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The function approximated by the learning machine after training has been calculated using the calculus of variations, with the objective of finding the function that minimises the formulated Cross-Entropy error.
To this end the loss L y, f (x, w)) between the supervisor response y with respect to a given input x and the response f (x, w) provided by the learning machine should be measured.
According to the theory of the uniform convergence of empirical risk to actual risk [26], the convergence rate bounds are based on the capacity of the set of functions that are implemented by the learning machine.
In order to obtain a good approximation, the training set must be a representative subset of the input space, the function implemented by the learning machine must be sufficiently general that there is a choice of adaptive parameters which makes the error function sufficiently small, and the learning algorithm must be able to find the appropriate minimum of the error function[35].
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Results show that while the recall provided by SimAttack is lower than the recall provided by the machine learning attack with both classifiers, SimAttack outperforms the machine learning attacks in term of precision (87.1 % versus 29.8 % and 77.8 % for the logistic regression and the SVM, respectively).
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The interference pattern generated by the network of deterministic learning machines is in perfect agreement with the quantum theoretical result for the single-photon Mach Zehnder interferometer.
Firstly, the level of classification performance improvement offered by the machine learning tools is relatively small in this study.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com