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math.GR2023
Lack of profinite rigidity among extensions with free quotient
Paweł Piwek
We present a construction that yields infinite families of non-isomorphic semidirect products sharing a specified profinite completion. Within each family, $m \ge 2…
stat.ML2023
Exact Count of Boundary Pieces of ReLU Classifiers: Towards the Proper Complexity Measure for Classification
Paweł Piwek, Adam Klukowski, Tianyang Hu
Classic learning theory suggests that proper regularization is the key to good generalization and robustness. In classification, current training schemes only target the complexity…
math.GR2023★ 1 cited
Profinite rigidity properties of central extensions of 2-orbifold groups
Paweł Piwek
We extend Wilkes' results on the profinite rigidity of SFSs to the setting of central extensions of 2-orbifold groups with higher-rank centre. We prove that both rigid and non-rigi…