Softmax_Temperature.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "<a href=\"https://colab.research.google.com/github/sascha-kirch/ML_Notebooks/blob/main/Softmax_Temperature.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Softmax Temperature Playground\n",
        "\n",
        "The Softmax operation is a commonly used transformation from logits (predictions of a classifier) to a probability distribution, where the sum of all values is 1.\n",
        "\n",
        "The Softmax operation can be enhanced by a temperature value that controls the \"smoothness\" of the resulting distribution, a technique often used in knowledge distilation or reinforcement learning. \n",
        "\n",
        "In this notebook we explore the effect of the temperature on the resulting distribution.\n",
        "\n",
        "- Step 1: Simulate Data\n",
        "- Step 2: Calculate Softmax\n",
        "- Step 3: Interpretation\n",
        "\n",
        "Softmax Equation:\n",
        "$P(x)^{(i)} = \\frac{e^{\\frac{x_i}{\\tau}}}{\\sum_j e^{\\frac{x_j}{\\tau}}}$, \n",
        "\n",
        "where $x$ are the input logits, $i$ is the index of the i-th logit, and $\\tau$ is the temperature with $\\tau > 0$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OPNHho4GZqBg"
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "id": "UaQWwU6Ncz6g"
      },
      "outputs": [],
      "source": [
        "def plot(labels, logits, title):\n",
        "  fig, ax = plt.subplots()\n",
        "  colors = ['#1b9e77', '#a9f971', '#fdaa48','#6890F0','#A890F0']\n",
        "  ax.bar(labels, logits, color=colors)\n",
        "  ax.set_title(title)\n",
        "\n",
        "  plt.show()\n",
        "\n",
        "def softmax(x, temp):\n",
        "    \"\"\"Compute softmax values for each sets of scores in x.\"\"\"\n",
        "    return np.exp(np.divide(x,temp)) / np.sum(np.exp(np.divide(x,temp)), axis=0)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Step 1: Simulate data\n",
        "Simulate prediction scores of a classifier with 10 classes"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ERSZ7KOGZv2Q"
