neural_networks_and_backpropagation.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UI45YofX1Lb3"
      },
      "outputs": [],
      "source": [
        "import math\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def f(x):\n",
        "  return (5*x**2 - 3*x + 5)"
      ],
      "metadata": {
        "id": "RuX6EsU_3xwr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "f(5)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UK9pktQW33Bu",
        "outputId": "1df34505-71d6-4cbb-c75e-74567d0b144a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "115"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "xs = np.arange(-5, 5, 0.2)\n",
        "xs"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qQL6EZQa334o",
        "outputId": "b1413812-250c-4832-c263-9ade65a921ff"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-5.0000000e+00, -4.8000000e+00, -4.6000000e+00, -4.4000000e+00,\n",
              "       -4.2000000e+00, -4.0000000e+00, -3.8000000e+00, -3.6000000e+00,\n",
              "       -3.4000000e+00, -3.2000000e+00, -3.0000000e+00, -2.8000000e+00,\n",
              "       -2.6000000e+00, -2.4000000e+00, -2.2000000e+00, -2.0000000e+00,\n",
              "       -1.8000000e+00, -1.6000000e+00, -1.4000000e+00, -1.2000000e+00,\n",
              "       -1.0000000e+00, -8.0000000e-01, -6.0000000e-01, -4.0000000e-01,\n",
              "       -2.0000000e-01,  4.4408921e-15,  2.0000000e-01,  4.0000000e-01,\n",
              "        6.0000000e-01,  8.0000000e-01,  1.0000000e+00,  1.2000000e+00,\n",
              "        1.4000000e+00,  1.6000000e+00,  1.8000000e+00,  2.0000000e+00,\n",
              "        2.2000000e+00,  2.4000000e+00,  2.6000000e+00,  2.8000000e+00,\n",
              "        3.0000000e+00,  3.2000000e+00,  3.4000000e+00,  3.6000000e+00,\n",
              "        3.8000000e+00,  4.0000000e+00,  4.2000000e+00,  4.4000000e+00,\n",
              "        4.6000000e+00,  4.8000000e+00])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ys = f(xs)\n",
        "plt.plot(xs, ys)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "UDoG0mOF39A_",
        "outputId": "7fb021e8-fe6e-4be6-a277-316c905fd633"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7849347772b0>]"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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fh0UDAD7dV8hbjomIqE3UGIz47z7LRrXThkaJDQMWFIdwa0xHdOnojWqDEZ/v5y7HRERke5/vL0S1wYguHb1xa0xH0XFYUByBXC7DtKGWUZSVe87BbAe3fxERkfMwmyWsvHwzxrSh0ZDLZWIDgQXFYdw3oBPUHkrkV9RhR26Z6DhEROREduSWIb+iDmoPJe4b0El0HAAsKA7Dy12JBwdFArDcAkZERGQrTd8rDyZGwstdKTiNBQuKA5kyJAoKuQx7zlTg+Hmx96cTEZFzOH5ejz1nKqCQy6z7wNkDFhQH0snPE2N6hwAAVnIUhYiIbGDV7nMAgDF9QtDJz1NsmCu0uKDs2rULd911F8LCwiCTybBx48Zmj0uShAULFiA0NBSenp5ITk7GqVOnmj2nsrISKSkpUKvV8PPzw/Tp01FTU9OqP4ir+POwKADAxpwSVNQYxIYhIiKHVlFjwIacYgDAn+3g1uIrtbig1NbWIjY2FsuWLbvq44sXL8Y777yD5cuXIyMjA97e3hg9ejTq6+utz0lJScHRo0exbds2bN68Gbt27cLMmTNv/E/hQgZEdkBsuAYNRjPWZBSIjkNERA5sTUYBGoxmxIZrMCCyg+g4zcikVmyTK5PJsGHDBowfPx6AZfQkLCwMzz77LJ577jkAgE6nQ3BwMFatWoVJkybh+PHj6NWrF/bt24f4+HgAwJYtWzB27FgUFRUhLCzsD39fvV4PjUYDnU4HtVp9o/Ed1qacYjy9LgcdfVXY/eJtcFfySh0REbVMg9GMoYt2oLzagH9O6o9x/dv+7p2WfH/b9JstLy8PWq0WycnJ1nMajQaJiYlIT08HAKSnp8PPz89aTgAgOTkZcrkcGRkZV31dg8EAvV7f7HBlt/cJRbBahfJqA74+XCI6DhEROaCvD5egvNqAYLUKt/cJFR3nN2xaULRaLQAgODi42fng4GDrY1qtFkFBQc0eVyqV8Pf3tz7n1xYuXAiNRmM9IiIibBnb4bgr5daZ1h/+nIdWDIIREZELkiQJH/5sudliSlKUXY7E21+iq5g3bx50Op31KCzkcu8PDoqESinHkWI99udfFB2HiIgcyP78izhSrIdKKbeusWVvbFpQQkIst8CWlpY2O19aWmp9LCQkBGVlzVdCNRqNqKystD7n11QqFdRqdbPD1fl7u+OeOMv1wo9+5i3HRER0/ZqWqrh3QCf4e7sLTnN1Ni0o0dHRCAkJwfbt263n9Ho9MjIykJSUBABISkpCVVUVsrKyrM/ZsWMHzGYzEhMTbRnH6TXtz7P1qBZFF+sEpyEiIkdQdLEOW45YplQ8MiRacJrf1+KCUlNTg5ycHOTk5ACwTIzNyclBQUEBZDIZ5syZg9deew1ffvklDh8+jClTpiAsLMx6p0/Pnj0xZswYzJgxA5mZmdi9ezdmzZqFSZMmXdcdPPSL7iG+GNYtEGYJ+CQ9X3QcIiJyAJ+k58MsAcO6BaJ7iK/oOL+rxQVl//79iIuLQ1xcHABg7ty5iIuLw4IFCwAAL7zwAmbPno2ZM2ciISEBNTU12LJlCzw8PKyvkZaWhh49emDkyJEYO3Yshg0bhhUrVtjoj+RamhZuW5tZgFqDUWwYIiKya7UGI9ZmWtbQavr+sFetWgdFFFdfB+VKZrOEkW/tRN6FWvzf3b0xdUiU6EhERGSnPkk/hwWbjiI60Bvb594KuVzWrr+/sHVQqP3J5TJMu7w88Ue782AyO1zfJCKidmAy/3Jr8SNDotq9nLQUC4oTuH9gOPy83JBfUYfvjl59LRkiInJt3x3VIr+iDn5ebpgQHy46zh9iQXECXu5KTB7cGQCwfNdZLtxGRETNSJKE5bvOAgAmD+4ML3el4ER/jAXFSUwdYlkJ8GBhFTLzKkXHISIiO5KZV4mDhVVwV8odZq4iC4qTCPRR4f6BliG7FZdbMhEREfDL98L9A8MR6KMSnOb6sKA4kRk3d4FMBmzPLcOp0mrRcYiIyA6cKq3G9twyyGSW7wlHwYLiRKIDvTGql2WjRo6iEBER8Mv3wahewYgO9Bac5vqxoDiZmbd0BQBszClGqb5ecBoiIhKpVF+PjTnFAH75fnAULChOZmDnDkiI6oBGk4SVu8+JjkNERAKt3H0OjSYJCVEdMLBzB9FxWoQFxQk1teS0jHzUcPl7IiKXVGMwIi3Dsk+bo42eACwoTmlkjyB07eiN6noj1l3ec4GIiFzLuswCVNcb0bWjN0b2CBIdp8VYUJyQXC6zztT+8Oc8NJrMghMREVF7ajSZrcvaz7i5i90va381LChOanxcJwT6qHBeV4+vDpaIjkNERO3oq4MlOK+rR6CPCuPjOomOc0NYUJyUh5vCuongCi5/T0TkMiRJst5aPG1oFDzcFIIT3RgWFCf2cGJneLkrkKutxq5TF0THISKidrDr1AXkaqvh5a7Aw4mdRce5YSwoTkzj5YZJCZEAgBW7zghOQ0RE7aHp835SQiQ0Xm6C09w4FhQn9+dhUVDIZdh9ugJHinWi4xARURs6UqzD7tMVUMhl+POwKNFxWoUFxcmFd/DCnf1CAQDvcfl7IiKn1vQ5f2e/UIR38BKcpnVYUFzAzFsstxx/c/g8CivrBKchIqK2UFhZh28Onwfwy+e+I2NBcQG9wzS4OSYQJrNkvS+eiIicy4c/58FklnBzTCB6h2lEx2k1FhQX0dSm1+0rQEWNQXAaIiKypYoaA/67rxCAc4yeACwoLmNYt0D07aRBfaMZH+3mKAoRkTP5aHceLjWa0LeTBsO6BYqOYxMsKC5CJpMhdUQ3AMAne/Khu9QoOBEREdmC7lIjPtlj2RQwdUQ3yGSOt6z91bCguJBRvYJxU7APqg1GrE4/JzoOERHZwOr0c6g2GHFTsA9G9QoWHcdmWFBciFwuw5PDLaMoH/6ch7oGo+BERETUGnUNRuvND08O7+aQmwL+HhYUF3Nnv1BE+nvhYl0j1mQUiI5DREStsCajABfrGhHp/8uaV86CBcXFKBVyPDG8KwDg/Z/OwmA0CU5EREQ3wmA04f2fLAuzPTG8K5QK5/pKd64/DV2Xewd0QojaA6V6Az7PKhIdh4iIbsDnWUUo1RsQovbAvQM6iY5jcywoLkilVFjvk1++8wyMJrPgRERE1BJGkxnLd1o2BZx5SxeolArBiWyPBcVFPTgoEgHe7iisvIQvD5aIjkNERC3w5cESFFZeQoC3Ox4cFCk6TptgQXFRnu4K/HlYNADg3z+egdksCU5ERETXw2yW8O8fLaMnfx4WDU935xs9AVhQXNrkpM7w9VDidFkNth7Vio5DRETXYetRLU6X1cDXQ4nJSZ1Fx2kzLCguTO3hhkeGRAEA/vXDaUgSR1GIiOyZJEn41w+nAQCPDImC2