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udlbook
2023-10-10 11:51:31 +01:00
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Notebooks/Chap03/3_3_Shallow_Network_Regions.ipynb
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@@ -4,7 +4,7 @@
"metadata": { "metadata": {
"colab": { "colab": {
"provenance": [], "provenance": [],
"authorship_tag": "ABX9TyMhLSGU8+odPS/CoW5PwKna", "authorship_tag": "ABX9TyN/5in7dmMxKCsN/wAMWi0P",
"include_colab_link": true "include_colab_link": true
}, },
"kernelspec": { "kernelspec": {
@@ -62,7 +62,7 @@
"source": [ "source": [
"The number of regions $N$ created by a shallow neural network with $D_i$ inputs and $D$ hidden units is given by Zaslavsky's formula:\n", "The number of regions $N$ created by a shallow neural network with $D_i$ inputs and $D$ hidden units is given by Zaslavsky's formula:\n",
"\n", "\n",
"\\begin{equation}N = \\sum_{j=1}^{D_{i}}\\binom{D}{j}=\\sum_{j=1}^{D_{i}} \\frac{D!}{(D-j)!j!} \\end{equation} <br>\n", "\\begin{equation}N = \\sum_{j=0}^{D_{i}}\\binom{D}{j}=\\sum_{j=1}^{D_{i}} \\frac{D!}{(D-j)!j!} \\end{equation} <br>\n",
"\n" "\n"
], ],
"metadata": { "metadata": {