      },
      "outputs": [],
      "source": [
        "logits = [\n",
        "    0.4,\n",
        "    0.3,\n",
        "    0.1,\n",
        "    0.02,\n",
        "    0.38,\n",
        "    0.18,\n",
        "    0.35,\n",
        "    0.44,\n",
        "    0.22,\n",
        "    0.59,\n",
        "]\n",
        "labels = [i for i in range(len(logits))]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "id": "uE5yaEzdagLw",
        "outputId": "629bbf78-3db7-46ac-ba04-cf6071968357"
      },
      "outputs": [
        {
          "data": {
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Vr7RmzRolJCQc9nGFhYVqamoKbfX19UdwSgAAYCmsKyMJCQmKiYmR1+tts9/r9SoxMbHd+n/+85/64osvdPHFF4f2BQKBH554wABt27ZN48aNa3ecw+GQw+EIZzQAANBHhXVlJDY2VmlpafJ4PKF9gUBAHo9HWVlZ7dZPmDBBH3zwgerq6kLbT3/6U5177rmqq6tTcnJy988AAAD0aWFdGZEkt9ut+fPnKz09XRkZGSotLVVzc7NcLpckKS8vT0lJSSopKVFcXJwmT57c5vjhw4dLUrv9AACgfwo7RnJzc9XY2KiioiI1NDQoNTVVlZWVoZtad+zYoehoPtgVAAAcnrBjRJLy8/OVn5/f4c82bdp00GMfffTRrjwlAACIUFzCAAAApogRAABgihgBAACmiBEAAGCKGAEAAKa69G4aAH1Dxf1N1iO0k1sQbz0CgKMMV0YAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmBpgPQAARIo/tbitR2jnF7HLrUcADokrIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwFSXYqSsrEwpKSmKi4tTZmamqqurO1371FNPKT09XcOHD9eQIUOUmpqqdevWdXlgAAAQWcKOkYqKCrndbhUXF6u2tlZTp05VTk6Odu/e3eH6kSNH6uabb1ZVVZXef/99uVwuuVwuvfzyy90eHgAA9H1hx8jy5cu1YMECuVwuTZo0SeXl5Ro8eLDWrl3b4frZs2fr5z//uSZOnKhx48apoKBAp59+ujZv3tzt4QEAQN8XVoy0tLSopqZG2dnZBx4gOlrZ2dmqqqo65PHBYFAej0fbtm3TOeec0+k6v98vn8/XZgMAAJFpQDiL9+zZo9bWVjmdzjb7nU6ntm7d2ulxTU1NSkpKkt/vV0xMjB588EGdf/75na4vKSnR4sWLwxmt3/lTi9t6hHZ+EbvcegQAQB/UK++mGTp0qOrq6rRlyxbdeeedcrvd2rRpU6frCwsL1dTUFNrq6+t7Y0wAAGAgrCsjCQkJiomJkdfrbbPf6/UqMTGx0+Oio6M1fvx4SVJqaqo++eQTlZSUaPbs2R2udzgccjgc4YwGAAD6qLCujMTGxiotLU0ejye0LxAIyOPxKCsr67AfJxAIyO/3h/PUAAAgQoV1ZUSS3G635s+fr/T0dGVkZKi0tFTNzc1yuVySpLy8PCUlJamkpETSD/d/pKena9y4cfL7/XrxxRe1bt06rVy5smfPBAAA9Elhx0hubq4aGxtVVFSkhoYGpaamqrKyMnRT644dOxQdfeCCS3Nzs66++mp9+eWXGjRokCZMmKD169crNze3584CAAD0WWHHiCTl5+crPz+/w5/9742pS5Ys0ZIlS7ryNAAAoB/gu2kAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAqQHWAwAA0BVX3d9kPUI7KwvirUfok7gyAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATHUpRsrKypSSkqK4uDhlZmaqurq607Vr1qzR2WefrREjRmjEiBHKzs4+6HoAANC/hB0jFRUVcrvdKi4uVm1traZOnaqcnBzt3r27w/WbNm3S5Zdfrtdee01VVVVKTk7WBRdcoJ07d3Z7eAAA0PeFHSPLly/XggUL5HK5NGnSJJWXl2vw4MFau3Zth+sff/xxXX311UpNTdWECRP00EMPKRAIyOPxdHt4AADQ94UVIy0tLaqpqVF2dvaBB4iOVnZ2tqqqqg7rMfbv36/vvvtOI0eO7HSN3++Xz+drswEAgMgUVozs2bNHra2tcjqdbfY7nU41NDQc1mP88Y9/1PHHH98maP5XSUmJ4uPjQ1tycnI4YwIAgD6kV99Ns2zZMm3cuFFPP/204uLiOl1XWFiopqam0FZfX9+LUwIAgN4U1rf2JiQkKCYmRl6vt81+r9erxMTEgx577733atmyZfrrX/+q008//aBrHQ6HHA5HOKMBAIA+KqwrI7GxsUpLS2tz8+l/b0bNysrq9Li7775bd9xxhyorK5Went71aQEAQMQJ68qIJLndbs2fP1/p6enKyMhQaWmpmpub5XK5JEl5eXlKSkpSSUmJJOmuu+5SUVGRNmzYoJSUlNC9Jcccc4yOOeaYHjwVAADQF4UdI7m5uWpsbFRRUZEaGhqUmpqqysrK0E2tO3bsUHT0gQsuK1euVEtLiy655JI2j1NcXKzbbrute9MDAIA+L+wYkaT8/Hzl5+d3+LNNmza1+fMXX3zRlacAAAD9BN9NAwAATBEjAADAFDECAABMESMAAMAUMQIAAEx16d00AHAkjXlkkfUI7XzpWmY9AhCxuDICAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMdSlGysrKlJKSori4OGVmZqq6urrTtR999JHmzp2rlJQURUVFqbS0tKuzAgCACBR2jFRUVMjtdqu4uFi1tbWaOnWqcnJytHv37g7X79+/X2PHjtWyZcuUmJjY7YEBAEBkCTtGli9frgULFsjlcmnSpEkqLy/X4MGDtXbt2g7XT58+Xffcc48uu+wyORyObg8MAAAiS1gx0tLSopqaGmVnZx94gOhoZWdnq6qqqseG8vv98vl8bTYAABCZBoSzeM+ePWptbZXT6Wyz3+l0auvWrT02VElJiRYvXtxjj4ejR+CJC61HaCf60pesRwCAfu2ofDdNYWGhmpqaQlt9fb31SAAA4AgJ68pIQkKCYmJi5PV62+z3er09enOqw+Hg/hIAAPqJsK6MxMbGKi0tTR6PJ7QvEAjI4/EoKyurx4cDAACRL6wrI5Lkdrs1f/58paenKyMjQ6WlpWpubpbL5ZIk5eXlKSkpSSUlJZJ+uOn1448/Dv33zp07VVdXp2OOOUbjx4/vwVMBAAB9Udgxkpubq8bGRhUVFamhoUGpqamqrKwM3dS6Y8cORUcfuOCya9cuTZs2LfTne++9V/fee69mzZqlTZs2df8MAABAnxZ2jEhSfn6+8vPzO/zZ/wZGSkqKgsFgV54GAAD0A0flu2kAAED/QYwAAABTxAgAADBFjAAAAFPECAAAMEWMAAAAU8QIAAAwRYwAAABTxAgAADBFjAAAAFPECAAAMEWMAAAAU8QIAAAwRYwAAABTxAgAADBFjAAAAFPECAAAMEWMAAAAU8QIAAAwRYwAAABTxAgAADBFjAAAAFPECAAAMEWMAAAAU8QIAAAwRYwAAABTxAgAADBFjAAAAFPECAAAMEWMAAAAU8QIAAAwRYwAAABTxAgAADBFjAAAAFPECAAAMEWMAAAAU8QIAAAwRYwAAABTxAgAADBFjAAAAFMDrAcA+oKr7m+yHqGdlQXx1iMAQI/gyggAADBFjAAAAFPECAAAMEWMAAAAU8QIAAAwRYwAAABTxAgAADDVpRgpKytTSkqK4uLilJmZqerq6oOuf+KJJzRhwgTFxcVpypQpevHFF7s0LAAAiDxhx0hFRYXcbreKi4tVW1urqVOnKicnR7t37+5w/VtvvaXLL79cV155pd59913NmTNHc+bM0Ycfftjt4QEAQN8XdowsX75cCxYskMvl0qRJk1ReXq7Bgwdr7dq1Ha6///779aMf/Ug33HCDJk6cqDvuuENnnHGGVqxY0e3hAQBA3xfWx8G3tLSopqZGhYWFoX3R0dHKzs5WVVVVh8dUVVXJ7Xa32ZeTk6Nnnnmm0+fx+/3y+/2hPzc1/fBR3D6fL5xxD0vgW/+hF/WywznP/S1H4dyxh547sP/7XpgkPNGH8Xq3/F/P/93rLp8v6pBr9vfRufn/sufw/2XviuT/L7v2uD+cazAYPPjCYBh27twZlBR866232uy/4YYbghkZGR0eM3DgwOCGDRva7CsrKwuOGjWq0+cpLi4OSmJjY2NjY2OLgK2+vv6gfXFUflFeYWFhm6spgUBAe/fu1bHHHquoqCNTb93l8/mUnJys+vp6DRs2zHqciMfr3bt4vXsXr3fv4vU+coLBoL7++msdf/zxB10XVowkJCQoJiZGXq+3zX6v16vExMQOj0lMTAxrvSQ5HA45HI42+4YPHx7OqGaGDRvGX+ZexOvdu3i9exevd+/i9T4y4uPjD7kmrBtYY2NjlZaWJo/HE9oXCATk8XiUlZXV4TFZWVlt1kvSq6++2ul6AADQv4T9axq326358+crPT1dGRkZKi0tVXNzs1wulyQpLy9PSUlJKikpkSQVFBRo1qxZuu+++3TRRRdp48aNeuedd7R69eqePRMAANAnhR0jubm5amxsVFFRkRoaGpSamqrKyko5nU5J0o4dOxQdfeCCy4wZM7Rhwwbdcsstuummm3TyySfrmWee0eTJk3vuLI4CDodDxcXF7X69hCOD17t38Xr3Ll7v3sXrbS8qGDzU+20AAACOHL6bBgAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRnpAWVmZUlJSFBcXp8zMTFVXV1uPFJFKSko0ffp0DR06VKNGjdKcOXO0bds267H6jWXLlikqKkrXXXed9SgRa+fOnbriiit07LHHatCgQZoyZYreeecd67EiUmtrq2699VaddNJJGjRokMaNG6c77rjj0F/ohiOCGOmmiooKud1uFRcXq7a2VlOnTlVOTo52795tPVrEef3117Vw4UK9/fbbevXVV/Xdd9/pggsuUHNzs/VoEW/Lli1atWqVTj/9dOtRItZXX32lmTNnauDAgXrppZf08ccf67777tOIESOsR4tId911l1auXKkVK1bok08+0V133aW7775bDzzwgPVo/RKfM9JNmZmZmj59ulasWCHph4/HT05O1jXXXKNFixYZTxfZGhsbNWrUKL3++us655xzrMeJWN98843OOOMMPfjgg1qyZIlSU1NVWlpqPVbEWbRokf7+97/rzTfftB6lX/jJT34ip9Ophx9+OLRv7ty5GjRokNavX284Wf/ElZFuaGlpUU1NjbKzs0P7oqOjlZ2draqqKsPJ+oempiZJ0siRI40niWwLFy7URRdd1ObvOXrec889p/T0dF166aUaNWqUpk2bpjVr1liPFbFmzJghj8ejTz/9VJL03nvvafPmzbrwwguNJ+ufwv44eBywZ88etba2hj4K/7+cTqe2bt1qNFX/EAgEdN1112nmzJkR99UCR5ONGzeqtrZWW7ZssR4l4n3++edauXKl3G63brrpJm3ZskXXXnutYmNjNX/+fOvxIs6iRYvk8/k0YcIExcTEqLW1VXfeeafmzZtnPVq/RIygT1q4cKE+/PBDbd682XqUiFVfX6+CggK9+uqriouLsx4n4gUCAaWnp2vp0qWSpGnTpunDDz9UeXk5MXIE/OlPf9Ljjz+uDRs26LTTTlNdXZ2uu+46HX/88bzeBoiRbkhISFBMTIy8Xm