieves a gain of 6% improvement in accuracy and 8% improvement in testingloss for MobileNetV1 with less than one-fourth of the network parametersremaining.

Robust Network Pruning With Sparse Entropic Wasserstein Regression