On the gradient conjecture at infinity: Finite spherical length for gradient trajectories of definable potentials
2 versions
BK
Benno Kuckuck
cs.NAmath.NAcs.LGmath.PRmath.GRstat.MLcs.AIcs.CL
On Valency
published · living versionsPreprints & journals
15 papers in the corpus · 2011–2026Finiteness Properties of Fibre Products over Virtually Nilpotent Quotients
0 citations
On the logical skills of large language models: evaluations using arbitrarily complex first-order logic problems
0 citations
An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning
1 citation
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations
1 citation
Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory
7 citations
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the -sense
1 citation
Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions
18 citations
Deep neural network approximation theory for high-dimensional functions
4 citations
Strong -error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations
2 citations
An overview on deep learning-based approximation methods for partial differential equations
113 citations
Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven SDEs with smooth drift coefficient functions with at most polynomially growing derivatives
1 citation
Full error analysis for the training of deep neural networks
48 citations
Strong error analysis for stochastic gradient descent optimization algorithms
52 citations
The Magnus property for direct products
3 citations
Subdirect products of groups and the n-(n+1)-(n+2) Conjecture
22 citations
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