+b/V6vV4mJiUZTRb78/Hy98MILeuONNzRmzBjrcSJWTU2Ndu/erTPOOCO0r7W1VW+88YZWrFghv9+vmJgYwwkjy+jRozVp0qQ2+yZOnKg///nPRhNFthtuuEGLFi3SZZddJkmaMmWKtm/frpKSEmLEAPeMdENsbKzS0tLk8XhC+wKBgDwej7Kysgwni0zBYFD5+fl6+umn9be//U0nnXSS9UgR7bzzztMHH3ygurq60Jaenq558+aprq6OEOlhM2fObPdW9U8//VQnnnii0USRbf/+/W2+YV6SYmJiFAgEjCbq37gy0k1ut1vz589Xenq6MjIyVFpaqubmZrlcLuvRIs7ChQu1YcMGPfvssxo6dKgaGhokSfHx8Ro0aJDxdJFn6NCh7e7HGTJkiI499lju0zkCrr/+es2YMUNLly7VL37xC1VXV2v16tVavXq19WgR6eKLL9add96pE044QaeddpreffddLV++XL/5zW+sR+ufgui2Bx54IHjCCScEY2NjgxkZGcG3337beqSIJKnD7ZFHHrEerd+YNWtWsKCgwHqMiPX8888HJ0+eHHQ4HMEJEyYEV69ebT1SxPL5fMGCgoLgCSecEIyLiwuOHTs2ePPNNwf9fr/1aP0SnzMCAABMcc8IAAAwRYwAAABTxAgAADBFjAAAAFPECAAAMEWMAAAAU8QIAAAwRYwAAABTxAgAADBFjAAAAFPECAAAMPX/ANhnodWIu+O0AAAAAElFTkSuQmCC",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot(labels, logits, \"Logits\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Step 2: Calculate Softmax for different Temperature values.\n",
        "Loop over different temperature values and calculate the softmax"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "hFxYM5nwbYAV",
        "outputId": "61787f7a-f7dd-4c0a-e7b4-406877bfe57e"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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Hjx4aNWqU8vLylJKSotGjR6usrEwFBQXq3r27ysvLL2m98+bN04033qiYmBiNGTNG7du3V2lpqYqKivR///d/2r17t7P2lltukaRLuvB28eLFOnDggE6fPi1Jeuedd/T4449Lku6++27nmbg//vGP+utf/6rU1FQ98MADql+/vvLy8hQWFua8EP3ccZgxY4bGjh2r9PR0paSk6N1339WSJUs0c+ZMNWvW7JLWC1yQt96eBFxN//znP82oUaNM165dTaNGjYy/v7/p2LGjGTduXLV7R5w9e9Y8+uijpl27dqZ+/fqmTZs21W4cZ4z7tzUbY8zrr79uoqOjTb169dzeOO7nzt0Q7eckmbFjxzq//uabb0xmZqYJDQ01jRo1MikpKWbv3r0mMjLSZGRkGGOMOXTokAkJCTG///3vq803ePBg07BhQ/P5558bY4z59ttvjaRLestpSUmJSU1NNY0bN65247hvv/3WTJo0yXTs2NH4+/ub0NBQ069fP/Pss8863zb+05uj/dTGjRuNJOfN8845dxO+bdu2VTtO69atM9dff70JCAgwXbt2rbbvL+3JmB/eOvzEE0+YyMhIExAQYHr27GneeOONam9JNuaHm6P17t3b+Pv7V3uL8JIlS5w3IIyLizPr1q274I3j3Pnss8/MyJEjTXh4uKlfv76JiIgwAwcONK+88opLnSdvaz73Fnt328aNG11qDx06ZIYMGWKCg4NNo0aNzMCBA83+/fvdzrtgwQLTpUsX5836nnvuOeNwOC6pJ+BifIyp4TliANe0NWvWaODAgdq9e7diYmK83c5FRUVFqUePHnrjjTe83QoAL+AaFqCO2rhxo4YPH35NhBUA4BoWoI565plnvN0CAFwyzrAAAADrcQ0LAACwHmdYAACA9QgsAADAerXioluHw6EjR46ocePGV/TW6AAA4PIxxujbb79Vq1at5Ot74XMotSKwHDlypNqnvQIAgGvDoUOHnHfmPp9aEVjOfQDXoUOHFBwc7OVuAADApSgvL1ebNm2cr+MXUisCy7lfAwUHBxNYAAC4xlzK5RxcdAsAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA69UosMybN09RUVEKDAxUQkKCtm7det7a//3f/9Udd9yhqKgo+fj4KD8//xfPCQAA6haPA8vy5cuVnZ2t6dOnq7i4WLGxsUpJSVFZWZnb+tOnT6t9+/Z68sknFR4eflnmBAAAdYuPMcZ4skNCQoL69OmjuXPnSpIcDofatGmjcePGaeLEiRfcNyoqShMmTNCECRMu25zSDx9PHRISohMnTvBpzQAAXCM8ef2u58nElZWV2rFjhyZNmuQc8/X1VXJysoqKimrUbE3mrKioUEVFhfPr8vLyGj03AAA2Wj77hLdbqGbY+BCvPr9HgeXYsWOqqqpSWFiYy3hYWJj27t1bowZqMmdubq4effTRGj1fTbRedPGzPFfb/2U+edGa/6nMvgqdeGaof563W8DP8Bfj1XWt/lw6Vvz2KnTiGd/0f3q7BVxFHgUWW0yaNEnZ2T/+0JeXl6tNmzZe7AiX07X6F+MfLHzhn1+LX/iv1X9I4Ori57L28CiwhIaGys/PT6WlpS7jpaWl572g9krMGRAQoICAgBo9HwAAuPZ49C4hf39/9e7dW4WFhc4xh8OhwsJCJSYm1qiBKzEnAACoXTz+lVB2drYyMjIUHx+vvn37Kj8/X6dOnVJmZqYkaeTIkYqIiFBubq6kHy6q/fe//+38/8OHD2vXrl1q1KiROnbseElzAgCAus3jwDJs2DAdPXpU06ZNU0lJieLi4rR27VrnRbMHDx6Ur++PJ26OHDminj17Or9+9tln9eyzzyopKUmbNm26pDkBAEDdVqOLbrOyspSVleX2sXMh5JyoqChdyq1eLjQnAACo2/gsIQAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsV6PAMm/ePEVFRSkwMFAJCQnaunXrBetXrFihrl27KjAwUDExMVqzZo3L4ydPnlRWVpZat26toKAgRUdHq6CgoCatAQCAWsjjwLJ8+XJlZ2dr+vTpKi4uVmxsrFJSUlRWVua2fvPmzRoxYoRGjx6tnTt3Ki0tTWlpadqzZ4+zJjs7W2vXrtWSJUv08ccfa8KECcrKytLq1atrvjIAAFBreBxY8vLyNGbMGGVmZjrPhDRo0EALFy50Wz979mwNGDBAOTk56tatm2bMmKFevXpp7ty5zprNmzcrIyND/fv3V1RUlO69917Fxsae98xNRUWFysvLXTYAAFB7eRRYKisrtWPHDiUnJ/84ga+vkpOTVVRU5HafoqIil3pJSklJcanv16+fVq9ercOHD8sYo40bN2rfvn267bbb3M6Zm5urkJAQ59amTRtPlgEAAK4xHgWWY8eOqaqqSmFhYS7jYWFhKikpcbtPSUnJRevnzJmj6OhotW7dWv7+/howYIDmzZunm266ye2ckyZN0okTJ5zboUOHPFkGAAC4xtTzdgPSD4Fly5YtWr16tSIjI/XOO+9o7NixatWqVbWzM5IUEBCggIAAL3QKAAC8waPAEhoaKj8/P5WWlrqMl5aWKjw83O0+4eHhF6z/7rvvNHnyZK1cuVKpqamSpOuvv167du3Ss88+6zawAACAusWjXwn5+/urd+/eKiwsdI45HA4VFhYqMTHR7T6JiYku9ZK0fv16Z/3Zs2d19uxZ+fq6tuLn5yeHw+FJewAAoJby+FdC2dnZysjIUHx8vPr27av8/HydOnVKmZmZkqSRI0cqIiJCubm5kqTx48crKSlJs2bNUmpqqpYtW6