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We present ISAAC (Input-baSed ApproximAte Curvature), a novel method thatconditions the gradient using selected second-order information and has anasymptotically vanishing computational overhead, assuming a batch size smallerthan the number of neurons. We show that it is possible to compute a goodconditioner based on only the input to a respective layer without a substantialcomputational overhead. The proposed method allows effective training even insmall-batch stochastic regimes, which makes it competitive to first-order aswell as second-order methods.

ISAAC Newton: Input-based Approximate Curvature for Newton's Method