Added visualization of gradients to appendix
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\pgfplotsset{
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/pgfplots/colormap/mako/.style={
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colormap={mako}{
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rgb=(0.18195582, 0.11955283, 0.23136943)
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rgb=(0.25307401, 0.23772973, 0.48316271)
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rgb=(0.21607792, 0.39736958, 0.61948028)
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rgb=(0.20344718, 0.56074869, 0.65649508)
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rgb=(0.25187832, 0.71827158, 0.67872193)
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rgb=(0.54578602, 0.8544913, 0.69848331)
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}
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},
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/pgfplots/colormap/rocket/.style={
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colormap={rocket}{
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rgb=(0.20973515, 0.09747934, 0.24238489)
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rgb=(0.43860848, 0.12177004, 0.34119475)
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rgb=(0.67824099, 0.09192342, 0.3504148)
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rgb=(0.8833417, 0.19830556, 0.26014181)
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rgb=(0.95381595, 0.46373781, 0.31769923)
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rgb=(0.96516917, 0.70776351, 0.5606593)
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}
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},
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/pgfplots/colormap/cividis/.style={
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colormap={cividis}{
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rgb=(0.130669, 0.231458, 0.43284)
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rgb=(0.298421, 0.332247, 0.423973)
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rgb=(0.42512, 0.431334, 0.447692)
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rgb=(0.555393, 0.537807, 0.471147)
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rgb=(0.695985, 0.648334, 0.440072)
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rgb=(0.849223, 0.771947, 0.359729)
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}
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},
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colormap/cividis,
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colormap/mako,
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colormap/rocket,
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}
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\newbibmacro{string+doiurlisbn}[1]{%
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\newbibmacro{string+doiurlisbn}[1]{%
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\iffieldundef{doi}{%
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\iffieldundef{doi}{%
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\iffieldundef{url}{%
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\iffieldundef{url}{%
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901
latex/presentations/midterm/res/2d_grad_L.csv
Normal file
901
latex/presentations/midterm/res/2d_grad_L.csv
Normal file
@ -0,0 +1,901 @@
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x_0,x_1,grad_0,grad_1,grad_norm
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901
latex/presentations/midterm/res/2d_grad_rep.csv
Normal file
901
latex/presentations/midterm/res/2d_grad_rep.csv
Normal file
@ -0,0 +1,901 @@
|
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|
x_0,x_1,grad_0,grad_1,grad_norm
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0.9913793103448278,1.1637931034482758,0.28981431177990363,1.9547298474722208,1.9760974449432473
