2 citations · 2 across the 4 of their papers we have counts for
4 papers
Counting tangles in coverings of closed 2-orbifolds via ribbon categories
Adam Klukowski
We describe what a typical covering of a closed 2-orbifold looks like on a small scale. Specifically, we prove that a uniformly random covering of degree n contains in expectation…
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…
Simple closed curves, non-kernel homology and Magnus embedding
Adam Klukowski
We consider the subspace of the homology of a covering space spanned by lifts of simple closed curves. Our main result is the existence of unbranched covers of surfaces where this…
Rate of Convergence of Polynomial Networks to Gaussian Processes
Adam Klukowski
We examine one-hidden-layer neural networks with random weights. It is well-known that in the limit of infinitely many neurons they simplify to Gaussian processes. For networks wit…