Deep neural network approximations for Monte Carlo algorithms — mentioned by jessaustin

Thu, 27 Aug 2020 14:53:34 GMT

[1] https://diffeqflux.sciml.ai/dev/layers/BasisLayers/ [2] https://diffeqflux.sciml.ai/dev/layers/TensorLayer/ [3] https://arxiv.org/abs/1908.10828

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Deep neural network approximations for Monte Carlo algorithms — mentioned by ChrisRackauckas

Thu, 27 Aug 2020 13:14:44 GMT

For reference, the DiffEqFlux library has a bunch of classical basis layers [1] and ways to tensor product them [2] for this reason. The real answer as to when to use a neural network is quite complicated [3], but in summary the results all point to the fact that for approximating an R^n -> R^m function, one only needs polynomially many parameters in order to do it well (as proven in a few cases like in that linked paper for "any case where Monte Carlo algorithms are not exponential in dimension"). Tensor products of classical basis functions have to cover every combination of terms…

Paper and discussion history. A mention is not an endorsement.

Deep neural network approximations for Monte Carlo algorithms · HackerPapers discussions

Deep neural network approximations for Monte Carlo algorithms — mentioned by jessaustin

Deep neural network approximations for Monte Carlo algorithms — mentioned by ChrisRackauckas