|
||||||
|
0.9913793103448278,1.25,0.5299840604370849,3.28682372175981,3.3292781923774992
|
||||||
|
1.077586206896552,-1.25,6.562250143507323,-7.870652497027351,10.247453228725893
|
||||||
|
1.077586206896552,-1.1637931034482758,5.941375978924929,-6.507807054409776,8.812008918536783
|
||||||
|
1.077586206896552,-1.0775862068965516,5.3525346980196025,-5.352534698019601,7.5696271630119
|
||||||
|
1.077586206896552,-0.9913793103448276,4.795726300791344,-4.38945964369183,6.501257318065563
|
||||||
|
1.077586206896552,-0.9051724137931034,4.270950787240153,-3.6032061072614723,5.587854228452426
|
||||||
|
1.077586206896552,-0.8189655172413792,3.778208157366029,-2.978398304563534,4.810999204013044
|
||||||
|
1.077586206896552,-0.7327586206896551,3.317498411168973,-2.4996604514330247,4.153805253086261
|
||||||
|
1.077586206896552,-0.646551724137931,2.8888215486489845,-2.1516167637049506,3.6020472842253035
|
||||||
|
1.077586206896552,-0.5603448275862069,2.492177569806063,-1.918891457214319,3.145328832413957
|
||||||
|
1.077586206896552,-0.47413793103448265,2.1275664746402096,-1.7861087477961386,2.7778991275722844
|
||||||
|
1.077586206896552,-0.38793103448275856,1.7949882631514238,-1.7378928512854164,2.4984504052312744
|
||||||
|
1.077586206896552,-0.3017241379310345,1.4944429353397055,-1.7588679835171606,2.308024321888415
|
||||||
|
1.077586206896552,-0.21551724137931028,1.2259304912050544,-1.8336583603263774,2.205721775669154
|
||||||
|
1.077586206896552,-0.12931034482758608,0.989450930747471,-1.9468881975480765,2.1838925793429116
|
||||||
|
1.077586206896552,-0.0431034482758621,0.7850042539669556,-2.0831817110172626,2.2261800735481905
|
||||||
|
1.077586206896552,0.0431034482758621,0.6125904608635072,-2.227163116568946,2.309875022711416
|
||||||
|
1.077586206896552,0.1293103448275863,0.4722095514371264,-2.363456630038132,2.410167857751749
|
||||||
|
1.077586206896552,0.2155172413793105,0.36386152568781316,-2.4766864672598308,2.503272072105596
|
||||||
|
1.077586206896552,0.3017241379310347,0.28754638361556756,-2.5514768440690476,2.5676286741954994
|
||||||
|
1.077586206896552,0.3879310344827587,0.24326412522038954,-2.5724519763007914,2.583928521649368
|
||||||
|
1.077586206896552,0.4741379310344829,0.23101475050227904,-2.524236079790069,2.5347851193865654
|
||||||
|
1.077586206896552,0.5603448275862071,0.250798259461236,-2.3914533703718885,2.4045683582738606
|
||||||
|
1.077586206896552,0.646551724137931,0.30261465209726046,-2.1587280638812576,2.1798354253136796
|
||||||
|
1.077586206896552,0.7327586206896552,0.38646392841035254,-1.810684376153183,1.8514676011228508
|
||||||
|
1.077586206896552,0.8189655172413794,0.5023460884005123,-1.3319465230226726,1.4235284095245455
|
||||||
|
1.077586206896552,0.9051724137931036,0.6502611320677394,-0.7071387203247346,0.9606688865891937
|
||||||
|
1.077586206896552,0.9913793103448278,0.8302090594120348,0.07911481610562503,0.8339701652081101
|
||||||
|
1.077586206896552,1.077586206896552,1.042189870433397,1.042189870433397,1.4738790493347687
|
||||||
|
1.077586206896552,1.1637931034482758,1.2862035651318258,2.1974622268235677,2.546204989641292
|
||||||
|
1.077586206896552,1.25,1.562250143507323,3.5603076694411424,3.8879835663194453
|
||||||
|
1.1637931034482758,-1.25,7.786713528639959,-8.526122175980975,11.546760019020882
|
||||||
|
1.1637931034482758,-1.1637931034482758,7.129962534339249,-7.129962534339249,10.08328971527461
|
||||||
|
1.1637931034482758,-1.0775862068965516,6.507807054409772,-5.941375978924924,8.812008918536776
|
||||||
|
1.1637931034482758,-0.9913793103448276,5.920247088851529,-4.944986725573003,7.713768165374703
|
||||||
|
1.1637931034482758,-0.9051724137931034,5.36728263766452,-4.125418990118496,6.769549819345841
|
||||||
|
1.1637931034482758,-0.8189655172413792,4.848913700848741,-3.4672969883964067,5.961049612611979
|
||||||
|
1.1637931034482758,-0.7327586206896551,4.365140278404197,-2.9552449362417477,5.271425071394751
|
||||||
|
