Minimal overparametrization makes exact certification from examples exponentially hard for depth-2 threshold circuits and log-precision Transformers.
Polynomial threshold functions, hyperplane arrangements, and random tensors.SIAM Journal on Mathematics of Data Science, 1(4):699–729, 2019
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Certification from Examples is Hard for Circuits and Transformers under Minimal Overparametrization
Minimal overparametrization makes exact certification from examples exponentially hard for depth-2 threshold circuits and log-precision Transformers.