Titlebook: Explorations in the Mathematics of Data Science; The Inaugural Volume Simon Foucart,Stephan Wojtowytsch Book 2024 The Editor(s) (if applica

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https://doi.org/10.1007/978-3-658-11649-1onally projected linear maps..We further show that fully connected and residual networks of large depth with polynomial activation functions can approximate any polynomial under certain width requirements. All proofs are entirely elementary.

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https://doi.org/10.1007/978-3-642-72043-7lows for reduced storage and asymptotic speed ups for our solver via sparse matrix computations. We conclude the article with the results of computational experiments performed with genomic datasets. These experiments illustrate the significant speed ups obtained by GETS over .’s implementation of the Lawson Hanson algorithm.

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Richard Colmorn,Michael Hülsmann noise, and (3) the heavy-ball ODE. In the case of stochastic gradient descent, the summability of . is used to prove that . almost surely—an improvement on the convergence almost surely up to a subsequence which follows from the . decay estimate.

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Learning Collective Behaviors from Observation,observations in agent systems. The foundational aspect of our learning methodologies resides in the formulation of tailored loss functions using the variational inverse problem approach, inherently equipping our methods with dimension reduction capabilities.

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