  This study addresses the challenge of inaccurate gradients in computing the
empirical Fisher Information Matrix during neural network pruning. We introduce
SWAP, a formulation of Entropic Wasserstein regression (EWR) for pruning,
capitalizing on the geometric properties of the optimal transport problem. The
``swap'' of the commonly used linear regression with the EWR in optimization is
analytically demonstrated to offer noise mitigation effects by incorporating
neighborhood interpolation across data points with only marginal additional
computational cost. The unique strength of SWAP is its intrinsic ability to
balance noise reduction and covariance information preservation effectively.
Extensive experiments performed on various networks and datasets show
comparable performance of SWAP with state-of-the-art (SoTA) network pruning
algorithms. Our proposed method outperforms the SoTA when the network size or
the target sparsity is large, the gain is even larger with the existence of
noisy gradients, possibly from noisy data, analog memory, or adversarial
attacks. Notably, our proposed method achieves a gain of 6% improvement in
accuracy and 8% improvement in testing loss for MobileNetV1 with less than
one-fourth of the network parameters remaining.
