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@ashwinhprasad
Created October 13, 2021 09:02
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How neural networks take advantage of non-linear curves to approximate any function
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Foundation_Of_Neural_Networks.ipynb",
"provenance": [],
"collapsed_sections": [
"fQAoZblteaFi",
"n_D8WWzFeOVx",
"pKyNZJMxeRKw"
]
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "fQAoZblteaFi"
},
"source": [
"## Importing Libraries"
]
},
{
"cell_type": "code",
"metadata": {
"id": "gf_zNoENW2LF"
},
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "n_D8WWzFeOVx"
},
"source": [
"## Adding 2 Lines"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 374
},
"id": "hbauG5L4XFVm",
"outputId": "84ce4dc2-561e-4aa9-840d-0fe714e0fac3"
},
"source": [
"x = np.arange(1,51,1)\n",
"y1 = np.arange(1,51,1)\n",
"y2 = np.arange(101,1,-2)\n",
"plt.figure(figsize=(10,6))\n",
"plt.plot(x,y1,c='blue',label='line1')\n",
"plt.plot(x,y2*0.23,c='blue',label='line2')\n",
"plt.plot(x,y1+(y2*0.23),c='red',label='add')\n",
"plt.plot(x,(y2*0.23)-y1,c='green',label='subtract')\n",
"plt.legend()\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "pKyNZJMxeRKw"
},
"source": [
"## Adding 2 Curves"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 265
},
"id": "rj8gYkggXs6Q",
"outputId": "2429b002-7859-407d-a886-351675a08933"
},
"source": [
"x = np.arange(0,10,0.1)\n",
"y3 = np.sin(x)*50\n",
"plt.plot(x,y3,label='curve 1')\n",
"\n",
"y4 = x**2\n",
"plt.plot(x,y4,label='curve 2')\n",
"\n",
"plt.plot(x,y4+y3,label='resultant')\n",
"\n",
"plt.legend()\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "BnaaQP8Eefaf"
},
"source": [
"## Linear function of linear values"
]
},
{
"cell_type": "code",
"metadata": {
"id": "8HzwBn8reegY",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 323
},
"outputId": "23750158-c83d-457a-988d-70928f0354b6"
},
"source": [
"m = 2\n",
"c = -15\n",
"k = -1\n",
"t = 2\n",
"x = np.arange(1,100,1)\n",
"y = m*x + c\n",
"z = k*y + t\n",
"\n",
"plt.figure(figsize=(8,5))\n",
"plt.plot(x,label='x')\n",
"plt.plot(y,label='y')\n",
"plt.plot(z,label='z')\n",
"plt.legend()\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "OFEDoz8VelJj"
},
"source": [
"## Non-Linear Function of Non-linear values"
]
},
{
"cell_type": "code",
"metadata": {
"id": "m9wRIY2-eocT",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 374
},
"outputId": "6231a2eb-3eb8-4306-948a-2b54e5be1db7"
},
"source": [
"x = np.arange(1,101,1)\n",
"y = x^2 - 3*x\n",
"z = y^2 + y*3 + 100\n",
"\n",
"plt.figure(figsize=(8,6))\n",
"plt.plot(x,label='x')\n",
"plt.plot(y,label='y')\n",
"plt.plot(z,label='z')\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
}
]
}
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