Softmax with Vanishing Gradient Problem

soft_var.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "scratchpad",
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/ariG23498/292c362efca9a177a252390a144aebb4/scratchpad.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lIYdn1woOS1n"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fvDYY2wt4GOr"
      },
      "source": [
        "a = np.random.normal(0,100,size=(10000))\n",
        "\n",
        "exp_a = np.exp(a)\n",
        "sum_exp_a = np.sum(exp_a)\n",
        "\n",
        "soft = exp_a/sum_exp_a"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 368
        },
        "id": "MaFlngHE4eK1",
        "outputId": "b0cd3412-43a7-457b-aea9-1d01d3dcc660"
      },
      "source": [
        "plt.hist(a)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([  16.,  121.,  543., 1688., 2673., 2780., 1550.,  518.,   98.,\n",
              "          13.]),\n",
              " array([-371.75536595, -296.81752459, -221.87968323, -146.94184188,\n",
              "         -72.00400052,    2.93384084,   77.87168219,  152.80952355,\n",
              "         227.74736491,  302.68520626,  377.62304762]),\n",
              " <a list of 10 Patch objects>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "0F5lL3jo4g0P",
        "outputId": "6007e166-4f22-4cdf-f4bb-3c27bc127f95"
      },
      "source": [
        "plt.plot(soft)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f33f691c2d0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD4CAYAAAD8Zh1EAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAP1klEQVR4nO3df5BdZ13H8feHpOG3tCUrlCQlQYNjcNTWnVrE0Y5ASTva/OGPSUaGgpXMqFUUBqcdnIr1L8BBZKhAEEQZaSmVwUwNRoE6Oo6t3Q5QmpTQJQWS8KNLwXaQAVr9+sc9hdvt7t6T9CZ379P3a+ZOz3nOs/d+n/tsP7l7zj3npKqQJE2/x026AEnSeBjoktQIA12SGmGgS1IjDHRJasTaSb3w+vXra/PmzZN6eUmaSrfddtvXqmpmqW0TC/TNmzczNzc3qZeXpKmU5AvLbXOXiyQ1wkCXpEYY6JLUCANdkhphoEtSI0YGepL3JLknyR3LbE+StyaZT3J7knPHX6YkaZQ+n9DfC2xfYftFwNbusRt4+6MvS5J0vEYGelX9G/D1FbrsAP62Bm4GTk9y1rgKlDRZVcUH547wnQf/d9KlaIRx7EPfABwZWj/atT1Ckt1J5pLMLSwsjOGlJZ1s/3THV3jtDbfzlo/eNelSNMIpPShaVXuqaraqZmdmljxzVdIqc/+3HwDg3m9+Z8KVaJRxBPoxYNPQ+sauTZJ0Co0j0PcCL+u+7XI+cF9VfXkMzytJOg4jL86V5FrgAmB9kqPAHwOnAVTVO4B9wMXAPPAt4BUnq1hJ0vJGBnpV7RqxvYDfGVtFkqQT4pmiktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCX1EvVpCvQKAa6pBWFTLoE9WSgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SSsqPOd/WhjoknqJVwBY9Qx0Sb14ca7Vz0CXtCIvzjU9DHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWpEr0BPsj3JoSTzSa5YYvvZSW5K8okktye5ePylSpJWMjLQk6wBrgEuArYBu5JsW9Ttj4Drq+ocYCfwl+MuVJK0sj6f0M8D5qvqcFV9F7gO2LGoTwE/0C0/DfjS+EqUtBp4ba7Vr0+gbwCODK0f7dqGvR54aZKjwD7gd5d6oiS7k8wlmVtYWDiBciWdcl6ba2qM66DoLuC9VbURuBh4X5JHPHdV7amq2aqanZmZGdNLS5KgX6AfAzYNrW/s2oZdBlwPUFX/CTwBWD+OAiVJ/fQJ9FuBrUm2JFnH4KDn3