
Exactly Computing the Local Lipschitz Constant of ReLU Networks
The Lipschitz constant of a neural network is a useful metric for provab...
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On Church's Thesis in Cubical Assemblies
We show that Church's thesis, the axiom stating that all functions on th...
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Numerical Asymptotic Results in Game Theory Using Sergeyev's Infinity Computing
Prisoner's Dilemma (PD) is a widely studied game that plays an important...
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Approximating the Derivative of Manifoldvalued Functions
We consider the approximation of manifoldvalued functions by embedding ...
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Polynomial Optimization for Bounding Lipschitz Constants of Deep Networks
The Lipschitz constant of a network plays an important role in many appl...
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Boxconstrained monotone L_∞approximations and Lipschitzcontinuous regularized functions
Let f:[0,1]→[0,1] be a nondecreasing function. The main goal of this wor...
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Approximate F_2Sketching of Valuation Functions
We study the problem of constructing a linear sketch of minimum dimensio...
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InfinityLaplacians on Scalar and VectorValued Functions and Optimal Lipschitz Extensions on Graphs
Extending functions from boundary values plays an important role in various applications. In this thesis we consider discrete and continuous formulations of the problem based on pLaplacians, in particular for p=∞ and tight Lipschitz extensions. The thesis gives an overview of the existing theory and provides some novel results on the approximation of tight Lipschitz extensions for vectorvalued functions.
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