sNNcKK2w4Li4qYNjYanmwJHS/T48WS56DhERHQNP54sx9ESPTzdFJg2NFp0nDbFguLi/L3dkZJomWC1bAdHUYiI7JUkSVi2wzJ6kpIYCX9vd8GJ2hYLCmHGLV3grpBjf/5FZORVio5DRERXkZFXif35F+GukGPG5aUinBkLCiFY7YEJ8eEAgGWXr20SEZF9afp8nhAfjmC1h+A0bc/mBcVkMmH+/PmIjo6Gp6cnunbtildffbXZpQNJkrBgwQKEhobC09MTycnJOHXqlK2jUAs8fmtXKOQy/HTqAg4WVomOQ0REVzhYWIWfTl2AQi7D47d2FR2nXdi8oCxatAjvvvsu/vWvf+H48eNYtGgRFi9ejKVLl1qfs3jxYrzzzjtYvnw5MjIy4O3tjdGjR6O+vt7Wceg6Rfh7YVz/MACwzhAnIiL70PS5PK5/GCL8vQSnaR82Lyh79uzBuHHjcMcddyAqKgr3338/Ro0ahczMTACW0ZMlS5bg5Zdfxrhx49CvXz988sknKCkpwcaNG20dh1rgyeHdIJMB246V4liJXnQcIiICcPy8HtuOlUIms3xOuwqbF5QhQ4Zg+/btOHnyJADg4MGD+Pnnn3H77bcDAPLy8qDVapGcnGz9GY1Gg8TERKSnp1/1NQ0GA/R6fbODbK9bkA/u6GvZrvuf208KTkNERACw5HvL5/EdfUPRLchHcJr2Y/OC8tJLL2HSpEno0aMH3NzcEBcXhzlz5iAlJQUAoNVaViwNDg5u9nPBwcHWx35t4cKF0Gg01iMiIsLWsemyOckxkMmArUdLcaRYJzoOEZFLO1Ksw9ajltGTOckxouO0K5sXlE8//RRpaWlYs2YNsrOz8fHHH+ONN97Axx9/fMOvOW/ePOh0OutRWFhow8R0pW5Bvrg71jIXZcn3nLhMRCRS0+fw3bFh6BbkKzhN+1La+gWff/556ygKAPTt2xf5+flYuHAhpk6dipCQEABAaWkpQkNDrT9XWlqK/v37X/U1VSoVVCqVraPS73hqZAy+OliC74+X4lBRFfqF+4mORETkcg4VVeH746WQyyyfy67G5iModXV1kMubv6xCoYDZbAYAREdHIyQkBNu3b7c+rtfrkZGRgaSkJFvHoRvQtaMPxvfvBICjKEREojR9/o7v3wldO7rO3JMmNi8od911F/72t7/h66+/xrlz57Bhwwa89dZbuOeeewAAMpkMc+bMwWuvvYYvv/wShw8fxpQpUxAWFobx48fbOg7doNkjY6CQy7AjtwwHCi6KjkNE5FIOFFzEjtwyKOQyzHbB0ROgDS7xLF26FPPnz8eTTz6JsrIyhIWF4bHHHsOCBQusz3nhhRdQW1uLmTNnoqqqCsOGDcOWLVvg4eH8K+M5iuhAb9wT1wmfZxVhyfen8PGfB4mORETkMppGT+6J64ToQG/BacSQSQ64O5xer4dGo4FOp4NarRYdx2kVVNRhxJs/wmSW8MUTQzCwcwfRkYiInF5W/kXc9+4eKOQy/PDscEQGOM/CbC35/uZePPS7IgO8MGGgZY+epvvwiYiobTV93k4YGO5U5aSlWFDomlJHdIPy8h49+85xp2Miora071wlfjp1AUq5DKkjXGfV2KthQaFrivD3wsQEy8J4b2/jKAoRUVtq+pydmBDhMnvu/B4WFPpDqSO6wU0hw54zFdh7tkJ0HCIip7T3bAX2nKmAm4KjJwALCl2HTn6emJQQCQB4a9tJOOC8aiIiuyZJEt66PHoyKSESnfw8BScSjwWFrsuTI7rCXSFHZl4l0s9wFIWIyJbSz1QgM68S7go5nhzRVXQcu8CCQtclVOOJhxItoyhvf89RFCIiW5EkCW9fvnPnocRIhGo4egKwoFALPDG8K1RKOfadu4ifT18QHYeIyCn8fPoC9p27CJVSjieGc/SkCQsKXbdgtQdSEjsD4FwUIiJbuHLuSUpiZwSruaJ6ExYUapHHh3eBh5scBwqq8OOJctFxiIgc2o8nynGgoAoebnI8PryL6Dh2hQWFWiTI1wNTk6IAAIu25MJs5igKEdGNMJslLNqSCwCYkhSFIF+OnlyJBYVa7InhXeHroUSuthpfHiwRHYeIyCF9ebAEudpq+Hoo8STnnvwGCwq1mJ+XOx6/1fKP6c1tJ9BgNAtORETkWBqMZry57QQA4PFbu8LPy11wIvvDgkI3ZNrQKHT0VaGw8hLWZhaIjkNE5FDWZhagsPISOvqqMG1olOg4dokFhW6Il7sST4+MAQAs3XEKtQaj4ERERI6h1mDE0h2nAABPj4yBl7tScCL7xIJCN+yBhAhEB3rjQk0DPvgpT3QcIiKH8MFPebhQ04DoQG88cHkzVvotFhS6YW4KOZ4ddRMAYMWuM6ioMQhORERk3ypqDFix6wwA4NlRN8FNwa/h38N3hlplbJ9Q9OmkRm2DCct+OCM6DhGRXVv2wxnUNpjQp5MaY/uEio5j11hQqFXkchleHNMDAPCfvfkoulgnOBERkX0quliH/+zNBwC8OKYH5HKZ4ET2jQWFWu3mmI4Y2i0ADSazdclmIiJq7q1tJ9FgMmNotwDcHNNRdBy7x4JCNvHCaMsoyoYDxTihrRachojIvpzQVmPDgWIAv3xe0rWxoJBNxEb4YWzfEEgS8I+tuaLjEBHZlX9szYUkAWP7hiA2wk90HIfAgkI289yo7lDIZfj+eBn2nasUHYeIyC7sO1eJ74+XQSGX4blR3UXHcRgsKGQzXTr6YGK85Z7+Rd/mQpK4kSARuTZJkrDoW8uo8sT4CHTp6CM4keNgQSGbenpkDFRKOfbnX8SO3DLRcYiIhNqRW4b9+RehUsqtq2/T9WFBIZsK0Xhg2tBoAMDiLSdgMnMUhYhck8ksYfEWy4aA04ZGI0TjITiRY2FBIZt74tauUHsocaL0l1nrRESuZsOBYpworYbaQ4knLu8AT9ePBYVsTuPlhidHdAMAvLH1BOoauJEgEbmWugYj3thqGT15ckQ3aLzcBCdyPCwo1CYeGRKF8A6e0OrrsWLXWdFxiIja1YpdZ6HV1yO8gyceGRIlOo5DYkGhNuHhpsC823sCAN7beRZaXb3gRERE7UOrq8d7Oy3/YTbv9p7wcFMITuSYWFCozYztG4L4zh1wqdGExVy8jYhcxOKtubjUaEJ85w4Y2zdEdByHxYJCbUYmk2H+nb0AAOuzi3GoqEpsICKiNnaoqArrsy03B8y/sxdkMm4IeKNYUKhNxUb44Z64TgCA1zYf5+JtROS0JEnCa5uPAwDuievEJe1biQWF2twLY7rDw02OzHOV2HJEKzoOEVGb2HJEi8xzlfBwk+OFMVzSvrVYUKjNhWo8MfMWyxoAC7/NhcFoEpyIiMi2DEYTFl5e0n7mLV0RqvEUnMjxsaBQu3j81i4I8lWhoLIOq3afEx2HiMimVu0+h4LKOgT5qvD4rV1Ex3EKLCjULrzclXh+tGXI8187TuNCjUFwIiIi27hQY8C/dpwGADw/uju83JWCEzmHNikoxcXFePjhhxEQEABPT0/07dsX+/fvtz4uSRIWLFiA0NBQeHp6Ijk5GadOnWqLKGRH7hsQjj6d1Kg2GLHk+5Oi4xAR2cSS70+i2mBEn05q3DcgXHQcp2HzgnLx4kUMHToUbm5u+Pbbb3Hs2DG8+eab6NChg/U5ixcvxjvvvIPly5cjIyMD3t7eGD16NOrruZiXM5PLZZh/h+W24zUZBThZWi04ERFR65wsrcaajAIAwPw7ekEu523FtmLzgrJo0SJERERg5cqVGDRoEKKjozFq1Ch07WqZJClJEpYsWYKXX34Z48aNQ79+/fDJJ5+gpKQEGzdutHUcsjOJXQIwpncIzBLw2tfHRcchImqV174+DrMEjOkdgsQuAaLjOBWbF5Qvv/wS8fHxmDBhAoKCghAXF4f333/f+nheXh60Wi2Sk5Ot5zQaDRITE5Genn7V1zQYDNDr9c0OclzzxvaAm0KGXSfL8cOJMtFxiIhuyA8nyrDrZDncFDLMG9tDdBynY/OCcvbsWbz77ruIiYnB1q1b8cQTT+Cpp57Cxx9/DADQai3rYAQHBzf7ueDgYOtjv7Zw4UJoNBrrERERYevY1I46B3hbN8/629fH0Wgyiw1ERNRCjSYz/nZ5FPiRIVHoHOAtOJHzsXlBMZvNGDBgAF5//XXExcVh5syZmDFjBpYvX37Drzlv3jzodDrrUVhYaMPEJMKs22Lg7+2O02U1WJtZIDoOEVGLrM0swOmyGvh7u2PWbTGi4zglmxeU0NBQ9OrVq9m5nj17oqDA8iUUEmLZOKm0tLTZc0pLS62P/ZpKpYJarW52kGPTeLrhmWTLP+o3vzuJytoGwYmIiK5PZW0D3vzOcifiM8kx0Hi6CU7knGxeUIYOHYoTJ040O3fy5El07twZABAdHY2QkBBs377d+rher0dGRgaSkpJsHYfs2IODItEzVA3dpUYs3sLdjonIMSzekgvdpUb0DFXjwUGRouM4LZsXlGeeeQZ79+7F66+/jtOnT2PNmjVYsWIFUlNTAVh2uJ0zZw5ee+01fPnllzh8+DCmTJmCsLAwjB8/3tZxyI4pFXK8Oq43AGDdvkJkF1wUnIiI6NqyCy5i3T7LNINXx/WGUsH1TtuKzd/ZhIQEbNiwAWvXrkWfPn3w6quvYsmSJUhJSbE+54UXXsDs2bMxc+ZMJCQkoKamBlu2bIGHh4et45Cdi4/yx/0DLQsbLdh0BCYzdzsmIvtkMktYsOkIAOD+geGIj/IXnMi5ySRJcrhvBL1eD41GA51Ox/koTuBCjQEj3vgR1fVGvDq+DyYP7iw6EhHRb6zem4/5G4/A10OJH54bjkAflehIDqcl398cmyLhAn1UeG6UZZ+ef2zJRQX36SEiO1NRY8A/Ls+Ve25Ud5aTdsCCQnYhJTESvULV0NcbsYgTZonIzizakgt9vRG9QtVISeTE2PbAgkJ2QamQ49Xxlgmzn+4v4oRZIrIb2QUX8en+IgDAq+M5Mba98F0muzGw8y8TZudv5IRZIhLPZJYwf6NlYuyEgeEY2JkTY9sLCwrZlZdu7wFfDyWOluixJiNfdBwicnFrMvJxtEQPtYcSL97O/XbaEwsK2ZVAHxWeH315wuzWE7jACbNEJMiFGgP+sdWy8Ohzozkxtr2xoJDdSUnsjN5hlyfMfssJs0QkxqJvLRNje4epkZLI5Q/aGwsK2R2FXIa/jusDAPgsqwhZ+ZwwS0TtKyv/Ij7LskyM/eu4PlDIZYITuR4WFLJLAzt3wAROmCUiAa6cGDsxPhwDO3cQnMg1saCQ3Xrx9h5Qeyhx7LweaZwwS0TtJC0jH8fOX54YO4YTY0VhQSG7FeijwnNNE2a3nECpvl5wIiJydqX6euvE2OdHd0cAJ8YKw4JCdi0lsTNiwzWoNhitm3QREbWVBZuOoLreiNhwDR7ixFihWFDIrinkMiy8tx+Uchm2Hi3FliPnRUciIie15ch5bD1aCqVchr/f148TYwVjQSG71ytMjcdu7QIAmL/pKHSXGgUnIiJno7vUiPmbjgIAHr+1K3qGXnunXWp7LCjkEGbfFoMugd4orzbg798eFx2HiJzM3789jvJqA7oEemPWbd1ExyGwoJCD8HBTYOG9fQEAazMLsfdsheBEROQs9p6twNrMQgDAwnv7wsNNITgRASwo5EASuwTgocvbnM9bfxj1jSbBiYjI0dU3mjBv/WEAwEOJkUjsEiA4ETVhQSGH8tLtPRDkq0LehVos3XFKdBwicnBLd5xC3oVaBPmq8BI3A7QrLCjkUNQebnh1vGUZ/Pd2nsWxEr3gRETkqI6V6PHezrMAgFfH94Haw01wIroSCwo5nNG9Q3B7nxAYzRJeWn+Iy+ATUYuZLn9+GM0SxvYNwejeIaIj0a+woJBD+r+7e8PXQ4lDRTqs3J0nOg4ROZiVu/NwqEgHtYcS/3t3b9Fx6CpYUMghBak98D9jewIA3vzuJAor6wQnIiJHUVhZhze/OwkA+J87eiLI10NwIroaFhRyWA8kRCCpSwAuNZrwlw2HIUm81ENE1yZJEv6y4TAuNZqQ1CUAE+MjREei38GCQg5LJpPh9Xv7QqWU46dTF7DhQLHoSERk5zYcKMZPpy5ApZTj9Xv7Qibjcvb2igWFHFp0oDfmJN8EAPjr5mMoq+aOx0R0dWXV9fjr5mMAgDnJNyE60FtwIroWFhRyeI/eHI3eYWpU1TVi3he81ENEvyVJEuZ9cRhVdY3oHabGozdHi45Ef4AFhRyem0KOtyb2h7tCju25Zfhsf5HoSERkZz7bX4TtuWVwv/x54abg15+94/9D5BS6h/jiudGWSz3/99VR3tVDRFaFlXX4v68sOxU/N/omdA/xFZyIrgcLCjmN6cO6YFCUP2obTHj2s4MwcwE3IpdnNkt49rODqG0wYVCUP6YP6yI6El0nFhRyGgq5DG9MiIWXuwKZeZX4iAu4Ebm8j3bnITOvEl7uCrwxIRYKOe/acRQsKORUIgO8MP/OXgCAxVtP4GRpteBERCTKydJqLN56AgAw/85eiAzwEpyIWoIFhZzOpIQIjOjeEQ1GM+Z+moNGk1l0JCJqZ40my7//BqMZI7p3xKQELsjmaFhQyOnIZDIsuq8f/LzccKRYj6U7TouORETtbOmO0zhSrIeflxsW3dePC7I5IBYUckpBag+8Nr4PAGDZD6eRU1glNhARtZucwios+8HyHyavje+DIDX32nFELCjktO7sF4a7Y8NgMkuY+2kOLjWYREciojZ2qcGEuZ/mwGSWcHdsGO7sFyY6Et0gFhRyan8d1xtBviqcLa/Foi25ouMQURtbtCUXZ8trEeSrwl/H9RYdh1qBBYWcmp+XOxbf3w8AsGrPOew+fUFwIiJqK7tPX8CqPecAAIvv7wc/L3exgahV2ryg/P3vf4dMJsOcOXOs5+rr65GamoqAgAD4+PjgvvvuQ2lpaVtHIRc1vHsQUhIjAQDPfXYQukuNghMRka3pLjXi+c8OAgBSEiMxvHuQ4ETUWm1aUPbt24f33nsP/fr1a3b+mWeewVdffYXPPvsMO3fuRElJCe699962jEIu7i9je6JzgBfO6+oxb/0hbihI5EQkScK89YdQoqtHpL8X/jK2p+hIZANtVlBqamqQkpKC999/Hx06dLCe1+l0+PDDD/HWW2/htttuw8CBA7Fy5Urs2bMHe/fubas45OK8VUr8c1IclHIZvjmsRVpGgehIRGQjaRkF+OawFkq5DO88GAdvlVJ0JLKBNisoqampuOOOO5CcnNzsfFZWFhobG5ud79GjByIjI5Genn7V1zIYDNDr9c0OopbqH+GHF8Z0BwD8dfMxHD/Pv0dEju74eT3+uvkYAOCFMd3RP8JPbCCymTYpKOvWrUN2djYWLlz4m8e0Wi3c3d3h5+fX7HxwcDC0Wu1VX2/hwoXQaDTWIyKCKwLSjXl0WBfrKrOpa7JRazCKjkREN6jWYETqmmzrarGPciNAp2LzglJYWIinn34aaWlp8PCwzeI48+bNg06nsx6FhYU2eV1yPXK5DG9O7I9gteXW4wWbjoqOREQ3aMGmozhbXotgtQpvTuwPOTcCdCo2LyhZWVkoKyvDgAEDoFQqoVQqsXPnTrzzzjtQKpUIDg5GQ0MDqqqqmv1caWkpQkJCrvqaKpUKarW62UF0o/y93fHPSXGQy4AvsouwPrtIdCQiaqH12UX4IrsIchnwz0lx8PfmLcXOxuYFZeTIkTh8+DBycnKsR3x8PFJSUqz/283NDdu3b7f+zIkTJ1BQUICkpCRbxyG6qsFdAvD0yJsAAC9vPIIz5TWCExHR9TpTXoOXNx4BADw98iYM7hIgOBG1BZtPdfb19UWfPn2anfP29kZAQID1/PTp0zF37lz4+/tDrVZj9uzZSEpKwuDBg20dh+h3zbqtG/aerUD62QqkpmVjY+pQeLgpRMciomuobzQhNS0bdQ0mJHUJwKzbuomORG1EyEqyb7/9Nu68807cd999uOWWWxASEoL169eLiEIuTCGXYcmk/gjwdkeuthp/+/q46EhE9Af+9vVx5GqrEeDtjiWT+kPBeSdOSyY54IpVer0eGo0GOp2O81Go1X48UYZHVu4DALybMgC39w0VnIiIrubbw+fxRFo2AGDVtASuFuuAWvL9zb14yOUN7x6Ex2613J74wheHUFhZJzgREf1aYWUdXvjiEADgsVu7sJy4ABYUIgDPjeqOuEg/VNcbMXvtATSazKIjEdFljSYzZq89gOp6I+Ii/fDcqO6iI1E7YEEhAuCmkGPpg3FQeyiRU1iF17/hfBQie/H6N8eRU1gFtYcSSx+Mg5uCX12ugP8vE10W3sELb0yIBQCs3H2O66MQ2YH12UVYufscAOAfE2IR3sFLbCBqNywoRFcY1TsEsy/ftjhv/WEcLtIJTkTkug4X6TBv/WEAwOzbumF076sv5knOiQWF6FeeSb4Jt/UIgsFoxmOr9+NCjUF0JCKXc6HGgMdW74fBaMZtPYLwTPJNoiNRO2NBIfoVuVyGtx/oj+hAb5To6pGals1Js0TtqNFkRmpaNkp09YgO9MbbD3CfHVfEgkJ0FRpPN6yYPBDe7gpk5FVyETeidvS3r48jI68S3u4KrJg8EBpPN9GRSAAWFKLfERPsi7ce6A8AWLXnHL7I4qRZorb2RVYRVu05BwB464H+iAn2FRuIhGFBIbqG0b1D8NTIGADAvA2HcaioSmwgIid2qKgK8zZYJsU+NTKGk2JdHAsK0R+YMzIGyT2D0GA047HVWZw0S9QGLJNis9BgNCO5ZxDmXP4PA3JdLChEf0Aul+GtB/qjS0dvnNfV40lOmiWyqUaTGU+mZeO8rh5dOnrjLU6KJbCgEF0XtYcbVkyOh49KiUxOmiWyqb99fRyZeZXwUSmxYnI81B6cFEssKETXrVuQD96+YtLsp/sLxQYicgKf7i+0Top9+4H+6BbkIzYQ2Q0WFKIW+FOvYDx9+dr4X9Yfxu7TFwQnInJcu09fwF8urxT79MgY/KlXsOBEZE9YUIha6OmRMbizXyiMZgmPr87CCW216EhEDueEthqPr86C0Szhzn6h1uJP1IQFhaiF5HIZ3pgQi0FR/qg2GDFtZSZK9fWiYxE5DK2uHo+szES1wYhBUf54Y0IsJ8XSb7CgEN0ADzcFVkwZiC4dLcvhT1u5DzUGo+hYRHavxmDEtFX7rHfsrJgyEB5uCtGxyA6xoBDdID8vd3w8bRACfdxx7Lyetx8T/YGm24mPn9cj0Mfy78fPy110LLJTLChErRDh74UPpybAw02OXSfLMX/jEUiSJDoWkd2RJAnzNx7BrpPl8HCT48OpCYjw9xIdi+wYCwpRK8VG+GHpgwMglwHr9hXi3z+eER2JyO4s++E01u0rhFwGLH1wAGIj/ERHIjvHgkJkA3/qFYz/vbs3AOAfW09g44FiwYmI7MeGA0V447uTAID/vbs3byem68KCQmQjU5KiMPOWLgCA5z8/iD1nuEYK0Z4zF/DC54cAADNv6YIpSVFiA5HDYEEhsqGXxvTAHX1D0WiS8NjqLJws5Rop5LpOllbjsdVZaDRJuKNvKF4a00N0JHIgLChENiSXy/DmxFjEd+6A6nojpn6UicLKOtGxiNpdYWUdpn6Uiep6I+I7d8CbE7nWCbUMCwqRjXm4KfD+lHh0vbz7ccoHGdDquJAbuQ6trh4PfbAX53X16NrRG+9PiedaJ9RiLChEbaCDtzvWzBiMzgFeKKisw0Mf7EV5tUF0LKI2V15twEMf7EVh5SV0DvDCmhmD0cGba51Qy7GgELWRYLUH0h5NRJjGA2fLazH5wwxU1TWIjkXUZi7WNmDyhxk4W16LMI3l73+w2kN0LHJQLChEbSi8g+W/IIN8VcjVVmPKR5nQ1zeKjkVkc/r6Rkz5KBO52moE+aqwZsZghHfgQmx041hQiNpYVKA30h5NhL+3Ow4V6TBt5T7Uct8eciK1BiOmrdyHw8U6+Hu7I+3RREQFeouORQ6OBYWoHcQE+2L19EFQeyiRlX8Rj368H/WNJtGxiFqtvtGERz/ej6z8i1B7KLF6+iDEBPuKjkVOgAWFqJ30DtPgk+mJ8FEpkX62Ao+tzoLByJJCjstgNOGx1VlIP1sBH5USn0xPRO8wjehY5CRYUIjaUf8IP6yclgBPNwV2nizHU2sPcAdkckiNJjOeWnsAO0+Ww9NNgZXTEtCf++uQDbGgELWzhCh/vD8lHu5KObYeLcXcTw/CyJJCDsRoMuPZTw9i69FSuCvleH9KPBKi/EXHIifDgkIkwLCYQCx/eADcFDJ8dbAET6Zlc04KOYT6RhOeTMvGlwdL4KaQYfnDAzAsJlB0LHJCLChEgtzWIxj/ThkId6Uc3x0rxfSPeXcP2bdagxHTP96H745ZRk7+nTIQt/XgzsTUNmxeUBYuXIiEhAT4+voiKCgI48ePx4kTJ5o9p76+HqmpqQgICICPjw/uu+8+lJaW2joKkd37U69grJqWAG93BXafrsDDXMyN7FRVXQMe/jADu09XwNtdgVXTEvCnXiwn1HZsXlB27tyJ1NRU7N27F9u2bUNjYyNGjRqF2tpa63OeeeYZfPXVV/jss8+wc+dOlJSU4N5777V1FCKHMKRrINJmDIaflxsOFFRh0oq9KKvm3j1kP8qq6zFpxV4cKKiCn5cb0mYMxpCuvKxDbUsmSZLUlr9BeXk5goKCsHPnTtxyyy3Q6XTo2LEj1qxZg/vvvx8AkJubi549eyI9PR2DBw/+w9fU6/XQaDTQ6XRQq9VtGZ+o3ZzQVmPyhxkoqzagc4AX/jM9ERH+XImTxCqsrMPDH2Ygv6IOQb4qrJ6eiO4hXOeEbkxLvr/bfA6KTqcDAPj7W2Z4Z2VlobGxEcnJydbn9OjRA5GRkUhPT2/rOER2q3uILz5/fAgi/D2RX1GHCcvTcbqsWnQscmGny6oxYXk68ivqEOHvic8fH8JyQu2mTQuK2WzGnDlzMHToUPTp0wcAoNVq4e7uDj8/v2bPDQ4OhlarverrGAwG6PX6ZgeRM4oM8MLnjw9BTJAPtPp6TFiejkNFVaJjkQs6VFSFCcvTodXXIybIB58/PgSRARzRo/bTpgUlNTUVR44cwbp161r1OgsXLoRGo7EeERERNkpIZH+C1R749LEkxIZrcLGuEQ+9n4G9ZytExyIXsvdsBR56PwMX6xoRG67Bp48lcVdiandtVlBmzZqFzZs344cffkB4eLj1fEhICBoaGlBVVdXs+aWlpQgJCbnqa82bNw86nc56FBYWtlVsIrvQwdsdaTMGI6lLAGoMRkz9KBObD5WIjkUu4OtD5zH1o0zUGIxI6hKAtBmD0cHbXXQsckE2LyiSJGHWrFnYsGEDduzYgejo6GaPDxw4EG5ubti+fbv13IkTJ1BQUICkpKSrvqZKpYJarW52EDk7H5USK6clILlnMAxGM2atOYAl359EG89rJxclSRKWfH