update html

Author: rsokl

docs/.doctrees/Module3_IntroducingNumpy/AutoDiff.doctree

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@@ -13,7 +13,7 @@
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     "<div class=\"alert alert-info\">\n",
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   },
   {
    "cell_type": "markdown",
-   "id": "b36fff16",
+   "id": "18124dc8",
    "metadata": {},
    "source": [
     "# Automatic Differentiation"
    ]
   },
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@@ -73,15 +73,15 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f49ecb98",
+   "id": "391e0110",
    "metadata": {},
    "source": [
     "## Introduction to MyGrad"
    ]
   },
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    "cell_type": "markdown",
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    "metadata": {},
    "source": [
     "\n",
@@ -146,23 +146,23 @@
   },
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-   "id": "9159288c",
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    "source": [
     "It is important to reiterate that MyGrad *never gives us the actual function* $\\frac{\\mathrm{d}f}{\\mathrm{d}x}$; it only computes the derivative evaluated at a specific input $x=10$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "8e505337",
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    "source": [
     "### MyGrad Adds \"Drop-In\" AutoDiff to NumPy\n"
    ]
   },
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     "\n",
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@@ -218,15 +218,15 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fdaebad6",
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    "metadata": {},
    "source": [
     "## Vectorized Auto-Differentiation"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "ac75b5a9",
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    "source": [
     "Like NumPy's array, MyGrad's tensor supports [vectorized operations](https://www.pythonlikeyoumeanit.com/Module3_IntroducingNumpy/VectorizedOperations.html), allowing us to evaluate the derivative of a function at multiple points simultaneously.\n",
@@ -273,15 +273,15 @@
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     "<div class=\"alert alert-info\">"
    ]
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-   "id": "769f3243",
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    "source": [
     "## Visualizing the Derivative\n",
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   },
   {
    "cell_type": "markdown",
-   "id": "32f3b8ef",
+   "id": "d9b0203f",
    "metadata": {},
    "source": [
     "## Seek and Derive"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e0fa9dee",
+   "id": "5811b985",
    "metadata": {},
    "source": [
     "Computers equipped with automatic differentiation libraries can make short work of derivatives that are well-beyond the reach of mere mortals.\n",
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     "<div class=\"alert alert-info\">\n",
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     "\n",
@@ -447,7 +447,7 @@
     "Let's take a simple example.\n",
     "We'll choose the function $f(x) = (x-8)^2$ and the starting point $x=-1.5$.\n",
     "As we search for $x_\\mathrm{min}$ we don't want to make our updates to $x_o$\n",
-    "too big, so we will scale our updates by a factor of $3/10$ (which is somewhat haphazardly here).\n",
+    "too big, so we will scale our updates by a factor of $3/10$ (the value of which is chosen somewhat haphazardly here).\n",
     "\n",
     "```python\n",
     "# Performing gradient descent on f(x) = (x - 8) ** 2\n",
@@ -491,15 +491,15 @@
   },
   {
    "cell_type": "markdown",
-   "id": "44c65efd",
+   "id": "3188cd27",
    "metadata": {},
    "source": [
     "## Reading Comprehension Exercise Solutions"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e2167a40",
+   "id": "92d9cc26",
    "metadata": {},
    "source": [
     "**Auto-differentiation: Solution**"
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docs/.doctrees/environment.pickle

@@ -594,7 +594,7 @@ <h2>Applying Automatic Differentiation: Solving Optimization Problems<a class="h
 <p>How does automatic differentiation help us to solve such a problem? The derivative of a function evaluated at some <span class="math notranslate nohighlight">\(x_o\)</span> tells us the slope of the function – whether it is decreasing or increasing – at <span class="math notranslate nohighlight">\(x_o\)</span>. This is certainly useful information for helping us search for <span class="math notranslate nohighlight">\(x_\mathrm{min}\)</span>: always look in the direction of decreasing slope, until the slope goes to <span class="math notranslate nohighlight">\(0\)</span>.</p>
 <p>We start our search for <span class="math notranslate nohighlight">\(x_{\mathrm{min}}\)</span> by picking a random starting for value for <span class="math notranslate nohighlight">\(x_o\)</span>, use the autodiff library to compute <span class="math notranslate nohighlight">\(\frac{\mathrm{d}f}{\mathrm{d}x}\big|_{x=x_{o}}\)</span> and then use that information to “step” <span class="math notranslate nohighlight">\(x_o\)</span> in the direction that “descends” <span class="math notranslate nohighlight">\(f(x)\)</span>. We repeat this process until we see that <span class="math notranslate nohighlight">\(\frac{\mathrm{d}f}{\mathrm{d}x}\big|_{x=x_{o}} \approx 0\)</span>. It must be noted that this approach towards finding <span class="math notranslate nohighlight">\(x_\mathrm{min}\)</span> is highly limited;
 saddle-points can stop us in our tracks, and we will only be able to find <em>local</em> minima with this strategy. Nonetheless, it is still very useful!</p>
-<p>Let’s take a simple example. We’ll choose the function <span class="math notranslate nohighlight">\(f(x) = (x-8)^2\)</span> and the starting point <span class="math notranslate nohighlight">\(x=-1.5\)</span>. As we search for <span class="math notranslate nohighlight">\(x_\mathrm{min}\)</span> we don’t want to make our updates to <span class="math notranslate nohighlight">\(x_o\)</span> too big, so we will scale our updates by a factor of <span class="math notranslate nohighlight">\(3/10\)</span> (which is somewhat haphazardly here).</p>
+<p>Let’s take a simple example. We’ll choose the function <span class="math notranslate nohighlight">\(f(x) = (x-8)^2\)</span> and the starting point <span class="math notranslate nohighlight">\(x=-1.5\)</span>. As we search for <span class="math notranslate nohighlight">\(x_\mathrm{min}\)</span> we don’t want to make our updates to <span class="math notranslate nohighlight">\(x_o\)</span> too big, so we will scale our updates by a factor of <span class="math notranslate nohighlight">\(3/10\)</span> (the value of which is chosen somewhat haphazardly here).</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Performing gradient descent on f(x) = (x - 8) ** 2</span>
 <span class="n">x</span> <span class="o">=</span> <span class="n">mg</span><span class="o">.</span><span class="n">Tensor</span><span class="p">(</span><span class="o">-</span><span class="mf">1.5</span><span class="p">)</span>
 <span class="n">step_scale</span> <span class="o">=</span> <span class="mf">0.3</span>