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Talk:Gradient descent: Difference between revisions
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→an easier to read simpler expression of the bi-variate function used for this task: added a new talk section.
(→Needs more information: Responded to Tigerofdarkness.) |
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::So I don't know where all this leaves us. There are doubtless several factors at work here and, as you say changing the initial guess leads to different results. Something else which leads to different results is whether one allows gradG to mutate 'x'. As the Go code stands it copies 'x' to 'y' and so doesn't mutate the former. However, it looks to me as though some translations may be indirectly mutating 'x' (depending on whether arrays are reference or value types in those languages) by simply assigning 'x' to 'y'. If I make this change in the Go code, the results are: x[0] = 0.10773473656605767, x[1] = -1.2231782829927973 and in the Wren code: x[0] = 0.10757894411096, x[1] = -1.2230849416131 so it does make quite a difference. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 10:11, 3 September 2020 (UTC)
:::Interesting.
:::I looked at the Go sample's gradG (which as you say, a lot of the others use). I'm not sufficiently au-fait with the mathematics to say how good an approximation the gradG function is but I see it involves dividing by h which starts out set to the tolerance and then gets halved on each iteration. It must be something like the actual gradient as the samples sort-of agree. I hadn't noticed the possibility of the mutation of x - that's a good point.
:::I substituted the actual gradient function (as used in the Fortran sample) and removed h and again, I get the same results as Fortran and Julia (to 6 places). That the original Algol 68 sample agreed with those is possibly a coincidence but I am now more confident that the result is in the region of the Julia/Fortran results.
:::I suspect that Julia is also using the actual gradient function as it is (I presume) using a built-in minimising function that uses the actual gradient function.
:::--[[User:Tigerofdarkness|Tigerofdarkness]] ([[User talk:Tigerofdarkness|talk]]) 12:08, 3 September 2020 (UTC)
::::Yes, to get consistent results, the answer does seem to be to use Fortran's gradient function.
::::I just substituted that in the Go code and obtained results of: x[0] = 0.10762682432948055, x[1] = -1.2232596548816101 which now agrees to 6 decimal places with the Fortran, Julia and your Algol 68 and Algol W solutions. So I'm going to update the Go example on the main page and suggest that those who've previously translated it update their translations accordingly. Thanks for your efforts here. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 13:14, 3 September 2020 (UTC)
:::::Thought I'd just add that Wren is now falling into line with updated results of: x[0] = 0.10762682432948, x[1] = -1.2232596548816. Perhaps my Math.exp function isn't so bad after all :) --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 13:59, 3 September 2020 (UTC)
== promoted from draft? ==
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:In general, I wait for a minimum of 3 months and 20 implementations before I promote one of my tasks out of draft. That way there is plenty of opportunity for discussion and tweaks if necessary. As far as I'm concerned, this doesn't even rise to the level of a draft yet, let alone a full task. Reverted back to draft (again). --[[User:Thundergnat|Thundergnat]] ([[User talk:Thundergnat|talk]]) 20:57, 1 July 2019 (UTC)
== an easier to read simpler expression of the bi-variate function used for this task ==
Use this algorithm to search for minimum values of the bi-variate function:
<big><big><big> ƒ(x, y) = (x-1)<sup>2</sup>''e''<sup>-(y<sup>2</sup>)</sup> + y(y+2)''e''<sup>-2(x<sup>2</sup>)</sup> </big></big></big>
─or eliding the negatives in the exponents─
<big><big><big> ƒ(x, y) = (x-1)<sup>2</sup> ÷ ''e''<sup>y<sup>2</sup></sup> + y(y+2) ÷ ''e''<sup>2(x<sup>2</sup>)</sup> </big></big></big>
A bigger font was used to clearly show an exponent used in the exponent of <big>''e''</big>. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 15:09, 5 September 2020 (UTC)
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