Minimal overparametrization makes exact certification from examples exponentially hard for depth-2 threshold circuits and log-precision Transformers.
On the limits of efficient teachability.Information Processing Letters, 79(6):267–272, 2001
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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.