146 lines
132 KiB
Plaintext
146 lines
132 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Sharktooth Functions in 1-dimension"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np \n",
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"import matplotlib.pyplot as plt"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"def max_conv_operator(samples, f_samples, input, L):\n",
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" return np.max(f_samples - L * np.abs(input - samples))\n",
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"\n",
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"def sharktooth_function(function, x_start, x_stop, number_of_sharkteeth, L, plot_arg):\n",
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" samples = np.random.uniform(x_start,x_stop, number_of_sharkteeth)\n",
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" f_samples = function(samples)\n",
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" x = np.linspace(x_start, x_stop, 10000)\n",
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" approximate_y = []\n",
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" for i in range(len(x)):\n",
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" approximate_y.append(max_conv_operator(samples, f_samples, x[i], L))\n",
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" error = np.max(np.abs(f(x) - approximate_y))\n",
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" if plot_arg == 1:\n",
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" plt.plot(x,approximate_y)\n",
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" else:\n",
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" return error"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"def f(x):\n",
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" return np.tanh(x)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"Text(0.5, 1.0, 'Sup of deviance from tanh(x) as the number of teeth increase and as we get closer to L, for tanh that is 1')"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"image/png": 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|
|
"text/plain": [
|
|
"<Figure size 1700x500 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"L = [1,4,8,16]\n",
|
|
"plt.figure(figsize=(17,5))\n",
|
|
"for L in L:\n",
|
|
" errors = []\n",
|
|
" for i in range(1,50):\n",
|
|
" errors.append(sharktooth_function(f,0,1,i,L,0))\n",
|
|
" import matplotlib.pyplot as plt\n",
|
|
" plt.plot(errors, label =L)\n",
|
|
"\n",
|
|
"plt.xlabel(\"Number of teeth\")\n",
|
|
"plt.ylabel(r\"$\\sup_{x\\in x_i} | \\tanh(x)- \\mathfrak{I}_{\\mathsf{ReLU}} ( \\mathsf{MC})|$\")\n",
|
|
"plt.legend()\n",
|
|
"plt.title(\"Sup of deviance from tanh(x) as the number of teeth increase and as we get closer to L, for tanh that is 1\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"sharktooth_function(np.tanh,-6,6,30,1,1)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "base",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.11.5"
|
|
},
|
|
"orig_nbformat": 4
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|