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Morten Hjorth-Jensen
2024-11-03 14:50:52 +01:00
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@@ -353,6 +353,11 @@ const thebe_selector_output = ".output, .cell_output"
Week 44, Convolutional Neural Networks (CNN)
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="week45.html">
Week 45, Convolutional Neural Networks (CCNs) and Recurrent Neural Networks (RNNs)
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
@@ -824,15 +829,15 @@ regression.</p>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
[[3.72796854]
[3.26269704]]
Eigenvalues of Hessian Matrix:[0.26876494 4.16606994]
[[3.7056279 ]
[3.11632514]]
Eigenvalues of Hessian Matrix:[0.27378241 4.9133261 ]
theta from own gd
[[3.72796854]
[3.26269704]]
[[3.7056279 ]
[3.11632514]]
theta from own sdg
[[3.70521262]
[3.29966563]]
[[3.62227539]
[3.09214577]]
</pre></div>
</div>
<img alt="_images/exercisesweek41_5_1.png" src="_images/exercisesweek41_5_1.png" />
@@ -954,15 +959,17 @@ first example shows results with ordinary leats squares.</p>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
[[3.89549614]
[2.9788957 ]]
Eigenvalues of Hessian Matrix:[0.34210288 4.43495138]
theta from own gd
[[3.89549614]
[2.9788957 ]]
[[4.39586211]
[2.54142449]]
Eigenvalues of Hessian Matrix:[0.29253829 4.61759155]
</pre></div>
</div>
<img alt="_images/exercisesweek41_16_1.png" src="_images/exercisesweek41_16_1.png" />
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own gd
[[4.39586211]
[2.54142449]]
</pre></div>
</div>
<img alt="_images/exercisesweek41_16_2.png" src="_images/exercisesweek41_16_2.png" />
</div>
</div>
</div>
@@ -1030,73 +1037,73 @@ theta from own gd
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
[[4.]
[3.]]
Eigenvalues of Hessian Matrix:[0.35622964 3.83344349]
0 [-10.84597523] [-10.53597191]
1 [-0.41603353] [0.39392645]
2 [-0.37737287] [0.35732012]
3 [-0.34230481] [0.32411551]
4 [-0.31049552] [0.29399649]
5 [-0.28164216] [0.26667634]
6 [-0.25547006] [0.24189496]
7 [-0.23173004] [0.21941643]
8 [-0.21019611] [0.19902677]
9 [-0.19066326] [0.18053184]
10 [-0.17294553] [0.1637556]
11 [-0.15687426] [0.14853831]
12 [-0.14229643] [0.13473512]
13 [-0.12907328] [0.12221462]
14 [-0.11707891] [0.11085761]
15 [-0.10619914] [0.10055596]
16 [-0.0963304] [0.09121162]
17 [-0.08737872] [0.08273561]
18 [-0.0792589] [0.07504726]
19 [-0.07189362] [0.06807336]
20 [-0.06521278] [0.06174752]
21 [-0.05915276] [0.05600952]
22 [-0.05365588] [0.05080473]
23 [-0.04866982] [0.04608361]
24 [-0.04414708] [0.04180121]
25 [-0.04004464] [0.03791676]
26 [-0.03632342] [0.03439327]
27 [-0.032948] [0.03119722]
28 [-0.02988625] [0.02829816]
29 [-0.02710901] [0.0256685]
Eigenvalues of Hessian Matrix:[0.28360073 4.6466172 ]
0 [-12.76941488] [-15.71728253]
1 [-0.06385864] [0.05142606]
2 [-0.0599611] [0.04828733]
3 [-0.05630145] [0.04534017]
4 [-0.05286516] [0.04257289]
5 [-0.0496386] [0.0399745]
6 [-0.04660896] [0.03753471]