8SqWuyYTCakdwzCCunJcBHpRQdjVyUze/iefLJJ7FmzRps2rQJ3bt3t57XaDTw9PQEADzxxBP45ptvsGrVKqjVasyePRsAsGfPnuv6PXgXD7kSk1nCwm+O44Of8wAAd/QLxRv3x8LTXSE4GTmLSw0mPPf5QXx96DwA4NFh0Zg3ticUcpngZORsWvL9bfOCIpNd/S/0ypUr8cgjjwCwLNT27LPPYu3atTAYDBg9ejT+/e9//+4lnl9jQSFX9N99BXh54xE0miT0C9dgxeR4hGg4L4BaR6urx8zV+3GoSAc3hQyvje+DBxIiRcciJyW0oLQHFhRyVRlnK/D4f7Jwsa4RQb4qfDA1Hv3C/UTHIgd1qKgKj368H2XVBnTwcsPyhwcisUuA6FjkxOxqHRQisp3ELgHYlDoMMUE+KKs2YMLydHx1kJNnqeW+OliCCcvTUVZtQEyQDzalDmM5IbvCgkLkYCIDvLD+ySEY0b0jDEYzZq89gLe2nYTZ7HCDoSSA2SzhrW0nMXvtARiMZozo3hHrn+QaJ2R/WFCIHJCvhxs+mJqAGTdb7pJ7Z/spzFqbjboG7oZMv6+uwYjZaw/gne2nAAAzbo7GB1MT4OvhJjgZ0W/x/jEiB6WQy/A/d/RCTJAv/mfjYXxzWIsT2mr866EB6BnKuVnU3PHzesxak40z5bVwU8jwt/F9MTGBi16S/eIICpGDm5gQgbRHByPIV4Uz5bUYt2w3Pkk/x/VSCIBlfZNP0s9h3LLdOFNeiyBfFdIeHcxyQnaPd/EQOYnK2gY8/9lBbM8tAwAk9wzGP+7vx1VAXdjF2gY8//khfH+8FAAwskcQ/jEhFv78O0GC8DZjIhclSRJW7TmHhd/kosFkRojaA0sm9cdg3p3hcvaercCcdTnQ6uvhrpBj3tgeeGRI1O+uVUXUHlhQiFzc0RIdZq89gLPltZDJgNkjuuGpkTFQKnhV19kZTWa8s/0Ulv5wGpIEdOnojaUPxqF3mEZ0NCKug0Lk6nqHabB59jBMjA+HJAHv7DiNSSv2ouhineho1IaKLtZh0oq9eGeHpZxMjA/H5tnDWE7IIXEEhcjJbcopxssbjqDaYITaQ4lXx/fB3bFhHOp3IpIk4cuDJZi/8Qj09Ub4qpR47Z4+GNe/k+hoRM3wEg8RNVNQUYen1h1ATmEVAODmmEC8Nr4POgd4iw1GrZZfUYuXNx7BT6cuAAD6R/jhnUlxXHiN7BILChH9RqPJjOU/nsHSH06jwWiGSinHUyNjMOPmLnBX8mqvo2kwmvH+T2fxzvZTMBjNcFfKMWtENzwxvCvcONeI7BQLChH9rrwLtXh542HsPl0BALgp2Aev39MX8VH+gpPR9dp/rhJ/2XAYJ0trAABDuwXgtfF9ER3IETGybywoRHRNkiRhU04JXt18DBW1DQCABwdF4KUxPaHx4rLn9kpX14i/bzmOtZmFAIAAb3fMv7MXxvXnnCJyDCwoRHRdquoa8Pdvc7Fun+ULL9DH8oXHSbT2pWkS7Kubj+FCjaVQTkqIwEu394CfFxddI8fBgkJELZKZZ7lkcLrMcslgcBd/vDCmBwZEdhCcjLILLmLxllzsPVsJAIgJ8sHr9/ZFAi/JkQNiQSGiFmswmrFi1xm8s8MyiRawLI3+7Kju6BXGf2ft7WiJDm99d9K6dQEnNZMzYEEhohtWXHUJ73x/Cp9nF8Fktnw83NkvFM/86SZ07egjOJ3zO1Neg7e2ncTXh84DsOxaff+AcDyVHINOfp6C0xG1DgsKEbXa2fIavP39KXx1sAQAIJcB9w0Ix1MjYxDhzzU2bK2wsg7/3H4K67OLcLkX4u7YMMxJjkEXFkNyEiwoRGQzx8/r8eZ3J6074ropZHhwUCRmjeiGILWH4HSOr0xfj3/9cBprMwvQaLJ8HCf3DMazo25Cz1B+vpFzYUEhIpvLLriIN787YV0/xV0hx9i+IZicFIUBkX6866cFJElCdkEVVqefwzeHtWgwWeb8DOsWiGdH3YQ4Tk4mJ8WCQkRtZs+ZC3jzu5PIyr9oPdc7TI3JgztjXP9O8HRXCExn3+oajPgypwSfpOfj2Hm99fzAzh3w7KibMKRroMB0RG2PBYWI2tzBwiqs3puPrw6WwHD5rh+1hxL3D4zAw4MjOW/iCmfLa/CfvQX4LKsQ1fVGAJa7cu6KDcPkwZ0RG+EnNiBRO2FBIaJ2c7G2AZ9lFeI/ewtQUFlnPX9zTCBSEjtjePeO8HBzvVGV+kYTfjxRjrSMfOtGfgAQ6e+FhwdHYsLACHTw5iJr5FpYUIio3ZnNEnadKsfq9HzsOFGGpk8WL3cFhnfviFG9QjCie5BTL6Wvq2vEjhOl+O5oKXaeLEddgwkAIJMBt3UPwuSkzrglpiPkcs7XIdfEgkJEQhVW1iEtowAbDxRDq6+3nlfKZUjs4o9RvULwp17BCHOCdT1Kqi5h27FSfHdMi4yzlTCaf/lIDVF7YHxcJ6QkRvLWbCKwoBCRnZAkCYeLdfjuqOULvGn33SZ9O2nwp17BSIjyR99wDXxUSkFJr1+NwYjDRTrsO1eJbcdKcbhY1+zxm4J9MKpXCEb1DkbfThre3UR0BRYUIrJL5y7UWkcb9udfxJWfPjIZ0LWjD/qFaxAb7ofYCD/0DPWFSilu/orBaMLx89U4WFiFg0VVOFSkw5nymt/kju/cwToqFBXoLSwvkb1jQSEiu3ehxoDtxy1zNQ4W6lBcdek3z3FTyNAjRI1+4RpEBXgjWOOBELUHgtUqBKs9bDL5tr7RhFJ9PUr1Bmj19SjV1eNcRS0OFemQq9VbF0+7Uic/T8RGaHDrTR0xsmcwAn1Urc5B5ApYUIjI4VyoMeBQURUOFuqsoxWVtQ3X/Bk/LzeEqD0QpPZAiFoF7+u4RFRrMEKrN6BMXw+tvh5VdY3XfL6/t/sVozoa9Av3YyEhukEsKETk8CRJQtHFSzhYVIUjxXqUVF2yjHDo66HV1VvXXrEFlVKOEI0HgtWWEZowP0/07aRBv3ANwjt4ch4JkY205Pvb/mekEZFLkslkiPD3QoS/F+7sF9bsMUmSoL9khPbyKEjp5Usz9UbTH76uh1KB4CvKSIjaA2pPJUsIkZ1hQSEihyOTyaDxcoPGyw3dQ3xFxyGiNiAXHYCIiIjo11hQiIiIyO6woBAREZHdYUEhIiIiuyO0oCxbtgxRUVHw8PBAYmIiMjMzRcYhIiIiOyGsoPz3v//F3Llz8corryA7OxuxsbEYPXo0ysrKREUiIiIiOyGsoLz11luYMWMGpk2bhl69emH58uXw8vLCRx99JCoSERER2QkhBaWhoQFZWVlITk7+JYhcjuTkZKSnp//m+QaDAXq9vtlBREREzktIQblw4QJMJhOCg4ObnQ8ODoZWq/3N8xcuXAiNRmM9IiIi2isqERERCeAQd/HMmzcPOp3OehQWFoqORERERG1IyFL3gYGBUCgUKC0tbXa+tLQUISEhv3m+SqWCSsXdQ4mIiFyFkBEUd3d3DBw4ENu3b7eeM5vN2L59O5KSkkREIiIiIjsibLPAuXPnYurUqYiPj8egQYOwZMkS1NbWYtq0aaIiERERkZ0QVlAeeOABlJeXY8GCBdBqtejfvz+2bNnym4mzVyNJEgDwbh4iIiIH0vS93fQ9fi0y6XqeZWeKiop4Jw8REZGDKiwsRHh4+DWf45AFxWw2o6SkBL6+vpDJZKLj2AW9Xo+IiAgUFhZCrVaLjuP0+H63L77f7Yvvd/typfdbkiRUV1cjLCwMcvm1p8EKu8TTGnK5/A+bl6tSq9VO/xfcnvD9bl98v9sX3+/25Srvt0ajua7nOcQ6KERERORaWFCIiIjI7rCgOAmVSoVXXnmFC9q1E77f7Yvvd/vi+92++H5fnUNOkiUiIiLnxhEUIiIisjssKERERGR3WFCIiIjI7rCgEBERkd1hQXFiBoMB/fv3h0wmQ05Ojug4TuncuXOYPn06oqOj4enpia5du+KVV15BQ0OD6GhOY9myZYiKioKHhwcSExORmZkpOpJTWrhwIRISEuDr64ugoCCMHz8eJ06cEB3LZfz973+HTCbDnDlzREexGywoTuyFF15AWFiY6BhOLTc3F2azGe+99x6OHj2Kt99+G8uXL8df/vIX0dGcwn//+1/MnTsXr7zyCrKzsxEbG4vRo0ejrKxMdDSns3PnTqSmpmLv3r3Ytm0bGhsbMWrUKNTW1oqO5vT27duH9957D/369RMdxb5I5JS++eYbqUePHtLRo0clANKBAwdER3IZixcvlqKjo0XHcAqDBg2SUlNTrb82mUxSWFiYtHDhQoGpXENZWZkEQNq5c6foKE6turpaiomJkbZt2ybdeuut0tNPPy06kt3gCIoTKi0txYwZM7B69Wp4eXmJjuNydDod/P39RcdweA0NDcjKykJycrL1nFwuR3JyMtLT0wUmcw06nQ4A+He5jaWmpuKOO+5o9vecLBxys0D6fZIk4ZFHHsHjjz+O+Ph4nDt3TnQkl3L69GksXboUb7zxhugoDu/ChQswmUwIDg5udj44OBi5ubmCUrkGs9mMOXPmYOjQoejTp4/oOE5r3bp1yM7Oxr59+0RHsUscQXEQL730EmQy2TWP3NxcLF26FNXV1Zg3b57oyA7tet/vKxUXF2PMmDGYMGECZsyYISg5UeulpqbiyJEjWLdunegoTquwsBBPP/000tLS4OHhITqOXeJS9w6ivLwcFRUV13xOly5dMHHiRHz11VeQyWTW8yaTCQqFAikpKfj444/bOqpTuN73293dHQBQUlKC4cOHY/DgwVi1ahXkcnb/1mpoaICXlxc+//xzjB8/3np+6tSpqKqqwqZNm8SFc2KzZs3Cpk2bsGvXLkRHR4uO47Q2btyIe+65BwqFwnrOZDJBJpNBLpfDYDA0e8wVsaA4mYKCAuj1euuvS0pKMHr0aHz++edITExEeHi4wHTOqbi4GCNGjMDAgQPxn//8x+U/VGwpMTERgwYNwtKlSwFYLj1ERkZi1qxZeOmllwSncy6SJGH27NnYsGEDfvzxR8TExIiO5NSqq6uRn5/f7Ny0adPQo0cPvPjii7y0Bs5BcTqRkZHNfu3j4wMA6Nq1K8tJGyguLsbw4cPRuXNnvPHGGygvL7c+FhISIjCZc5g7dy6mTp2K+Ph4DBo0CEuWLEFtbS2mTZsmOprTSU1NxZo1a7Bp0yb4+vpCq9UCADQaDTw9PQWncz6+vr6/KSHe3t4ICAhgObmMBYWoFbZt24bTp0/j9OnTvymAHJxsvQceeADl5eVYsGABtFot+vfvjy1btvxm4iy13rvvvgsAGD58eLPzK1euxCOPPNL+gcjl8RIPERER2R3O5CMiIiK7w4JCREREdocFhYiIiOwOCwoRERHZHRYUIiIisjssKERERGR3WFCIiIjI7rCgEBERkd1hQSEiIiK7w4JCREREdocFhYiIiOwOCwoRERHZnf8HO5IQnAYDfgQAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "So what really is derivative??\n",
        "It provides the response that we get when we try to increase the input value of the function by very small amount i.e the small amount tends to be zero."
