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Is Deeper Better only when Shallow is Good?

Neural Information Processing Systems

While current works account for the importance ofdepth for the expressivepower ofneural-networks, itremains an open question whether these benefits are exploited during a gradient-based optimization process.







GloballyConvergentNewtonMethodsfor Ill-conditionedGeneralizedSelf-concordantLosses

Neural Information Processing Systems

Second, in the non-parametric machine learning setting, we provide an explicit algorithm combining the previous scheme with Nyström projection techniques, andprovethatitachievesoptimal generalization bounds with atime complexity of orderO(ndfλ), a memory complexity of orderO(df2λ) and no dependence on the condition number, generalizing the results known for leastsquaresregression.Here nisthenumberofobservationsand dfλ istheassociated degrees of freedom.