7 [-0.04376424] [0.03524382]
8 [-0.04109314] [0.03309276]
9 [-0.03858507] [0.03107298]
10 [-0.03623008] [0.02917648]
11 [-0.03401882] [0.02739573]
12 [-0.03194252] [0.02572366]
13 [-0.02999295] [0.02415365]
14 [-0.02816236] [0.02267946]
15 [-0.02644351] [0.02129525]
16 [-0.02482956] [0.01999552]
17 [-0.02331412] [0.01877511]
18 [-0.02189117] [0.0176292]
19 [-0.02055507] [0.01655322]
20 [-0.01930051] [0.01554291]
21 [-0.01812253] [0.01459427]
22 [-0.01701644] [0.01370353]
23 [-0.01597786] [0.01286715]
24 [-0.01500267] [0.01208182]
25 [-0.014087] [0.01134442]
26 [-0.01322722] [0.01065202]
27 [-0.01241991] [0.01000189]
28 [-0.01166188] [0.00939144]
29 [-0.01095011] [0.00881824]
theta from own gd
[[3.93097189]
[3.06536011]]
0 [-0.02458986] [0.02328321]
1 [-0.0223048] [0.02111958]
2 [-0.01954657] [0.01850791]
3 [-0.0169027] [0.01600453]
4 [-0.01453883] [0.01376627]
5 [-0.01247862] [0.01181553]
6 [-0.01070096] [0.01013233]
7 [-0.00917325] [0.00868581]
8 [-0.0078625] [0.00744471]
9 [-0.00673864] [0.00638056]
10 [-0.00577528] [0.00546839]
11 [-0.00494959] [0.00468658]
12 [-0.00424194] [0.00401653]
13 [-0.00363545] [0.00344227]
14 [-0.00311567] [0.00295011]
15 [-0.00267021] [0.00252832]
16 [-0.00228844] [0.00216684]
17 [-0.00196125] [0.00185703]
18 [-0.00168084] [0.00159152]
19 [-0.00144052] [0.00136398]
20 [-0.00123456] [0.00116896]
21 [-0.00105805] [0.00100183]
22 [-0.00090678] [0.00085859]
23 [-0.00077713] [0.00073584]
24 [-0.00066602] [0.00063063]
25 [-0.0005708] [0.00054047]
26 [-0.00048919] [0.00046319]
27 [-0.00041925] [0.00039697]
28 [-0.0003593] [0.00034021]
29 [-0.00030793] [0.00029157]
[[3.96374557]
[3.02919609]]
0 [-0.01028178] [0.00828003]
1 [-0.00965425] [0.00777467]
2 [-0.00887675] [0.00714854]
3 [-0.00810172] [0.0065244]
4 [-0.00737473] [0.00593895]
5 [-0.00670653] [0.00540084]
6 [-0.00609674] [0.00490977]
7 [-0.0055417] [0.00446279]
8 [-0.00503695] [0.00405631]
9 [-0.00457811] [0.0036868]
10 [-0.00416103] [0.00335092]
11 [-0.00378195] [0.00304564]
12 [-0.00343739] [0.00276817]
13 [-0.00312423] [0.00251598]
14 [-0.0028396] [0.00228676]
15 [-0.0025809] [0.00207843]
16 [-0.00234577] [0.00188907]
17 [-0.00213205] [0.00171697]
18 [-0.00193781] [0.00156054]
19 [-0.00176127] [0.00141837]
20 [-0.00160081] [0.00128915]
21 [-0.00145497] [0.0011717]
22 [-0.00132241] [0.00106495]
23 [-0.00120193] [0.00096793]
24 [-0.00109243] [0.00087975]
25 [-0.00099291] [0.0007996]
26 [-0.00090245] [0.00072675]
27 [-0.00082023] [0.00066054]
28 [-0.0007455] [0.00060036]
29 [-0.00067758] [0.00054567]
theta from own gd wth momentum
[[3.99925917]
[3.00070146]]
[[3.99782845]
[3.00174877]]
</pre></div>
</div>
</div>
@@ -1149,17 +1156,17 @@ theta from own gd wth momentum
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
[[3.86751196]
[3.13877544]]
Eigenvalues of Hessian Matrix:[0.29322629 4.30627615]
0 [-14.05912765] [-16.736807]
1 [-2.16077156e-14] [-1.19631285e-14]
2 [-1.70002901e-16] [-1.23687362e-16]
3 [-1.70002901e-16] [-1.23687362e-16]