      ],
      "metadata": {
        "id": "FEQJQoIg4R1G"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "h = 0.001\n",
        "x = 3.0\n",
        "print(f(x),f(x + h))\n",
        "print((f(x + h) - f(x))/ h)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "A_IQqOSd5Cp-",
        "outputId": "0eea7388-3da8-463d-9a3d-265ab71ccc2f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "41.0 41.027004999999996\n",
            "27.004999999995505\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "i.e. at x = 3, the slop is 27. If we increase the value of x at point x = 3 by just 0.001, it will increse 27.004 time h."
      ],
      "metadata": {
        "id": "XvToX1T-5JpF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "h = 0.0000001\n",
        "x = -3.0\n",
        "print(f(x),f(x + h))\n",
        "print((f(x + h) - f(x))/ h)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zW8qw6GZ54om",
        "outputId": "96a2e885-1924-488e-a380-8c01b4db1bcb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "59.0 58.999996700000054\n",
            "-32.99999946193566\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "here the negative sign says, on slight increase of the value of input to f(x) the output gets reduced i.e slope is negative"
      ],
      "metadata": {
        "id": "syeYwiSn6CQk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "h = 0.0000000001\n",
        "x = 0.3\n",
        "print(f(x),f(x + h))\n",
        "print((f(x + h) - f(x))/ h)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "glyr7Ge66Vod",
        "outputId": "a9453031-7f75-4099-cc6f-43456bb112e7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4.55 4.55\n",
            "0.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a = 3.0\n",
        "b = -5.0\n",
        "c = 4.0\n",
        "\n",
        "d = a * b + c\n",
        "print(d)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "84ewlkq46cdU",
        "outputId": "e53a7d28-8b67-46f0-ee66-dadf9de521f7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-11.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "h = 0.0001\n",
        "\n",
        "a = 3.0\n",
        "b = -5.0\n",
        "c = 4.0\n",
        "\n",
        "d1 = a * b + c\n",
        "c += h\n",
        "d2 = a * b + c\n",
        "\n",
        "print('d1: ', d2, '   d2:', d2)\n",
        "print('slope:: ', (d2 - d1)/h)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wPgIe2FC8kaz",
        "outputId": "a0a2af38-10d9-4524-eac8-98c8661a1188"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "d1:  -10.9999    d2: -10.9999\n",
            "slope::  0.9999999999976694\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "So what we saw here is on increment of different variable here, namely a, b, and c. The slope are different. When we bump a by h; what it does is it increment the negative value of the b i.e it is actually increasing the output in negative direction and hence it's slope is negative.\n",
        "\n",
        "Similarly on bumping b we get slope of positive cause on adding on the value of b which is negative produce slighly less negative number and thus slope is positive."
      ],
      "metadata": {
        "id": "mO7Iy9nA-xEt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# class Value:\n",
        "#   def __init__(self, data):\n",
        "#     self.data = data\n",
        "\n",
        "#   def __repr__(self):\n",
        "#     return f\"Value (data = {self.data})\"\n",
        "\n",
        "#   def __add__(self, other): #if a and b are Value object then on a + b, python will do a.__add__(b)\n",
        "#     return Value(self.data + other.data)\n",
        "\n",
        "#   def __mul__(self, other):\n",
        "#     return Value(self.data * other.data)\n",
        "\n",
        "#   def __div__(self, other):\n",
        "#     return Value(self.data/other.data)"
      ],
      "metadata": {
        "id": "xQHxLQfV-nNu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# a = Value(2.0)\n",
        "# b = Value(3.0)\n",
        "# c = a + b\n",
        "# print(a*b + c)"
      ],
      "metadata": {
        "id": "kz5N4CT580Vi"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "LzKlBvQQ-L_O"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class Value:\n",
        "  def __init__(self, data, _prev = (), _op = '', label = ''):\n",
        "    self.data = data\n",
        "    self._prev = _prev\n",
        "    self._op = _op\n",
        "    self.label = label\n",
        "    self.grad = 0 #by default we assume the grad is 0 i.e. no effect.\n",
        "\n",
        "\n",
        "  def __repr__(self):\n",
        "    return f\"Value (data = {self.data})\"\n",
        "\n",
        "  def __add__(self, other): #if a and b are Value object then on a + b, python will do a.__add__(b)\n",
        "    return Value(self.data + other.data, (self, other), '+')\n",
        "\n",
        "  def __mul__(self, other):\n",
        "    return Value(self.data * other.data, (self, other), '*')\n",
        "\n",
        "  def __div__(self, other):\n",
        "    return Value(self.data/other.data, (self, other), '/')"
      ],
      "metadata": {
        "id": "dSXbWYQqAyec"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a = Value(2.0, label = 'a')\n",
        "b = Value(3.0, label = 'b')\n",
        "c = a + b; c.label = 'c'\n",
        "e = a* b; e.label = 'e'\n",
        "d = e - c; d.label = 'd'\n",
        "f = Value(-1, label = 'f')\n",
        "# g = e - d; g.label = 'g'\n",
        "L = d * f; L.label = 'Output'\n",
        "print(d._prev, d._op, c._prev, a._prev)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8f9d050a-ad53-41fb-a8dc-01d5020a5517",
        "id": "H1LqUlR5Ayed"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(Value (data = 6.0), Value (data = 5.0)) - (Value (data = 2.0), Value (data = 3.0)) ()\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from graphviz import Digraph"
      ],
      "metadata": {
        "id": "89V0ppkNVlup"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def trace(root):\n",
        "  nodes, edges = set(), set()\n",
        "  def build(v):\n",
        "    if v not in nodes:\n",
        "      nodes.add(v)\n",
        "      for child in v._prev:\n",
        "        edges.add((child, v))\n",
        "        build(child)\n",
        "  build(root)\n",
        "  return nodes, edges\n",
        "\n",
        "def draw_dot(root):\n",
        "  dot = Digraph(format = 'svg', graph_attr = {'rankdir':'LR'})\n",
        "\n",
        "  nodes, edges = trace(root)\n",
        "  for n in nodes:\n",
        "    uid = str(id(n))\n",
        "\n",
        "    dot.node(name = uid, label =f\"{n.label} | data {n.data:.4f} | grad {n.grad:.4f}\" , shape = 'record')\n",
        "\n",
        "    if n._op: #if value is result of some operation, create an op node for it\n",
        "      dot.node(name = uid + n._op, label = n._op)\n",
        "      dot.edge(uid + n._op, uid)\n",
        "\n",
        "  for n1, n2 in edges:\n",
        "    dot.edge(str(id(n1)), str(id(n2)) + n2._op)\n",
        "\n",
        "  return dot"
      ],
      "metadata": {
        "id": "SjtvqgumEY_x"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "draw_dot(L)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "id": "Y6h1NP3qVR86",
        "outputId": "94caf5df-ecdb-435d-a4c3-4d7cffffcd8f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
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    },
    {
      "cell_type": "code",
      "source": [
        "print(trace(c))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uO4qt_LrVVxq",
        "outputId": "8ab6452e-ffe6-494a-e252-f2af39312f0f"
      },
      "execution_count": null,
      "outputs": [
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            "({Value (data = 3.0), Value (data = 2.0), Value (data = 5.0)}, {(Value (data = 3.0), Value (data = 5.0)), (Value (data = 2.0), Value (data = 5.0))})\n"
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      "cell_type": "code",
      "source": [
        "draw_dot(c)"
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      "metadata": {
        "colab": {
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          "height": 243
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        "id": "ImVsczc6Yz-4",
        "outputId": "46f4a702-35bc-4e8b-ca29-e2d120fc4293"
      },
      "execution_count": null,
      "outputs": [
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      "cell_type": "markdown",
      "source": [
        "Now we backpropagate from output to the intial nodes. As of above figure while backpropagating; first we calculate the derivative of c with respect to c; then derviative of a w.r.t. c and then derivative of a w.r.t. c.\n",
        "\n",
        "\n",
        "This shows how the input: a and b is impacting the output c."
