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This paper studies the exact certification problem for neural networks, showing that even minimal overparametrization can make certification exponentially hard for threshold circuits of depth≥2 and log-precision Transformers. It also characterizes approximate certification, revealing that allowing polynomially many mistakes still requires exponentially large certificates.
This simulation study examines the double descent phenomenon for least-squares interpolation on contaminated data in linear regression, comparing the performance of the least-squares interpolator with robust alternatives.