kV9vgi8ECDJjzIIdPepSNIpNDLQq+pB4HJgP3Ang2+zHEhydZJLum6vAV6Z5FPAtcDLq7y/iSSdSmv7dKqqfQwOdg63XTW0fBB4wXhLkyQdD88UlaRGGOiS1AgDXZIaYaBLWplfb5gaBrqkXjxhdPUz0CWpEQa6pF7c87L6GeiSVua+lqlhoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CX14m3fVz8DXZIaYaBLWpEXW5weBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuaUWeTzQ9DHRJvcQvpK96vQI9yfYkh5LMJ7limT6/luRgkgNJ3j/eMiVJo6wd1SHJGuAa4MXAUeDWJHur6uBQn63AlcALquobSX7wZBUsSVpan0/o5wHzVXW4qr4LXAfsWNTnlcA1VfUNgKq6Z7xlSpJG6RPoG4AjQ+tHu7ZhzwWem+Q/ktycZPtST5Rkd5K5JHMLCwsnVrGkifBqi6vfuA6KrgW2AhcAu4B3JTl9caeq2lNVs1U1OzMzM6aXlnQyeSx0evQJ9GPApqH1jV3bsKPA3qp6oKruBj7LIOAlSadIn0C/FdiaZEuSdcBOYO+iPh9m8OmcJOsZ7II5PMY6JUkjjAz0qnoQuBzYD9wJXF9VB5JcneSSrtt+4N4kB4GbgNdW1b0nq2hJ0iON/NoiQFXtA/YtartqaLmAV3cPSdIEeKaoJDXCQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAl9VLeu2jVM9AlrSjeqmhqGOiS1AgDXZIaYaBLUiMMdElqhIEuaUXlveemhoEuSY0w0CX1Eu8uuuoZ6JLUCANdkhphoEtSIwx0SWqEgS6pFy/OtfoZ6JJW5MW5poeBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjegV6Em2JzmUZD7JFSv0++UklWR2fCVKkvoYGehJ1gDXABcB24BdSbYt0e+pwKuAW8ZdpCRptD6f0M8D5qvqcFV9F7gO2LFEvz8F3gB8e4z1SVotvDbXqtcn0DcAR4bWj3Zt35PkXGBTVf3jSk+UZHeSuSRzCwsLx12spFPPS3NNj0d9UDTJ44A3A68Z1beq9lTVbFXNzszMPNqXliQN6RPox4BNQ+sbu7aHPBX4MeBfk3weOB/Y64FRSTq1+gT6rcDWJFuSrAN2Ansf2lhV91XV+qraXFWbgZuBS6pq7qRULEla0shAr6oHgcuB/cCdwPVVdSDJ1UkuOdkFSposj4VOj7V9OlXVPmDforarlul7waMvS9Kq49HRVc8zRSWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjDHRJ/fiF9FXPQJekRhjoklbk+UTTw0CXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXVIvXptr9TPQJakRBrqkFcWrc00NA13Sisp9LVPDQJekRhjoknpxz8vqZ6BLUiMMdElqhIEuSY0w0CWpEQa6JDWiV6An2Z7kUJL5JFcssf3VSQ4muT3Jx5I8e/ylSpJWMjLQk6wBrgEuArYBu5JsW9TtE8BsVf04cAPwxnEXKklaWZ9P6OcB81V1uKq+C1wH7BjuUFU3VdW3utWbgY3jLVPSpHnC6OrXJ9A3AEeG1o92bcu5DPjIUhuS7E4yl2RuYWGhf5WSpJHGelA0yUuBWeBNS22vqj1VNVtVszMzM+N8aUkniRfnmh5re/Q5BmwaWt/YtT1MkhcBrwN+vqq+M57yJEl99fmEfiuwNcmWJOuAncDe4Q5JzgHeCVxSVfeMv0xJ0igjA72qHgQuB/YDdwLXV9WBJFcnuaTr9ibgKcAHk3wyyd5lnk6SdJL02eVCVe0D9i1qu2po+UVjrkuSdJw8U1SSGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCX1EuVl+da7Qx0SWqEgS5JjTDQJakRBrqkXuJ1dFc9A12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEvqxastrn4GuqQVecb/9DDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEb0CPcn2JIeSzCe5Yontj0/ygW77LUk2j7tQSdLKRgZ6kjXANcBFwDZgV5Jti7pdBnyjqn4Y+HPgDeMuVJK0srU9+pwHzFfVYYAk1wE7gINDfXYAr++WbwDeliR1Eq7mc/2tR3jXvx8e99NKWsZd93wTgA9/8ksc+NL9E66mDb/3wq380k88a+zP2yfQNwBHhtaPAj+9XJ+qejDJfcDTga8Nd0qyG9gNcPbZZ59Qwac/6TS2PuMpJ/Szko7flvVP5p8PfpWf+aGnc/qTTpt0OU142hNPzvvYJ9DHpqr2AHsAZmdnT+jT+4XPeyYXPu+ZY61LklrQ56DoMWDT0PrGrm3JPknWAk8D7h1HgZKkfvoE+q3A1iRbkqwDdgJ7F/XZC1zaLf8K8PGTsf9ckrS8kbtcun3ilwP7gTXAe6rqQJKrgbmq2gu8G3hfknng6wxCX5J0CvXah15V+4B9i9quGlr+NvCr4y1NknQ8PFNUkhphoEtSIwx0SWqEgS5Jjcikvl2YZAH4wgn++HoWnYX6GOCYHxsc82PDoxnzs6tqZqkNEwv0RyPJXFXNTrqOU8kxPzY45seGkzVmd7lIUiMMdElqxLQG+p5JFzABjvmxwTE/NpyUMU/lPnRJ0iNN6yd0SdIiBrokNWLqAn3UDaunRZJNSW5KcjDJgSSv6trPTPIvSe7q/ntG154kb+3GfXuSc4ee69Ku/11JLl3uNVeLJGuSfCLJjd36lu7m4vPdzcbXde3L3nw8yZVd+6EkL5nMSPpJcnqSG5J8JsmdSZ7f+jwn+YPu9/qOJNcmeUJr85zkPUnuSXLHUNvY5jXJTyX5dPczb02SkUVV1dQ8GFy+93PAc4B1wKeAbZOu6wTHchZwbrf8VOCzDG7C/Ubgiq79CuAN3fLFwEeAAOcDt3TtZwKHu/+e0S2fMenxjRj7q4H3Azd269cDO7vldwC/1S3/NvCObnkn8IFueVs3948HtnS/E2smPa4Vxvs3wG92y+uA01ueZwa3pLwbeOLQ/L68tXkGfg44F7hjqG1s8wr8V9c33c9eNLKmSb8px/kGPh/YP7R+JXDlpOsa09j+AXgxcAg4q2s7CzjULb8T2DXU/1C3fRfwzqH2h/VbbQ8Gd7z6GPALwI3dL+vXgLWL55jBNfif3y2v7fpl8bwP91ttDwZ377qb7gsIi+evxXnm+/cYPrObtxuBl7Q4z8DmRYE+lnnttn1mqP1h/ZZ7TNsul6VuWL1hQrWMTfcn5jnALcAzqurL3aavAM/olpcb+7S9J28B/hD4v2796cB/V9WD3fpw/Q+7+Tjw0M3Hp2nMW4AF4K+73Ux/leTJNDzPVXUM+DPgi8CXGczbbbQ9zw8Z17xu6JYXt69o2gK9OUmeAvw98PtVdf/wthr809zM90qT/CJwT1XdNulaTqG1DP4sf3tVnQP8D4M/xb+nwXk+A9jB4B+zZwFPBrZPtKgJmMS8Tlug97lh9dRIchqDMP+7qvpQ1/zVJGd1288C7unalxv7NL0nLwAuSfJ54DoGu13+Ajg9g5uLw8PrX+7m49M05qPA0aq6pVu/gUHAtzzPLwLurqqFqnoA+BCDuW95nh8yrnk91i0vbl/RtAV6nxtWT4XuiPW7gTur6s1Dm4ZvuH0pg33rD7W/rDtafj5wX/en3X7gwiRndJ+MLuzaVp2qurKqNlbVZgZz9/Gq+nXgJgY3F4dHjnmpm4/vBXZ2347YAmxlcABp1amqrwBHkvxI1/RC4CANzzODXS3nJ3lS93v+0JibnechY5nXbtv9Sc7v3sOXDT3X8iZ9UOEEDkJczOAbIZ8DXjfpeh7FOH6WwZ9jtwOf7B4XM9h3+DHgLuCjwJld/wDXdOP+NDA79Fy/Acx3j1dMemw9x38B3/+Wy3MY/I86D3wQeHzX/oRufb7b/pyhn39d914cosfR/wmP9SeBuW6uP8zg2wxNzzPwJ8BngDuA9zH4pkpT8wxcy+AYwQMM/hK7bJzzCsx279/ngLex6MD6Ug9P/ZekRkzbLhdJ0jIMdElqhIEuSY0w0CWpEQa6JDXCQJekRhjoktSI/weefeWmNQvatwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O7U3GpeH4uvg"
      },
      "source": [
        "a = np.random.normal(0,100,size=(10000))\n",
        "b = a/100\n",
        "\n",
        "exp_b = np.exp(b)\n",
        "sum_exp_b = np.sum(exp_b)\n",
        "\n",
        "soft = exp_b/sum_exp_b"
      ],
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 368
        },
        "id": "89xBxvUh5ATO",
        "outputId": "2b5baff5-7cb6-4222-8a76-43d7077a02bc"
      },
      "source": [
        "plt.hist(a)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([  16.,  109.,  604., 1622., 2845., 2803., 1468.,  446.,   80.,\n",
              "           7.]),\n",
              " array([-379.70849519, -302.57685139, -225.44520758, -148.31356378,\n",
              "         -71.18191998,    5.94972383,   83.08136763,  160.21301143,\n",
              "         237.34465523,  314.47629904,  391.60794284]),\n",
              " <a list of 10 Patch objects>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "kGtW1A8C5CFx",
        "outputId": "d2abf261-18cf-4903-dcf9-41ffd82e3afe"
      },
      "source": [
        "plt.plot(soft)"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f33f6a8c950>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}