      ],
      "metadata": {
        "id": "bM4l1MBzZajf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def check_grad():\n",
        "\n",
        "  h = 0.0001\n",
        "\n",
        "  a = Value(2.0, label = 'a')\n",
        "  b = Value(3.0, label = 'b')\n",
        "  c = a + b; c.label = 'c'\n",
        "  e = a* b; e.label = 'e'\n",
        "  d = e + c; d.label = 'd'\n",
        "  f = Value(-1, label = 'f')\n",
        "  L = d * f; L.label = 'Output'\n",
        "  L1 = L.data\n",
        "\n",
        "  a = Value(2.0, label = 'a')\n",
        "  b = Value(3.0, label = 'b')\n",
        "  c = a + b; c.label = 'c'\n",
        "  e = a* b; e.label = 'e'\n",
        "  e.data += h\n",
        "  d = e + c; d.label = 'd'\n",
        "  f = Value(-1, label = 'f')\n",
        "  L = d * f; L.label = 'Output'\n",
        "  L2 = L.data\n",
        "\n",
        "  print((L2 - L1)/h)\n",
        "\n",
        "check_grad()"
      ],
      "metadata": {
        "id": "QhsarosLbWt-",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6570a2fb-e939-42ae-c8cb-f5dc874024a9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-0.9999999999976694\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# L = d * f\n",
        "# dL/dd = ? is what we want i.e. f\n",
        "f.grad = d.data\n",
        "d.grad = f.data\n",
        "# dL/de = dl/dd * dd/de == f * d(e+c)/de == f * 1\n",
        "e.grad = f.data * 1\n",
        "c.grad = f.data * 1\n",
        "\n",
        "# dl/db = dl/dd * dd/db = f *(d(e+c)/db) = f*(d(a*b)/db + d(a+b)/db) = f*(a + 1)\n",
        "b.grad = f.data * (a.data + 1)\n",
        "# dl/da = dl/dd * dd/da = f* (d(e + c)/da) = f * (d(ab)/da + d(a + b)/da) = f * (b + 1)\n",
        "a.grad = f.data * (b.data + 1)\n"
      ],
      "metadata": {
        "id": "bvRnXo_AQYue"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "L.grad = 1.0\n",
        "\n",
        "draw_dot(L)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "id": "Iu8-p_a1N7r6",
        "outputId": "57d314f9-9895-4b94-c800-c57dc971f307"
      },
      "execution_count": null,
      "outputs": [
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      "source": [
        "print(b.data, b.grad)"
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      "metadata": {
        "colab": {
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        },
        "id": "ZJUM4Ihs0qLF",
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      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "3.0 -3.0\n"
          ]
        }
      ]
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      "source": [
        "a.data += 0.1 * a.grad\n",
        "b.data += 0.1 * b.grad\n",
        "f.data += 0.1 * f.grad\n",
        "# c.data += c.grad\n",
        "\n",
        "e = a * b\n",
        "c = a + b\n",
        "d = e + c\n",
        "L = f * d\n",
        "\n",
        "draw_dot(L)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
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    },
    {
      "cell_type": "markdown",
      "source": [
        "# Here the data of output node is moving forward to 0"
      ],
      "metadata": {
        "id": "-LjIUZBB0YNc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "---\n",
        "# A NEURON"
      ],
      "metadata": {
        "id": "9k_TNh_21Ran"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class Value:\n",
        "  def __init__(self, data, _prev = (), _op = '', label = ''):\n",
        "    self.data = data\n",
        "    self._prev = _prev\n",
        "    self._op = _op\n",
        "    self.label = label\n",
        "    self.grad = 0 #by default we assume the grad is 0 i.e. no effect.\n",
        "\n",
        "\n",
        "  def __repr__(self):\n",
        "    return f\"Value (data = {self.data})\"\n",
        "\n",
        "  def __add__(self, other): #if a and b are Value object then on a + b, python will do a.__add__(b)\n",
        "    return Value(self.data + other.data, (self, other), '+')\n",
        "\n",
        "  def __mul__(self, other):\n",
        "    return Value(self.data * other.data, (self, other), '*')\n",
        "\n",
        "  def __div__(self, other):\n",
        "    return Value(self.data/other.data, (self, other), '/')\n",
        "\n",
        "  # def tanh(self):\n",
        "  #   n = self.data\n",
        "  #   t = (math.exp(2*n) - 1)/(math.exp(2*x) + 1)\n",
        "  #   out = Value(t, (self, ), 'tanh')\n",
        "  #   return out\n",
        "  def tanh(self):\n",
        "    return Value((math.exp(2*self.data) - 1)/(math.exp(2*self.data) + 1), (self, ), 'tanh')"
      ],
      "metadata": {
        "id": "Tp92ti-G1bmL"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x1 = Value(-2.0, label = 'x1')\n",
        "x2 = Value(0.9, label = 'x2')\n",
        "\n",
        "w1 = Value(3.0, label = 'w1')\n",
        "w2 = Value(-1.0, label = 'w2')\n",
        "\n",
        "b = Value(4.0, label = 'b')\n",
        "print(b.data)\n",
        "\n",
        "x1w1 = x1 * w1; x1w1.label = 'x1w1'\n",
        "x2w2 = x2 * w2; x2w2.label = 'x2w2'\n",
        "\n",
        "x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1w1 + x2w2'\n",
        "n = x1w1x2w2 + b; n.label = 'n'\n",
        "o = n.tanh(); o.label = 'Output'\n",
        "draw_dot(o)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 495
        },
        "id": "M4LlAnyB7Tmm",
        "outputId": "fd23afbb-20b8-4dd9-f411-ec07e990ffbf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4.0\n"
          ]
        },
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      "source": [
        "#backpropagation\n",
        "o.grad = 1.0\n",
        "\n",
        "# do/dn = 1 - tanh(n) ** 2 = 1 - o** 2\n",
        "n.grad = 1 - o.data ** 2\n",
        "\n",
        "#do/db = do/dn * dn/db = (1 - o**2) * 1 = 1 - o**2\n",
        "b.grad = 1- o.data ** 2\n",
        "\n",
        "#d(o)/d(x1w1x2w2) = do/dn * dn/d(x1w1x2w2) = (1 - o** 2) * 1\n",
        "x1w1x2w2.grad = 1 - o.data** 2\n",
        "\n",
        "# do/d(x1w1) = do/dn * dn/d(x1w1x2w2) * d(x1w1x2w2)/d(x1w1) == (1 - o**2) (1) (1)\n",
        "x2w2.grad = 1- o.data**2\n",
        "x1w1.grad = 1 - o.data** 2\n",
        "\n",
        "# do/dx1 = do/dn * dn/(d(x1w1x2w2))* d(x1w1x2w2)/dx1w1 * d(x1w1)/dx1 = (1 - o**2) * (1) * (w1)\n",
        "x1.grad = (1 - o.data ** 2) * w1.data\n",
        "w1.grad = (1 - o.data ** 2) * x1.data\n",
        "\n",
        "x2.grad = (1 - o.data ** 2)  * w2.data\n",
        "w2.grad = (1- o.data**2) * x2.data"
      ],
      "metadata": {
        "id": "B9xXB4H9-4qP"
      },
      "execution_count": null,
      "outputs": []
    },
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      "cell_type": "code",
      "source": [
        "def check_grad():\n",
        "\n",
        "  h = 0.001\n",
        "\n",
        "  x1 = Value(-2.0, label = 'x1')\n",
        "  x2 = Value(0.9, label = 'x2')\n",
        "\n",
        "  w1 = Value(3.0, label = 'w1')\n",
        "  w2 = Value(-1.0, label = 'w2')\n",
        "\n",
        "  b = Value(4.0, label = 'b')\n",
        "\n",
        "  x1w1 = x1 * w1; x1w1.label = 'x1w1'\n",
        "  x2w2 = x2 * w2; x2w2.label = 'x2w2'\n",
        "\n",
        "  x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1w1 + x2w2'\n",
        "  n = x1w1x2w2 + b; n.label = 'n'\n",
        "  o = n.tanh(); o.label = 'Output'\n",
        "  o1 = o.data\n",
        "\n",
        "  x1 = Value(-2.0, label = 'x1')\n",
        "  x2 = Value(0.9, label = 'x2')\n",
        "  w1 = Value(3.0, label = 'w1')\n",
        "  w2 = Value(-1.0, label = 'w2')\n",
        "  x1.data += h\n",
        "\n",
        "  b = Value(4.0, label = 'b')\n",
        "\n",
        "  x1w1 = x1 * w1; x1w1.label = 'x1w1'\n",
        "  x2w2 = x2 * w2; x2w2.label = 'x2w2'\n",
        "\n",
        "  x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1w1 + x2w2'\n",
        "  n = x1w1x2w2 + b; n.label = 'n'\n",
        "  o = n.tanh(); o.label = 'Output'\n",
        "  o2 = o.data\n",
        "\n",
        "  print((o2 - o1)/h)\n",
        "\n",
        "check_grad()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gju5v5craUp6",
        "outputId": "9b80fc59-c758-48e5-c261-ea45bf3bae3d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.036219559918171385\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "draw_dot(o)"
      ],
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          "height": 477
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        "id": "83IJQJNTSfha",
        "outputId": "b86a33bf-f277-427f-eb9e-e9c4adb97b32"
      },
      "execution_count": null,
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          "metadata": {},
          "execution_count": 30
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      "cell_type": "code",
      "source": [
        "class Value:\n",
        "  def __init__(self, data, _prev = (), _op = '', label = ''):\n",
        "    self.data = data\n",
        "    self._prev = _prev\n",
        "    self._op = _op\n",
        "    self.label = label\n",
        "    self.grad = 0 #by default we assume the grad is 0 i.e. no effect.\n",
        "    self._backward = lambda: None\n",
        "\n",
        "\n",
        "  def __repr__(self):\n",
        "    return f\"Value (data = {self.data})\"\n",
        "\n",
        "  def __add__(self, other): #if a and b are Value object then on a + b, python will do a.__add__(b)\n",
        "    out = Value(self.data + other.data, (self, other), '+')\n",
        "\n",
        "    def _backward():\n",
        "      #d(a + b)/da = 1\n",
        "      self.grad = 1 * out.grad\n",
        "      other.grad = 1 * out.grad\n",
        "    out._backward = _backward\n",
        "\n",
        "    return out\n",
        "\n",
        "  def __mul__(self, other):\n",
        "    out = Value(self.data * other.data, (self, other), '*')\n",
        "    #d(ab)/da = b\n",
        "    def _backward():\n",
        "      self.grad = other.data * out.grad\n",
        "      other.grad = self.data * out.grad\n",
        "\n",
        "    out._backward = _backward\n",
        "    return out\n",
        "\n",
        "  def __div__(self, other):\n",
        "    return Value(self.data/other.data, (self, other), '/')\n",
        "\n",
        "  # def tanh(self):\n",
        "  #   n = self.data\n",
        "  #   t = (math.exp(2*n) - 1)/(math.exp(2*x) + 1)\n",
        "  #   out = Value(t, (self, ), 'tanh')\n",
        "  #   return out\n",
        "  def tanh(self):\n",
        "    t = (math.exp(2*self.data) - 1)/(math.exp(2*self.data) + 1)\n",
        "    out = Value(t, (self, ), 'tanh')\n",
        "    # d(tanh(a))/da = 1 - a ** 2\n",
        "    def _backward():\n",
        "      self.grad = (1 - t ** 2) * out.grad\n",
        "    out._backward = _backward\n",
        "\n",
        "    return out"
      ],
      "metadata": {
        "id": "m2InSsc3a2fQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x1 = Value(-2.0, label = 'x1')\n",
        "x2 = Value(0.9, label = 'x2')\n",
        "\n",
        "w1 = Value(3.0, label = 'w1')\n",
        "w2 = Value(-1.0, label = 'w2')\n",
        "\n",
        "b = Value(4.0, label = 'b')\n",
        "print(b.data)\n",
        "\n",
        "x1w1 = x1 * w1; x1w1.label = 'x1w1'\n",
        "x2w2 = x2 * w2; x2w2.label = 'x2w2'\n",
        "\n",
        "x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1w1 + x2w2'\n",
        "n = x1w1x2w2 + b; n.label = 'n'\n",
        "o = n.tanh(); o.label = 'Output'\n",
        "draw_dot(o)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 495
        },
        "id": "jBSGIi4bX5Kj",
        "outputId": "58a148ee-48d2-484b-8be2-890c00e8930e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4.0\n"
          ]
        },
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          "metadata": {},
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      "cell_type": "code",
      "source": [
        "#topological sorting of nodes(Values) such that we can loop on that sort to backpropagate from last node to first node\n",
        "top = []\n",
        "visited = set()\n",
        "def build_top(v):\n",
        "  if v not in visited:\n",
        "    visited.add(v)\n",
        "    for child in v._prev:\n",
        "      build_top(child)\n",
        "    top.append(v)\n",
        "build_top(o)\n",
        "top\n",
        "\n",
        "for i in top:\n",
        "  i._backward()"
      ],
      "metadata": {
        "id": "_T_GQGKzZCfd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class Value:\n",
        "  def __init__(self, data, _prev = (), _op = '', label = ''):\n",
        "    self.data = data\n",
        "    self._prev = _prev\n",
        "    self._op = _op\n",
        "    self.label = label\n",
        "    self.grad = 0.0 #by default we assume the grad is 0 i.e. no effect.\n",
        "    self._backward = lambda: None\n",
        "\n",
        "\n",
        "  def __repr__(self):\n",
        "    return f\"Value (data = {self.data})\"\n",
        "\n",
        "  def __add__(self, other): #if a and b are Value object then on a + b, python will do a.__add__(b)\n",
        "    out = Value(self.data + other.data, (self, other), '+')\n",
        "    def _backward():\n",
        "      #d(a + b)/da = 1\n",
        "      self.grad += 1 * out.grad\n",
        "      other.grad += 1 * out.grad\n",
        "    out._backward = _backward\n",