1.1637931034482758,-0.646551724137931,3.9159623703308855,-2.5738870494895227,4.686113083289537
|
||||||
|
1.1637931034482758,-0.5603448275862069,3.5013799766288063,-2.3078475439747423,4.193545281377965
|
||||||
|
1.1637931034482758,-0.47413793103448265,3.1213930972979607,-2.1417506355324116,3.7855238280405588
|
||||||
|
1.1637931034482758,-0.38793103448275856,2.776001732338348,-2.0602205399975393,3.4569776237883376
|
||||||
|
1.1637931034482758,-0.3017241379310345,2.4652058817499682,-2.0478814732051336,3.204849226985798
|
||||||
|
1.1637931034482758,-0.21551724137931028,2.1890055455328206,-2.0893576509901997,3.026080083561029
|
||||||
|
1.1637931034482758,-0.12931034482758608,1.9474007236869066,-2.169273289187749,2.915152857364382
|
||||||
|
1.1637931034482758,-0.0431034482758621,1.7403914162122258,-2.2722526036327855,2.8621834630821916
|
||||||
|
1.1637931034482758,0.0431034482758621,1.5679776231087774,-2.382919810160318,2.852518299367129
|
||||||
|
1.1637931034482758,0.1293103448275863,1.430159344376562,-2.4858991246053552,2.8679348332940324
|
||||||
|
1.1637931034482758,0.2155172413793105,1.3269365800155795,-2.565814762802903,2.888627024106913
|
||||||
|
1.1637931034482758,0.3017241379310347,1.2583093300258301,-2.60729094058797,2.8950489493102105
|
||||||
|
1.1637931034482758,0.3879310344827587,1.2242775944073137,-2.594951873795564,2.8692561502038934
|
||||||
|
1.1637931034482758,0.4741379310344829,1.22484137316003,-2.513421778260691,2.7959838026783492
|
||||||
|
1.1637931034482758,0.5603448275862071,1.2600006662839796,-2.3473248698183604,2.664120065519543
|
||||||
|
1.1637931034482758,0.646551724137931,1.3297554737791615,-2.0812853643035796,2.4698174806470874
|
||||||
|
1.1637931034482758,0.7327586206896552,1.4341057956455767,-1.6999274775513549,2.224053250720033
|
||||||
|
1.1637931034482758,0.8189655172413794,1.5730516318832253,-1.187875425396694,1.9711771769254673
|
||||||
|
1.1637931034482758,0.9051724137931036,1.7465929824921063,-0.5297534236746059,1.825164577890344
|
||||||
|
1.1637931034482758,0.9913793103448278,1.9547298474722208,0.28981431177990363,1.9760974449432473
|
||||||
|
1.1637931034482758,1.077586206896552,2.1974622268235677,1.2862035651318258,2.546204989641292
|
||||||
|
1.1637931034482758,1.1637931034482758,2.474790120546146,2.474790120546146,3.4998817525033066
|
||||||
|
1.1637931034482758,1.25,2.786713528639959,3.8709497621878715,4.769698559876432
|
||||||
|
1.25,-1.25,9.21875,-9.21875,13.03728127812697
|
||||||
|
1.25,-1.1637931034482758,8.526122175980975,-7.786713528639959,11.546760019020882
|
||||||
|
1.25,-1.0775862068965516,7.870652497027348,-6.562250143507318,10.247453228725888
|
||||||
|
1.25,-0.9913793103448276,7.252340963139121,-5.529984060437083,9.1201520357017
|
||||||
|
1.25,-0.9051724137931034,6.671187574316289,-4.674539495264257,8.1459230995939
|
||||||
|
1.25,-0.8189655172413792,6.127192330558858,-3.980540663823853,7.3066538054033
|
||||||
|
1.25,-0.7327586206896551,5.620355231866825,-3.4326117819508797,6.585682696422656
|
||||||
|
1.25,-0.646551724137931,5.150676278240191,-3.0153770654803393,5.96841394092694
|
||||||
|
1.25,-0.5603448275862069,4.718155469678953,-2.7134607302472418,5.442780555070663
|
||||||
|
1.25,-0.47413793103448265,4.322792806183115,-2.5114869920865956,4.999410420900515
|
||||||
|
1.25,-0.38793103448275856,3.964588287752675,-2.3940800668334075,4.631369091078224
|
||||||
|
1.25,-0.3017241379310345,3.643541914387634,-2.345864170322687,4.333413941398081
|
||||||
|
1.25,-0.21551724137931028,3.35965368608799,-2.351463518389438,4.100811330549243
|
||||||
|
1.25,-0.12931034482758608,3.112923602853745,-2.395502326868671,3.927941541728588
|
||||||
|
1.25,-0.0431034482758621,2.903351664684899,-2.4626048115953916,3.807081998975245
|
||||||
|
1.25,0.0431034482758621,2.7309378715814505,-2.537395188404609,3.7277870111604665
|
||||||
|
1.25,0.1293103448275863,2.5956822235434007,-2.6044976731313296,3.6770877518718152
|
||||||
|
1.25,0.2155172413793105,2.497584720570749,-2.648536481610562,3.640422356107945
