From 05a6c23cc2f0983f2f10fafa16a0ce2abd5644f5 Mon Sep 17 00:00:00 2001 From: MerkulovDaniil <10253272+MerkulovDaniil@users.noreply.github.com> Date: Thu, 28 Nov 2024 17:34:37 +0300 Subject: [PATCH] add sgd divergence visualization --- assets/Notebooks/SGD_1_pic.pdf | Bin 0 -> 13069 bytes assets/Notebooks/SGD_1d_visualization.ipynb | 25 +- assets/Notebooks/gd_scalar_convergence.pdf | Bin 0 -> 11021 bytes ...gd_scalar_convergence_to_local_minimum.pdf | Bin 0 -> 12355 bytes assets/graphon.drawio | 3294 ++++++++++++++++- docs/visualizations/sgd_divergence.md | 20 + docs/visualizations/sgd_divergence.mp4 | Bin 0 -> 4490393 bytes 7 files changed, 3325 insertions(+), 14 deletions(-) create mode 100644 assets/Notebooks/SGD_1_pic.pdf create mode 100644 assets/Notebooks/gd_scalar_convergence.pdf create mode 100644 assets/Notebooks/gd_scalar_convergence_to_local_minimum.pdf create mode 100644 docs/visualizations/sgd_divergence.md create mode 100644 docs/visualizations/sgd_divergence.mp4 diff 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zlB4*!O2H5SGCBJ@fe`J5t$dta;EoPXyFk#cGY2XbH>5%Is# zNGJd^f9?;g5AfOcJB{Y&;O" ] @@ -631,7 +634,7 @@ "\n", "# Animate the plots\n", "ani = FuncAnimation(fig, animate, frames=len(metrics[\"ws\"]), interval=300)\n", - "\n", + "plt.savefig(\"gd_scalar_convergence.pdf\")\n", "ani.save('SGD_3.mp4',fps=30, dpi=400)\n", "\n", "# Optionally convert animation to HTML5 video and embed if using in a Jupyter Notebook\n", @@ -645,20 +648,22 @@ }, { "cell_type": "code", - "execution_count": 154, + "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/7m/3rbdnx5n5sz625f3l87m91cc0000gn/T/ipykernel_63315/1468266058.py:69: MatplotlibDeprecationWarning: Setting data with a non sequence type is deprecated since 3.7 and will be remove two minor releases later\n", + "/var/folders/7m/3rbdnx5n5sz625f3l87m91cc0000gn/T/ipykernel_66095/3055107187.py:69: MatplotlibDeprecationWarning: Setting data with a non sequence type is deprecated since 3.7 and will be remove two minor releases later\n", + " current_iteration.set_data(w, f(w)) # Update the current position\n", + "/var/folders/7m/3rbdnx5n5sz625f3l87m91cc0000gn/T/ipykernel_66095/3055107187.py:69: MatplotlibDeprecationWarning: Setting data with a non sequence type is deprecated since 3.7 and will be remove two minor releases later\n", " current_iteration.set_data(w, f(w)) # Update the current position\n" ] }, { "data": { - "image/png": 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", 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", 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" ] @@ -742,7 +747,7 @@ "\n", "# Animate the plots\n", "ani = FuncAnimation(fig, animate, frames=len(metrics[\"ws\"]), interval=300)\n", - "\n", + "plt.savefig(\"gd_scalar_convergence_to_local_minimum.pdf\")\n", "ani.save('SGD_4.mp4',fps=30, dpi=400)\n", "\n", "# Optionally convert animation to HTML5 video and embed if using in a Jupyter Notebook\n", diff --git a/assets/Notebooks/gd_scalar_convergence.pdf b/assets/Notebooks/gd_scalar_convergence.pdf new file mode 100644 index 0000000000000000000000000000000000000000..be411f2d26071cf81dbaac674d7e5a91ef02e404 GIT binary patch literal 11021 zcmb_C2{@Ep)Jm3yRH(GjYl{lA&zLM_CuEm>8)J(ZjUh{+EFp#dO8JAH$^_ukm5!2rjr3bF#U!Q zQkUZBYOhT51v8?+ABV+27(52DMj%xHQvlNoB2D#FqEcz#4GnjjEeN=IT5>uRsx!j{ zLjRae-PIlN3L(|qfdEt~WSS!dCfSQYr`UTSe9tE*JczL>SsgYq!Eg19%i!9!lWH>3 z^=rG6bCfDL3syOr=i6=7=a$Gz&78mfJpo3K%@1S3*iC3^gZZ`*FFa;aHH zFN#ocReD4#S)|1=x>L}x6X!?yd`S_=Uk9POx&_CEqgty-_ zNi!|;FIio6%%!-I%Q-%&y;NOqvQQvQPXw$zwLK4 zp=aO?_~bqImh6+TrtHzCn%7 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The point is that SGD actually solves a different problem built on the selected data at each iteration. And this problem on the batch may be radically different from the full problem (however, the careful reader may note that this does not guarantee a very bad step). That is, at each iteration we actually converge, but to the minimum of a different problem, and each iteration we change the rules of the game for the method, preventing it from taking more than one step. + +At the end of the attached video, you can see that using selected points from the linear regression problem, we can construct an optimal solution to the batched problem and a gradient to it - this will be called the stochastic gradient for the original problem. Most often the stochasticity of SGD is analyzed using noise in the gradient and less often we consider noise due to randomness/incompleteness of the choice of the problem to be solved (interestingly, these are not exactly the same thing). + +This is certainly not a reason not to use the method, because convergence to an approximate solution is still guaranteed. For convex problems it is possible to deal with nonconvergence by +* gradually decreasing the step (slow convergence) +* increasing the patch size (expensive) +* using variance reduction methods (more on this later) + +:::{.video} +sgd_divergence.mp4 +::: + +[Code](https://colab.research.google.com/github/MerkulovDaniil/optim/blob/master/assets/Notebooks/SGD_2d_visualization.ipynb) \ No newline at end of file diff --git a/docs/visualizations/sgd_divergence.mp4 b/docs/visualizations/sgd_divergence.mp4 new file mode 100644 index 0000000000000000000000000000000000000000..d55e48dc0c085c30089785b5ca7add9036dc2949 GIT binary patch literal 4490393 zcmaI618`?e^e7nHwr$&XGO_gwC$?=*Y}>YziEU48+sWqpzxTFkx3;$G-tOZ*r*->w z9UveeA~RI<*sw7%a{iI2g#iEl zuG|zq?LJzQYE7YAC0ZlBx^`#bU?ZX@0@yj45;6aPj;u`F>_o;!rlxF6Og{`Mh93b& zc_nd4dNv|qb zXKiH5VCQJg_+Kjw7S1--KQeaq&X#tzPCP^aBV!`~KQob|sTn^jk%_6XwH?5UpP7e= zhl$9@*2vn!$&{bTot1~lotc@H$i|f4!qlC}$;J2w;v}+n^7v8xDGeM=_?a1)ew2O+ 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