        "    return out\n",
        "\n",
        "  def __mul__(self, other):\n",
        "    out = Value(self.data * other.data, (self, other), '*')\n",
        "    #d(ab)/da = b\n",
        "    def _backward():\n",
        "      self.grad += other.data * out.grad\n",
        "      other.grad += self.data * out.grad\n",
        "    out._backward = _backward\n",
        "    return out\n",
        "\n",
        "  def __div__(self, other):\n",
        "    return Value(self.data/other.data, (self, other), '/')\n",
        "  # def tanh(self):\n",
        "  #   n = self.data\n",
        "  #   t = (math.exp(2*n) - 1)/(math.exp(2*x) + 1)\n",
        "  #   out = Value(t, (self, ), 'tanh')\n",
        "  #   return out\n",
        "\n",
        "  def tanh(self):\n",
        "    t = (math.exp(2*self.data) - 1)/(math.exp(2*self.data) + 1)\n",
        "    out = Value(t, (self, ), 'tanh')\n",
        "    # d(tanh(a))/da = 1 - a ** 2\n",
        "    def _backward():\n",
        "      self.grad = (1 - t ** 2) * out.grad\n",
        "    out._backward = _backward\n",
        "    return out\n",
        "\n",
        "\n",
        "  def backward(self):\n",
        "    top = []\n",
        "    visited = set()\n",
        "    def build_top(v):\n",
        "      if v not in visited:\n",
        "        visited.add(v)\n",
        "        for child in v._prev:\n",
        "          build_top(child)\n",
        "        top.append(v)\n",
        "    build_top(self)\n",
        "\n",
        "    self.grad = 1\n",
        "    for node in reversed(top):\n",
        "      node._backward()\n"
      ],
      "metadata": {
        "id": "8ZO_2sAR_83-"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x1 = Value(-2.0, label = 'x1')\n",
        "x2 = Value(0.9, label = 'x2')\n",
        "\n",
        "w1 = Value(3.0, label = 'w1')\n",
        "w2 = Value(-1.0, label = 'w2')\n",
        "\n",
        "b = Value(4.0, label = 'b')\n",
        "print(b.data)\n",
        "\n",
        "x1w1 = x1 * w1; x1w1.label = 'x1w1'\n",
        "x2w2 = x2 * w2; x2w2.label = 'x2w2'\n",
        "\n",
        "x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1w1 + x2w2'\n",
        "n = x1w1x2w2 + b; n.label = 'n'\n",
        "o = n.tanh(); o.label = 'Output'\n",
        "draw_dot(o)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 495
        },
        "id": "Jo8OogyRcAD3",
        "outputId": "a38884ea-43be-4d18-da22-8f6eefb9a060"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4.0\n"
          ]
        },
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        "o.backward()\n",
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        "o.backward()\n",
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        "a = Value(3.0, label = 'a')\n",
        "b = a + a; b.label = 'b'\n",
        "\n",
        "b.backward()\n",
        "draw_dot(b)"
      ],
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      "execution_count": null,
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      "source": [
        "class Value:\n",
        "  def __init__(self, data, _prev = (), _op = '', label = ''):\n",
        "    self.data = data\n",
        "    self._prev = _prev\n",
        "    self._op = _op\n",
        "    self.label = label\n",
        "    self.grad = 0.0 #by default we assume the grad is 0 i.e. no effect.\n",
        "    self._backward = lambda: None\n",
        "\n",
        "\n",
        "  def __repr__(self):\n",
        "    return f\"Value (data = {self.data})\"\n",
        "\n",
        "  def __add__(self, other): #if a and b are Value object then on a + b, python will do a.__add__(b)\n",
        "    other = other if isinstance(other, Value) else Value(other)\n",
        "    out = Value(self.data + other.data, (self, other), '+')\n",
        "    def _backward():\n",
        "      #d(a + b)/da = 1\n",
        "      self.grad += 1 * out.grad\n",
        "      other.grad += 1 * out.grad\n",
        "    out._backward = _backward\n",
        "    return out\n",
        "\n",
        "  def __radd__(self, other):\n",
        "    return self + other\n",
        "\n",
        "  def __sub__(self, other):\n",
        "    other = other if isinstance(other, Value) else Value(other)\n",
        "    out = Value(self.data - other.data, (self, other), '-')\n",
        "    def _backward():\n",
        "      #d(a - b)/da = 1\n",
        "      #d(a -b)/db = -1\n",
        "      self.grad += 1 * out.grad\n",
        "      other.grad -= 1 * out.grad\n",
        "    out._backward = _backward\n",
        "    return out\n",
        "\n",
        "  def __rsub__(self, other):\n",
        "    return self - other\n",
        "\n",
        "  def __mul__(self, other):\n",
        "    other = other if isinstance(other, Value) else Value(other)\n",
        "    out = Value(self.data * other.data, (self, other), '*')\n",
        "    #d(ab)/da = b\n",
        "    def _backward():\n",
        "      self.grad += other.data * out.grad\n",
        "      other.grad += self.data * out.grad\n",
        "    out._backward = _backward\n",
        "    return out\n",
        "\n",
        "\n",
        "  def __rmul__(self, other):\n",
        "    return self * other\n",
        "\n",
        "  # def __truediv__(self, other):\n",
        "  #   other = other if isinstance(other, Value) else Value(other)\n",
        "  #   return Value(self.data/other.data, (self, other), '/')\n",
        "\n",
        "  # def __truediv__(self, other):\n",
        "  #   other = other if isinstance(other, Value) else Value(other)\n",
        "  #   out = Value(self.data*(other.data ** -1), (self, other), '/')\n",
        "  #   def _backward():\n",
        "  #     #idk so let's just follow the tutorial\n",
        "  #   out._backward = _backward\n",
        "  #   return out\n",
        "\n",
        "  def __truediv__(self, other):\n",
        "    return self * (other ** -1)\n",
        "\n",
        "\n",
        "  def __rtruediv__(self, other):\n",
        "    return other * (self ** -1)\n",
        "\n",
        "\n",
        "  def tanh(self):\n",
        "    t = (math.exp(2*self.data) - 1)/(math.exp(2*self.data) + 1)\n",
        "    out = Value(t, (self, ), 'tanh')\n",
        "    # d(tanh(a))/da = 1 - a ** 2\n",
        "    def _backward():\n",
        "      self.grad = (1 - t ** 2) * out.grad\n",
        "    out._backward = _backward\n",
        "    return out\n",
        "\n",
        "  def exp(self):\n",
        "    x = self. data\n",
        "    out = Value(math.exp(x), (self, ), 'exp')\n",
        "    def _backward():\n",
        "      self.grad += out.data * out.grad\n",
        "    out._backward = _backward\n",
        "    return out\n",
        "\n",
        "  def __pow__(self, other):\n",
        "    assert isinstance(other, (int, float, Value)), \"please have int or float or Value for this to be valid [for now]\"\n",
        "    other = other if isinstance(other, Value) else Value(other)\n",
        "    out = Value(self.data ** other.data, (self, ), f'** {other.data}')\n",
        "    def _backward():\n",
        "      self.grad += other.data * (self.data ** (other.data - 1)) * out.grad\n",
        "    out._backward = _backward\n",
        "    return out\n",
        "\n",
        "  def backward(self):\n",
        "    top = []\n",
        "    visited = set()\n",
        "    def build_top(v):\n",
        "      if v not in visited:\n",
        "        visited.add(v)\n",
        "        for child in v._prev:\n",
        "          build_top(child)\n",
        "        top.append(v)\n",
        "    build_top(self)\n",
        "\n",
        "    self.grad = 1\n",
        "    for node in reversed(top):\n",
        "      node._backward()\n"
      ],
      "metadata": {
        "id": "X7Er2nXRihHO"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a = Value(2.0, label = 'a')\n",
        "b = Value(3, label = 'b')\n",
        "c = a ** 2\n",
        "c._backward()\n",
        "print(c, c.grad)\n",
        "\n",
        "a - b"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6jL7NO4_nywk",
        "outputId": "605ef0b4-09b4-4305-e47a-f632b7f6c699"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Value (data = 4.0) 0.0\n"
          ]
        },
        {
          "output_type": "execute_result",
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              "Value (data = -1.0)"
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      "cell_type": "code",
      "source": [
        "x1 = Value(-2.0, label = 'x1')\n",
        "x2 = Value(0.9, label = 'x2')\n",
        "\n",
        "w1 = Value(3.0, label = 'w1')\n",
        "w2 = Value(-1.0, label = 'w2')\n",
        "\n",
        "b = Value(4.0, label = 'b')\n",
        "print(b.data)\n",
        "\n",
        "x1w1 = x1 * w1; x1w1.label = 'x1w1'\n",
        "x2w2 = x2 * w2; x2w2.label = 'x2w2'\n",
        "\n",
        "# x1w1x2w2m = x1w1 - x2w2; x1w1x2w2.label = 'x1w1 - x2w2m'\n",
        "x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1w1 + x2w2'\n",
        "\n",
        "n = x1w1x2w2 + b; n.label = 'n'\n",
        "o = n.tanh(); o.label = 'Output'\n",
        "o.backward()\n",
        "draw_dot(o)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 495
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        "id": "KewbA8Pjn2zA",
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      "execution_count": null,
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          "name": "stdout",
          "text": [
            "4.0\n"
          ]
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          "metadata": {},
          "execution_count": 97
        }
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    },
    {
      "cell_type": "code",
      "source": [
        "x1 = Value(-2.0, label = 'x1')\n",
        "x2 = Value(0.9, label = 'x2')\n",
        "\n",
        "w1 = Value(3.0, label = 'w1')\n",
        "w2 = Value(-1.0, label = 'w2')\n",
        "\n",
        "b = Value(-5.0, label = 'b')\n",
        "print(b.data)\n",
        "\n",
        "x1w1 = x1 * w1; x1w1.label = 'x1w1'\n",
        "x2w2 = x2 * w2; x2w2.label = 'x2w2'\n",
        "\n",
        "# x1w1x2w2m = x1w1 - x2w2; x1w1x2w2.label = 'x1w1 - x2w2m'\n",
        "x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1w1 + x2w2'\n",
        "\n",
        "n = x1w1x2w2 - b; n.label = 'n'\n",
        "o = n.tanh(); o.label = 'Output'\n",
        "o.backward()\n",
        "draw_dot(o)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 495
        },
        "id": "9YeQExfT6Hbj",
        "outputId": "4351ce3d-d98c-4d1a-dee7-6c26e4e448a8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-5.0\n"
          ]
        },
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    {
      "cell_type": "code",
      "source": [
        "x1 = Value(-2.0, label = 'x1')\n",
        "x2 = Value(0.9, label = 'x2')\n",
        "\n",
        "w1 = Value(3.0, label = 'w1')\n",
        "w2 = Value(-1.0, label = 'w2')\n",
        "\n",
        "b = Value(-5.0, label = 'b')\n",
        "# print(b.data)\n",
        "\n",
        "x1w1 = x1 * w1; x1w1.label = 'x1w1'\n",
        "x2w2 = x2 * w2; x2w2.label = 'x2w2'\n",
        "\n",
        "# x1w1x2w2m = x1w1 - x2w2; x1w1x2w2.label = 'x1w1 - x2w2m'\n",
        "x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1w1 + x2w2'\n",
        "\n",
        "n = x1w1x2w2 + b; n.label = 'n'\n",
        "\n",
        "#-------------\n",
        "e = (2 * n).exp()\n",
        "o = (e -1 )/(e + 1); o.label = 'Output'\n",
        "# o = n.tanh(); o.label = 'Output'\n",
        "#--------\n",
        "\n",
        "o.backward()\n",
        "draw_dot(o)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 556
        },
        "id": "Ln2gm9Ny7JRh",
        "outputId": "3eebed24-d78d-4d36-810e-c5a1e42a51d4"
      },
      "execution_count": null,
      "outputs": [
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    {
      "cell_type": "code",
      "source": [
        "#data to check with if the karpathy and Me are on same page\n",
        "\n",
        "x1 = Value(2.0, label = 'x1')\n",
        "x2 = Value(0.0, label = 'x2')\n",
        "\n",
        "w1 = Value(-3.0, label = 'w1')\n",
        "w2 = Value(1.0, label = 'w2')\n",
        "\n",
        "b = Value(6.8813735870195432, label = 'b')\n",
        "\n",
        "x1w1 = x1 * w1; x1w1.label = 'x1w1'\n",
        "x2w2 = x2 * w2; x2w2.label = 'x2w2'\n",
        "\n",
        "# x1w1x2w2m = x1w1 - x2w2; x1w1x2w2.label = 'x1w1 - x2w2m'\n",
        "x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1w1 + x2w2'\n",
        "\n",
        "n = x1w1x2w2 + b; n.label = 'n'\n",
        "\n",
        "#-------------\n",
        "e = (2 * n).exp()\n",
        "o = (e -1 ) / ((e + 1)); o.label = 'Output'\n",
        "# o = n.tanh(); o.label = 'Output'\n",
        "#--------\n",
        "\n",
        "o.backward()\n",
        "draw_dot(o)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 556
        },
        "id": "XrE6MwKP9Pd4",
        "outputId": "72e63269-7174-4c6f-892c-a6b24c0756ec"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
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          },
          "metadata": {},
          "execution_count": 101
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "\n",
        "\n",
        "x1 = torch.Tensor([2.0]).double(); x1.requires_grad = True\n",
