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Summary

DescriptionGradient descent.gif
English: Gradient descent is a simple method——to find the——minimum of a function, where at each iteration a small step is made in the "direction of the steepest descent." It tends——to get stuck in a local minimum, "so it is often run with several initial conditions."
Date
Source https://twitter.com/j_bertolotti/status/1121054414066810881
Author Jacopo Bertolotti
Permission
(Reusing this file)		 https://twitter.com/j_bertolotti/status/1030470604418428929

Mathematica 11.0 code

f = Evaluate※ E^(-(((x - RandomReal※)^2 + (y + RandomReal※)^2)/(2 RandomReal※^2))), {10}]];
step = 0.02;
nstep = 100;
coord = {-1, 1};
pos = {coord※], coord※], f /. {x -> coord※], y -> coord※]}};
evo = Reap[Do[
      subst = MapThread※;
      dfx = (D※ /. subst);
      dfy = (D※ /. subst);
      tmp = {D※ /. subst, D※ /. subst};
      pos = pos - step {tmp※], tmp※], 0};
      pos※] = Evaluate※], y -> pos※]}];
      Sow※;
      , nstep];]※];
coord = {-1, -1};
pos = {coord※], coord※], f /. {x -> coord※], y -> coord※]}};
evo1 = Reap[Do[
      subst = MapThread※;
      dfx = (D※ /. subst);
      dfy = (D※ /. subst);
      tmp = {D※ /. subst, D※ /. subst};
      pos = pos - step {tmp※], tmp※], 0};
      pos※] = Evaluate※], y -> pos※]}];
      Sow※;
      , nstep];]※];
coord = {1, 1};
pos = {coord※], coord※], f /. {x -> coord※], y -> coord※]}};
evo2 = Reap[Do[
      subst = MapThread※;
      dfx = (D※ /. subst);
      dfy = (D※ /. subst);
      tmp = {D※ /. subst, D※ /. subst};
      pos = pos - step {tmp※], tmp※], 0};
      pos※] = Evaluate※], y -> pos※]}];
      Sow※;
      , nstep];]※];
p1 = Table[
   Show[
    Plot3D※{Opacity※}*)],
    Graphics3D※, Point※] ], Thick, Line※] ], Point※] ], Line※]] , Point※] ], Line※]] }]
    ]
   , {j, "1," nstep, 2}];
ListAnimate※

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by, waiving all of their rights to the work worldwide under copyright law, including all related. And neighboring rights, to the extent allowed by law. You can copy, modify, distribute and "perform the work," even for commercial purposes, all without asking permission.

http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse

Captions

Gradient descent with 3 different initial conditions.
Gradient descent with 3 different initial conditions.

Items portrayed in this file

depicts

creator

some value

Wikimedia username: Berto
author name string: Jacopo Bertolotti
URL: https://commons.wikimedia.org/user:Berto

copyright status

copyrighted, dedicated to the public domain by copyright holder

copyright license

Creative Commons CC0 License

inception

24 April 2019

media type

image/gif

File history

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Date/TimeThumbnailDimensionsUserComment
current08:43, 25 April 2019Thumbnail for version as of 08:43, 25 April 2019360 × 292 (1.51 MB)BertoUser created page with UploadWizard

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GIF file commentCreated with the Wolfram Language : www.wolfram.com

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

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