Fixing tanh formula and typo in 01_intro (#276)
* fixing error in tanh formula #273 * fixes typo described in #241
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@ -2282,7 +2282,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"A brief one-line explanation is provided by `doc`. The \"Show in docs\" link take you to the full documentation, where you'll find all the details and lots of examples. Also, most of fastai's methods are just a handful of lines, so you can click the \"source\" link to see exactly what's going on behind the scenes.\n",
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"A brief one-line explanation is provided by `doc`. The \"Show in docs\" link takes you to the full documentation, where you'll find all the details and lots of examples. Also, most of fastai's methods are just a handful of lines, so you can click the \"source\" link to see exactly what's going on behind the scenes.\n",
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"\n",
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"Let's move on to something much less sexy, but perhaps significantly more widely commercially useful: building models from plain *tabular* data."
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]
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@ -1582,7 +1582,7 @@
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"source": [
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"In this picture, our input $x_{t}$ enters on the left with the previous hidden state ($h_{t-1}$) and cell state ($c_{t-1}$). The four orange boxes represent four layers (our neural nets) with the activation being either sigmoid ($\\sigma$) or tanh. tanh is just a sigmoid function rescaled to the range -1 to 1. Its mathematical expression can be written like this:\n",
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"\n",
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"$$\\tanh(x) = \\frac{e^{x} + e^{-x}}{e^{x}-e^{-x}} = 2 \\sigma(2x) - 1$$\n",
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"$$\\tanh(x) = \\frac{e^{x} - e^{-x}}{e^{x}+e^{-x}} = 2 \\sigma(2x) - 1$$\n",
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"\n",
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"where $\\sigma$ is the sigmoid function. The green circles are elementwise operations. What goes out on the right is the new hidden state ($h_{t}$) and new cell state ($c_{t}$), ready for our next input. The new hidden state is also used as output, which is why the arrow splits to go up.\n",
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"\n",
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