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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. It's important because the Fisher matrix is known to be much better for nonlinear optimization than the Hessian. The experiment that you mention show that |H| is also much better than the Hessian. So the big question is, which is better: |H| or F, where both matrices are used in the same setup. However, this assumption is clearly false due to the presence of the large number of saddle points in high dimensional spaces.