        "w1 = torch.Tensor([0]).double(); w1.requires_grad = True\n",
        "x2 = torch.Tensor([-3.0]).double(); x2.requires_grad = True\n",
        "w2 = torch.Tensor([1.0]).double(); w2.requires_grad = True\n",
        "\n",
        "b = torch.Tensor([6.88]).double(); b.requires_grad = True\n",
        "\n",
        "n = x1 * w1 + x2 * w2 + b\n",
        "o = torch.tanh(n)\n",
        "\n",
        "print(o.data.item())\n",
        "o.backward()\n",
        "\n",
        "\n",
        "print('======')\n",
        "print('x2', x2.grad.item())\n",
        "print('x2', w2.grad.item())\n",
        "print('x1', x1.grad.item())\n",
        "print('w1', w1.grad.item())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yqfG72Cb940J",
        "outputId": "8a486c3f-5b27-4beb-a1f0-54e119207adc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.99914745060906\n",
            "======\n",
            "x2 0.0017043719414160845\n",
            "x2 -0.0051131158242482535\n",
            "x1 0.0\n",
            "w1 0.003408743882832169\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "x1 = torch.Tensor([2.0]).double(); x1.requires_grad = True\n",
        "w1 = torch.Tensor([0.9]).double(); w1.requires_grad = True\n",
        "x2 = torch.Tensor([3.0]).double(); x2.requires_grad = True\n",
        "w2 = torch.Tensor([-1.0]).double(); w2.requires_grad = True\n",
        "\n",
        "b = torch.Tensor([-5.0]).double(); b.requires_grad = True\n",
        "\n",
        "n = x1 * w1 + x2 * w2 + b\n",
        "o = torch.tanh(n)\n",
        "\n",
        "print(o.data.item())\n",
        "o.backward()\n",
        "\n",
        "\n",
        "print('======')\n",
        "print('x2', x2.grad.item())\n",
        "print('x2', w2.grad.item())\n",
        "print('x1', x1.grad.item())\n",
        "print('w1', w1.grad.item())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uox10QDbJe78",
        "outputId": "b915ac0b-9000-4661-ea8b-974bf90cb33b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-0.9999917628572959\n",
            "======\n",
            "x2 -1.6474217557776724e-05\n",
            "x2 4.942265267333017e-05\n",
            "x1 1.4826795409223097e-05\n",
            "w1 3.294843511555345e-05\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import random\n",
        "#single layer\n",
        "class Neuron:\n",
        "  def __init__(self, nin):\n",
        "    self.w = [Value(random.uniform(-1, 1)) for _ in range(nin)]\n",
        "    self.b = Value(random.uniform(-1, 1))\n",
        "\n",
        "  def parameters(self):\n",
        "    return self.w + [self.b]\n",
        "\n",
        "  def __call__(self, x):\n",
        "    #w * x + b\n",
        "    # zip(self.w, x)\n",
        "    activation = sum((wi * xi for wi, xi in zip(self.w, x)), self.b) #initializing sum equal to self.b and adding on top of it\n",
        "    out = activation.tanh()\n",
        "    return out\n",
        "\n",
        "\n",
        "x = [2.0, 3.0]\n",
        "n = Neuron(2)\n",
        "n(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "D_5wKsR0Jwmy",
        "outputId": "778fb9f6-1480-4874-ab73-4547d7b5e31c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Value (data = 0.9960893966011871)"
            ]
          },
          "metadata": {},
          "execution_count": 175
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#multiple layers\n",
        "class Layer:\n",
        "  def __init__(self, nin, nout):\n",
        "    self.neurons = [Neuron(nin) for _ in range(nout)]\n",
        "\n",
        "  def parameters(self):\n",
        "    # params = []\n",
        "    # for neuron in self.neurons:\n",
        "    #   ps = neuron.paramters()\n",
        "    #   params.extend(ps)\n",
        "    # return params\n",
        "    return [p for neuron in self.neurons for p in neuron.parameters()]\n",
        "\n",
        "\n",
        "  def __call__(self, x):\n",
        "    out = [n(x) for n in self.neurons]\n",
        "    return out[0] if len(out) == 1 else out\n",
        "\n",
        "\n",
        "x = [2.0, 3.0]\n",
        "n = Layer(2, 3)\n",
        "n(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fc2E5iOmMq-8",
        "outputId": "075ec2a3-e390-41bf-8da1-0dd16cdcc63b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[Value (data = 0.9986620079485523),\n",
              " Value (data = -0.9968895174558812),\n",
              " Value (data = -0.9937103818794959)]"
            ]
          },
          "metadata": {},
          "execution_count": 176
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "class MLP:\n",
        "  def __init__(self, nin, nouts):\n",
        "    sz = [nin] + nouts\n",
        "    self.layers = [Layer(sz[i], sz[i+ 1]) for i in range(len(nouts))]\n",
        "\n",
        "\n",
        "  def parameters(self):\n",
        "    return [p for layer in self.layers for p in layer.parameters()]\n",
        "\n",
        "  def __call__(self, x):\n",
        "    for layer in self.layers:\n",
        "      x = layer(x)\n",
        "    return x\n",
        "\n",
        "\n",
        "x = [2.0, 3.0, -1.0]\n",
        "n = MLP(3, [4,4,1]) #three layers with each having one nodes in it...the input layer is x i.e. has three nodes on it\n",
        "n(x)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zECKFh3CgYjU",
        "outputId": "62139a8a-6e8e-492f-d557-ff19fd6782d1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Value (data = 0.667576620583414)"
            ]
          },
          "metadata": {},
          "execution_count": 183
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# draw_dot(n(x))"
      ],
      "metadata": {
        "id": "ErVSUOYDiP-S"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "xs = [\n",
        "    [2, 3, -1],\n",
        "    [3, -1, 0.5],\n",
        "    [0.5, 1, 1],\n",
        "    [1 ,1, -1]\n",
        "]\n",
        "\n",
        "\n",
        "ys = [1, -1, -1, 1]"
      ],
      "metadata": {
        "id": "1g40cA5iilfD"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ypred = [n(x) for x in xs]\n",
        "loss = sum((yout - yht) ** 2 for yht, yout in zip(ys, ypred))\n",
        "loss"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "18SHi5IUjoUp",
        "outputId": "a33125b1-c6ea-4b7f-edfb-3ffaf4097822"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Value (data = 0.12992790838643037)"
            ]
          },
          "metadata": {},
          "execution_count": 261
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "loss.backward()"
      ],
      "metadata": {
        "id": "h3vPsa0DnUIs"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for p in n.parameters():\n",
        "  p.data -= 0.01 * p.grad"
      ],
      "metadata": {
        "id": "Pkp5owXdoBU_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# n.layers[0].neurons[0].w[0].grad\n",
        "ypred"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FQ9YslZHn5aN",
        "outputId": "f4178f9e-5ab0-44e7-fc18-e38df2edeb9c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[Value (data = 0.8405243738902637),\n",
              " Value (data = -0.999134149335222),\n",
              " Value (data = -0.9955576092722607),\n",
              " Value (data = 0.6767741524404548)]"
            ]
          },
          "metadata": {},
          "execution_count": 264
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# draw_dot(loss)"
      ],
      "metadata": {
        "id": "AU_g3WRcoEFN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Repeat this::\n",
        "ypred = [n(x) for x in xs]\n",
        "loss = sum((yout - yht) ** 2 for yht, yout in zip(ys, ypred))\n",
        "print(loss)\n",
        "loss.backward()\n",
        "for p in n.parameters():\n",
        "  p.data -= 0.01 * p.grad\n",
        "ypred"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-1TW0PIvoU95",
        "outputId": "a54316f7-57c6-4d23-a9d6-75ec94e5eb8f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Value (data = 1.2293530007899813e-08)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[Value (data = 0.9999260640215463),\n",
              " Value (data = -0.9999990220686588),\n",
              " Value (data = -0.9999712498008604),\n",
              " Value (data = 0.9999225437491372)]"
            ]
          },
          "metadata": {},
          "execution_count": 287
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "here we can see as we rerun this cell multiple time the loss data goes on decreasing and the ypred is approx equal to the ys"
      ],
      "metadata": {
        "id": "VYyX-BcwuR5f"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "n.parameters() #these are my weight and biases [trained one]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QkaUKQJYujSQ",
        "outputId": "a1221e32-b779-4d19-832d-d7028039e6e1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[Value (data = -1.6059188838003848),\n",
              " Value (data = -3.919090702777019),\n",
              " Value (data = 3.26062541250129),\n",
              " Value (data = -2.5658174728185568),\n",
              " Value (data = 2.198271545279142),\n",
              " Value (data = 3.0541791833140057),\n",
              " Value (data = -2.1479743420508703),\n",
              " Value (data = 2.7671426619488875),\n",
              " Value (data = 0.22611237119836772),\n",
              " Value (data = 2.3508822228626785),\n",
              " Value (data = -0.9269100402959847),\n",
              " Value (data = 0.23791065104697978),\n",
              " Value (data = -0.09086947413297673),\n",
              " Value (data = -0.7907942707320443),\n",
              " Value (data = 3.9974246020121003),\n",
              " Value (data = 1.5125306408017176),\n",
              " Value (data = 1.148023516468438),\n",
              " Value (data = 0.7602806448868945),\n",
              " Value (data = -0.26613275196684744),\n",
              " Value (data = 0.22653173740877028),\n",
              " Value (data = -0.8101190071303758),\n",
              " Value (data = 1.014215072484437),\n",
              " Value (data = 2.864036874089211),\n",
              " Value (data = 0.22676611534313473),\n",
              " Value (data = 3.076002262632313),\n",
              " Value (data = 0.5807297247400748),\n",
              " Value (data = 1.23862195942793),\n",
              " Value (data = 0.14590722866832598),\n",
              " Value (data = -0.3611763520271301),\n",
              " Value (data = 2.2464904384172817),\n",
              " Value (data = 0.7947101777067418),\n",
              " Value (data = -2.3406403039919637),\n",
              " Value (data = -1.8264813089475445),\n",
              " Value (data = 2.343033659138578),\n",
              " Value (data = -0.739206865651042),\n",
              " Value (data = -0.0409374740867473),\n",
              " Value (data = -0.6556105002843172),\n",
              " Value (data = -3.3924635930291727),\n",
              " Value (data = -3.1652577393866204),\n",
              " Value (data = 0.7148658675604224),\n",
              " Value (data = -0.5925289537873374)]"
            ]
          },
          "metadata": {},
          "execution_count": 288
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for k in range(20):\n",
        "  #forward pass\n",
        "  ypred = [n(x) for x in xs]\n",
        "  loss = sum((yout - yht)** 2 for yht, yout in zip(ys, ypred))\n",
        "\n",
        "  #back pass\n",
        "  for p in n.parameters():\n",
        "    p.grad = 0\n",
        "  loss.backward()\n",
        "\n",
        "  #update\n",
        "  for p in n.parameters():\n",
        "\n",
        "    p.data -= 0.01 * p.grad  # here we have p.grad; remember to flush this value in back pass such that it won't accumulate again and again\n",
        "\n",
        "  print(k, loss.data)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ARbiqVTEuw_V",
        "outputId": "d8409076-0dc0-41c1-cbdc-e06e3e2ec66f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0 5.638626433679897e-11\n",
            "1 5.6386264285070796e-11\n",
            "2 5.6386264234518086e-11\n",
            "3 5.638626418278992e-11\n",
            "4 5.638626413106174e-11\n",
            "5 5.638626408050939e-11\n",
            "6 5.638626402995668e-11\n",
            "7 5.6386263978228516e-11\n",
            "8 5.638626392650034e-11\n",
            "9 5.638626387594798e-11\n",
            "10 5.638626382539528e-11\n",
            "11 5.638626377366711e-11\n",
            "12 5.6386263721938934e-11\n",
            "13 5.638626367138658e-11\n",
            "14 5.6386263620833875e-11\n",
            "15 5.63862635691057e-11\n",
            "16 5.638626351737753e-11\n",
            "17 5.6386263466825175e-11\n",
            "18 5.638626341627247e-11\n",
            "19 5.63862633645443e-11\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ypred"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "V7JGWsUQvOTc",
        "outputId": "f5c6d340-7dc3-480c-d403-cd337d0fd776"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[Value (data = 0.9999947045956272),\n",
              " Value (data = -0.9999999986106696),\n",
              " Value (data = -0.9999994339555406),\n",
              " Value (data = 0.9999947061783527)]"
            ]
          },
          "metadata": {},
          "execution_count": 295
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "JBNOhlpevWBG"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}