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* N is the number of test positions.
* R<span style="vertical-align: sub;">i</span> is the result of the game corresponding to position i; '''-1'''* for black win, '''0''' for draw and '''+1''' for white win.
* q<span style="vertical-align: sub;">i</span> is corresponding to position i, the [[Score|value]] returned by the chess engine evaluation function. (Computing the gradient on the [[Quiescence Search|QS]] is a waste of time - it is much faster to run the QS saving the [[Principal variationVariation|PV]] and then compute the gradient using the evaluation function of the end-of-PV position - and not worry too much about the fact that tweaking the evaluation function could result in a different position being picked <ref>[http://www.talkchess.com/forum/viewtopic.php?t=64189&start=36 Re: Texel tuning method question] by [[Álvaro Begué]], [[CCC]], June 07, 2017</ref>).
* [https://en.wikipedia.org/wiki/Sigmoid_function Sigmoid] is implemented by [https://en.wikipedia.org/wiki/Hyperbolic_function hyperbolic tangent] to convert [[Centipawns|centipawn scores]] into an expected result in [-1,1].
<span style="font-size:120%;">Sigmoid(s) = tanh(0.0043s)</span>
