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Neural networks tend to achieve better accuracy with training if they arelarger -- even if the resulting models are overparameterized. Nevertheless,carefully removing such excess parameters before, during, or after training mayalso produce models with similar or even improved accuracy. In many cases, thatcan be curiously achieved by heuristics as simple as removing a percentage ofthe weights with the smallest absolute value -- even though magnitude is not aperfect proxy for weight relevance. With the premise that obtainingsignificantly better performance from pruning depends on accounting for thecombined effect of removing multiple weights, we revisit one of the classicapproaches for impact-based pruning: the Optimal Brain Surgeon(OBS). We proposea tractable heuristic for solving the combinatorial extension of OBS, in whichwe select weights for simultaneous removal, as well as a systematic update ofthe remaining weights. Our selection method outperforms other methods underhigh sparsity, and the weight update is advantageous even when combined withthe other methods.

The Combinatorial Brain Surgeon: Pruning Weights That Cancel One Another in Neural Networks