MathDB5 problems
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The conjecture that deep learning-based PDE solvers circumvent the curse of dimensionality
Deep learning-based PDE solvers are considered in the setting of high-dimensional partial differential equations (PDEs), where the curse of dimensionality refers to computational d…
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Polynomial-growth targets exhibit depth separation without the curse of dimensionality
Depth-separation conjecture for polynomial-growth targets. Such phenomena also occur for target functions which are at most polynomially growing in the input dimension of the consi…
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Existence of a deep learning method overcoming the curse of dimensionality for PDEs
Let PDEs be numerical approximation problems, and let the curse of dimensionality refer to the unfavorable growth of computational complexity with the dimension of the underlying p…
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The smooth-function replacement conjecture for neural network approximation
The paper considers approximation in the topology and discusses infinitely wide neural networks, including multi-layer networks and deep residual networks of bounded…
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The curse-of-dimensionality conjecture for independence tests
Curse-of-dimensionality conjecture. These tests suffer from the well-known curse of dimensionality as the dimension increases.