On learning Boolean functions and punctured Reed-Muller-codes

The problem of learning an affine Boolean function from noisy examples is considered. This problem is equivalent to the decoding of a binary message encoded with a random linear code and can be also viewed as the problem to decode a message encoded with a randomly punctured Reed-Muller code of first order. The error exponent of the error probability of a learning machine based on spectral learning techniques is shown to be lower bounded by the random coding error exponent.