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Nathan Linial coauthored the 1993 Fourier analysis of AC0 with Yishay Mansour and Noam Nisan. The paper relates constant circuit depth to low-level concentration of Fourier weight, using a switching lemma to control behavior under restrictions. This yields low-degree approximation and learning consequences. circuit depth, circuit size and approximation accuracy remain separate parameters of the bound.^[ref]

Noam Nisan coauthored the 1993 analysis of constant-depth circuits with Nathan Linial and Yishay Mansour. Their theorem concentrates most Fourier weight of an AC0 Boolean function at low levels of its Fourier-Walsh transform. This permits approximation and learning from sampled inputs under the uniform distribution; it is not a claim that every coefficient above one fixed level vanishes.^[ref]

Yishay Mansour coauthored Constant Depth Circuits, Fourier Transform, and Learnability by Nathan Linial and others with Nathan Linial and Noam Nisan. Their analysis turns low-level concentration in the Fourier-Walsh transform into an approximation-based learning method for AC0. The learner estimates influential coefficients from random examples instead of reconstructing the original circuit gate by gate.^[ref]