|
||||||
|
1.25,0.3017241379310347,2.4366453626634956,-2.6541358296773137,3.6030095234076747
|
||||||
|
1.25,0.3879310344827587,2.4128641498216408,-2.6059199331665917,3.5514408489470135
|
||||||
|
1.25,0.4741379310344829,2.426241082045184,-2.4885130079134035,3.4755348910287176
|
||||||
|
1.25,0.5603448275862071,2.4767761593341264,-2.286539269752757,3.370857750716778
|
||||||
|
1.25,0.646551724137931,2.564469381688466,-1.9846229345196607,3.242719753823795
|
||||||
|
1.25,0.7327586206896552,2.6893207491082047,-1.56738821804912,3.1127402586247235
|
||||||
|
1.25,0.8189655172413794,2.851330261593341,-1.0194593361761444,3.028098677189146
|
||||||
|
1.25,0.9051724137931036,3.0504979191438766,-0.3254605047357399,3.067810635427807
|
||||||
|
1.25,0.9913793103448278,3.28682372175981,0.5299840604370849,3.3292781923774992
|
||||||
|
1.25,1.077586206896552,3.5603076694411424,1.562250143507323,3.8879835663194453
|
||||||
|
1.25,1.1637931034482758,3.8709497621878715,2.786713528639959,4.769698559876432
|
||||||
|
1.25,1.25,4.21875,4.21875,5.966213466261495
|
||||||
|
@ -40,3 +40,82 @@
|
|||||||
}
|
}
|
||||||
|
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
|
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
\begin{frame}[t]
|
||||||
|
\frametitle{Proximal Decoding: Visualization of Gradients}
|
||||||
|
|
||||||
|
\begin{figure}[H]
|
||||||
|
\centering
|
||||||
|
|
||||||
|
\begin{subfigure}[c]{0.5\textwidth}
|
||||||
|
|
||||||
|
\centering
|
||||||
|
|
||||||
|
\begin{tikzpicture}[scale=0.8]
|
||||||
|
\begin{axis}[xmin = -1.25, xmax=1.25,
|
||||||
|
ymin = -1.25, ymax=1.25,
|
||||||
|
xlabel={$x_1$}, ylabel={$x_2$},
|
||||||
|
grid=major, grid style={dotted},
|
||||||
|
view={0}{90}]
|
||||||
|
\addplot3[point meta=\thisrow{grad_norm},
|
||||||
|
point meta min=1,
|
||||||
|
point meta max=3,
|
||||||
|
quiver={u=\thisrow{grad_0},
|
||||||
|
v=\thisrow{grad_1},
|
||||||
|
scale arrows=.05,
|
||||||
|
every arrow/.append style={%
|
||||||
|
line width=.3+\pgfplotspointmetatransformed/1000,
|
||||||
|
-{Latex[length=0pt 5,width=0pt 3]}
|
||||||
|
},
|
||||||
|
},
|
||||||
|
quiver/colored = {mapped color},
|
||||||
|
colormap/rocket,
|
||||||
|
-stealth,
|
||||||
|
]
|
||||||
|
table[col sep=comma] {res/2d_grad_L.csv};
|
||||||
|
\end{axis}
|
||||||
|
\end{tikzpicture}
|
||||||
|
|
||||||
|
\caption{$\nabla L \left(\boldsymbol{y} \mid \boldsymbol{x} \right) $ for a repetition code with $n=2$
|
||||||
|
\footnotemark}
|
||||||
|
\end{subfigure}%
|
||||||
|
\begin{subfigure}[c]{0.5\textwidth}
|
||||||
|
\centering
|
||||||
|
|
||||||
|
\begin{tikzpicture}[scale=0.8]
|
||||||
|
\begin{axis}[xmin = -1.25, xmax=1.25,
|
||||||
|
ymin = -1.25, ymax=1.25,
|
||||||
|
xlabel={$x_1$}, ylabel={$x_2$},
|
||||||
|
grid=major, grid style={dotted},
|
||||||
|
view={0}{90}]
|
||||||
|
\addplot3[point meta=\thisrow{grad_norm},
|
||||||
|
point meta min=1,
|
||||||
|
point meta max=4,
|
||||||
|
quiver={u=\thisrow{grad_0},
|
||||||
|
v=\thisrow{grad_1},
|
||||||
|
scale arrows=.03,
|
||||||
|
every arrow/.append style={%
|
||||||
|
line width=.3+\pgfplotspointmetatransformed/1000,
|
||||||
|
-{Latex[length=0pt 5,width=0pt 3]}
|
||||||
|
},
|
||||||
|
},
|
||||||
|
quiver/colored = {mapped color},
|
||||||
|
colormap/rocket,
|
||||||
|
-stealth,
|
||||||
|
]
|
||||||
|
table[col sep=comma] {res/2d_grad_rep.csv};
|
||||||
|
\end{axis}
|
||||||
|
\end{tikzpicture}
|
||||||
|
|
||||||
|
\caption{$\nabla h \left( \boldsymbol{x} \right) $ for a repetition code with $n=2$}
|
||||||
|
\end{subfigure}%
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
\footnotetext{In an AWGN Channel $L\left( \boldsymbol{y} \mid \boldsymbol{x} \right)
|
||||||
|
\propto \frac{1}{2} \left| \boldsymbol{x} - \boldsymbol{y} \right|^2
|
||||||
|
\Rightarrow \nabla L\left( \boldsymbol{y} \mid \boldsymbol{x}\right)
|
||||||
|
\propto \left( \boldsymbol{x} - \boldsymbol{y} \right) $}
|
||||||
|
|
||||||
|
\end{frame}
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user