A function f is d-resilient if all its Fourier coefficients of degree at most d are zero, i.e. f is uncorrelated with all low-degree parities. We study the notion of approximate resilience of Boolean functions, where we say that f is α-approximately d-resilient if f is α-close to a [−1, 1]-valued d-resilient function in `1 distance. We show that approximate… (More)