Minimal overparametrization makes exact certification from examples exponentially hard for depth-2 threshold circuits and log-precision Transformers.
How many queries are needed to learn?Journal of the ACM (JACM), 43(5):840–862, 1996
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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.