Any fixed parity of size at least logarithmic in the dimension requires exponentially many perturbed-gradient steps before the expected correlation loss moves away from its trivial value.
Noise-tolerant learning, the parity problem, and the statistical query model
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Hardness of Learning Fixed Parities with Neural Networks
Any fixed parity of size at least logarithmic in the dimension requires exponentially many perturbed-gradient steps before the expected correlation loss moves away from its trivial value.