4 [-1.70002901e-16] [-1.23687362e-16]
[[3.60911869]
[3.33987045]]
Eigenvalues of Hessian Matrix:[0.31385073 4.08833652]
0 [-17.89749468] [-19.42504764]
1 [-6.56419363e-15] [-6.5758826e-15]
2 [-4.99600361e-16] [-5.64393388e-16]
3 [-4.99600361e-16] [-5.64393388e-16]
4 [-4.99600361e-16] [-5.64393388e-16]
beta from own Newton code
[[3.86751196]
[3.13877544]]
[[3.60911869]
[3.33987045]]
</pre></div>
</div>
</div>
@@ -1248,22 +1255,20 @@ beta from own Newton code
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
[[3.90340018]
[3.20732292]]
Eigenvalues of Hessian Matrix:[0.30252911 4.09446058]
[[4.41451936]
[2.55289042]]
Eigenvalues of Hessian Matrix:[0.33812981 4.19713213]
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own gd
[[3.90340018]
[3.20732292]]
[[4.41451936]
[2.55289042]]
</pre></div>
</div>
<img alt="_images/exercisesweek41_22_2.png" src="_images/exercisesweek41_22_2.png" />
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[3.86364839]
[3.23799188]]
[[4.38642255]
[2.56985133]]
</pre></div>
</div>
</div>
@@ -1345,15 +1350,17 @@ Eigenvalues of Hessian Matrix:[0.30252911 4.09446058]
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
[[4.38463079]
[2.57169626]]
Eigenvalues of Hessian Matrix:[0.27355018 4.06502525]
[[3.89425071]
[3.03737777]]
Eigenvalues of Hessian Matrix:[0.32691458 3.94394646]
theta from own gd
[[4.38343773]
[2.57278714]]
theta from own sdg with momentum
[[4.35254442]
[2.58244397]]
[[3.89408559]
[3.03753095]]
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg with momentum
[[3.92801972]
[3.02259232]]
</pre></div>
</div>
</div>
@@ -1428,9 +1435,9 @@ theta from own sdg with momentum
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own AdaGrad
[[2.0000375 ]
[2.99981967]
[4.00017395]]
[[1.99987339]
[3.00070766]
[3.99931264]]
</pre></div>
</div>
</div>
@@ -1512,9 +1519,9 @@ theta from own sdg with momentum
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own RMSprop
[[1.99998686]
[2.9995237 ]
[4.00046845]]
[[1.99430797]
[3.0204309 ]
[3.97790579]]
</pre></div>
</div>
</div>
@@ -1600,9 +1607,9 @@ theta from own sdg with momentum
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own ADAM
[[1.99990776]
[3.0005044 ]
[3.99956442]]
[[1.99988575]
[3.00066222]
[3.99946201]]
</pre></div>
</div>
</div>
@@ -1675,7 +1682,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
return asarray(x, dtype=self.dtype)
</pre></div>
</div>
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x11edfa8b0&gt;]
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x12288f460&gt;]
</pre></div>
</div>
<img alt="_images/exercisesweek41_39_2.png" src="_images/exercisesweek41_39_2.png" />
@@ -1710,7 +1717,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.collections.PathCollection at 0x11ef1aac0&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.collections.PathCollection at 0x110657310&gt;
</pre></div>
</div>
<img alt="_images/exercisesweek41_41_1.png" src="_images/exercisesweek41_41_1.png" />