bt27drwYIFkqTg4GAlJSUpJydHQUFBioyM1Ntvv62XX35ZeXl5l3GpAADgWuVxYBk2bJiOHj2qadOmqaSkRHFxcVq7dq3zwtqDBw+6nC3p16+fli5dqilTpmjy5Mnq1KmTVq1apR49ejhrli1bpkmTJunOO+/U119/rcjISM2cOVP33XffZVgiAAC41tXootusrCxlZWW5fWzTpk3VxtLT05Wenn7e+cLDw7Vo0aKatAIAAOoAPksIAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANarUWCZN2+eoqKiFBgYqISEBG3duvWC9StWrFDXrl0VGBiomJgYrVmzplrNxx9/rEGDBikkJEQNGzZUnz59dPDgwZq0BwAAahmPA8vy5cuVnZ2t6dOnq7i4WLGxsUpJSVFZWZnb+s2bN2vEiBEaPXq0du7cqbS0NKWlpWnPnj3Oms8++0w33nijunbtqk2bNunDDz/U1KlTFRgYWPOVAQCAWsPjwJKXl6cxY8YoMzNT0dHRKigoUIMGDbRw4UK39bNnz9aAAQOUk5Ojbt26acaMGerVq5fmzp3rrHn44Yf1u9/9Tk8//bR69uypDh06aNCgQWrRokXNVwYAAGoNjwJLZWWlduzYoeTk5B8n8PVVcnKyioqK3O5TVFTkUi9JKSkpznqHw6E333xTnTt3VkpKilq0aKGEhAStWrXqvH1UVFSovLzcZQMAALWXR4Hl2LFjqqqqUlhYmMt4WFiYSkpK3O5TUlJywfqysjKdPHlSTz75pAYMGKC33npLgwcP1n/913/p7bffdjtnbm6uQkJCnFubNm08WQYAALjGeP1dQg6HQ5J0++23609/+pPi4uI0ceJEDRw4UAUFBW73mTRpkk6cOOHcDh06dDVbBgAAV1k9T4pDQ0Pl5+en0tJSl/HS0lKFh4e73Sc8PPyC9aGhoapXr56io6Ndarp166b33nvP7ZwBAQEKCAjwpHUAAHAN8+gMi7+/v3r37q3CwkLnmMPhUGFhoRITE93uk5iY6FIvSevXr3fW+/v7q0+fPvrkk09cavbt26fIyEhP2gMAALWUR2dYJCk7O1sZGRmKj49X3759lZ+fr1OnTikzM1OSNHLkSEVERCg3N1eSNH78eCUlJWnWrFlKTU3VsmXLtH37di1YsMA5Z05OjoYNG6abbrpJN998s9auXat//OMf2rRp0+VZJQAAuKZ5HFiGDRumo0ePatq0aSopKVFcXJzWrl3rvLD24MGD8vX98cRNv379tHTpUk2ZMkWTJ09Wp06dtGrVKvXo0cNZM3jwYBUUFCg3N1f333+/unTpoldffVU33njjZVgiAAC41nkcWCQpKytLWVlZbh9zd1YkPT1d6enpF5xz1KhRGjVqVE3aAQAAtZzX3yUEAABwMQQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALBejQLLvHnzFBUVpcDAQCUkJGjr1q0XrF+xYoW6du2qwMBAxcTEaM2aNeetve++++Tj46P8/PyatAYAAGohjwPL8uXLlZ2drenTp6u4uFixsbFKSUlRWVmZ2/rNmzdrxIgRGj16tHbu3Km0tDSlpaVpz5491WpXrlypLVu2qFWrVp6vBAAA1FoeB5a8vDyNGTNGmZmZio6OVkFBgRo0aKCFCxe6rZ89e7YGDBignJwcdevWTTNmzFCvXr00d+5cl7rDhw9r3Lhx+vvf/6769evXbDUAAKBW8iiwVFZWaseOHUpOTv5xAl9fJScnq6ioyO0+RUVFLvWSlJKS4lLvcDh09913KycnR927d79oHxUVFSovL3fZAABA7eVRYDl27JiqqqoUFhbmMh4WFqaSkhK3+5SUlFy0/qmnnlK9evV0//33X1Ifubm5CgkJcW5t2rTxZBkAAOAa4/V3Ce3YsUOzZ8/WSy+9JB8fn0vaZ9KkSTpx4oRzO3To0BXuEgAAeJNHgSU0NFR+fn4qLS11GS8tLVV4eLjbfcLDwy9Y/+6776qsrExt27ZVvXr1VK9ePR04cEB//vOfFRUV5XbOgIAABQcHu2wAAKD28iiw+Pv7q3fv3iosLHSOORwOFRYWKjEx0e0+iYmJLvWStH79emf93XffrQ8//FC7du1ybq1atVJOTo7WrVvn6XoAAEAtVM/THbKzs5WRkaH4+Hj17dtX+fn5OnXqlDIzMyVJI0eOVEREhHJzcyVJ48ePV1JSkmbNmqXU1FQtW7ZM27dv14IFCyRJzZs3V/PmzV2eo379+goPD1eXLl1+6foAAEAt4HFgGTZsmI4ePapp06appKREcXFxWrt2rfPC2oMHD8rX98cTN/369dPSpUs1ZcoUTZ48WZ06ddKqVavUo0ePy7cKAABQq3kcWCQpKytLWVlZbh/btGlTtbH09HSlp6df8vxffvllTdoCAAC1lNffJQQAAHAxBBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsF6NAsu8efMUFRWlwMBAJSQkaOvWrResX7Fihbp27arAwEDFxMRozZo1zsfOnj2rhx56SDExMWrYsKFatWqlkSNH6siRIzVpDQAA1EIeB5bly5crOztb06dPV3FxsWJjY5WSkqKysjK39Zs3b9aIESM0evRo7dy5U2lpaUpLS9OePXskSadPn1ZxcbGmTp2q4uJivfbaa/rkk080aNCgX7YyAABQa3gcWPLy8jRmzBhlZmYqOjpaBQUFatCggRYuXOi2fvbs2RowYIBycnLUrVs3zZgxQ7169dLcuXMlSSEhIVq/fr2GDh2qLl266Fe/+pXmzp2rHTt26ODBg79sdQAAoFbwKLBUVlZqx44dSk5O/nECX18lJyerqKjI7T5FRUUu9ZKUkpJy3npJOnHihHx8fNSkSRO3j1dUVKi8vNxlAwAAtZdHgeXYsWOqqqpSWFiYy3hYWJhKSkrc7lNSUuJR/ZkzZ/TQQw9pxIgRCg4OdluTm5urkJAQ59amTRtPlgEAAK4xVr1L6OzZsxo6dKiMMZo/f/556yZNmqQTJ044t0OHDl3FLgEAwNVWz5Pi0NBQ+fn5qbS01GW8tLRU4eHhbvcJDw+/pPpzYeXAgQPasGHDec+uSFJAQIACAgI8aR0AAFzDPDrD4u/vr969e6uwsNA55nA4VFhYqMTERLf7JCYmutRL0vr1613qz4WV/fv361//+peaN2/uSVsAAKCW8+gMiyRlZ2crIyND8fHx6tu3r/Lz83Xq1CllZmZKkkaOHKmIiAjl5uZKksaPH6+kpCTNmjVLqampWrZsmbZv364FCxZI+iGsDBkyRMXFxXrjjTdUVVXlvL6lWbNm8vf3v1xrBQAA1yiPA8uwYcN09OhRTZs2TSUlJYqLi9PatWudF9YePHhQvr4/nrjp16+fli5dqilTpmjy5Mnq1KmTVq1apR49ekiSDh8+rNWrV0uS4uLiXJ5r48aN6t+/fw2XBgAAaguPA4skZWVlKSsry+1jmzZtqjaWnp6u9PR0t/VRUVEyxtSkDQAAUEdY9S4hAAAAdwgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGA9AgsAALAegQUAAFiPwAIAAKxHYAEAANYjsAAAAOsRWAAAgPUILAAAwHoEFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABYj8ACAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BBYAAGC9GgWWefPmKSoqSoGBgUpISNDWrVsvWL9ixQp17dpVgYGBiomJ0Zo1a1weN8Zo2rRpatmypYKCgpScnKz9+/fXpDUAAFALeRxYli9fruzsbE2fPl3FxcWKjY1VSkqKysrK3NZv3rxZI0aM0OjRo7Vz506lpaUpLS1Ne/bscdY8/fTT+stf/qKCggJ98MEHatiwoVJSUnTmzJmarwwAANQaHgeWvLw8jRkzRpmZmYqOjlZBQYEaNGighQsXuq2fPXu2BgwYoJycHHXr1k0zZsxQr169NHfuXEk/nF3Jz8/XlClTdPvtt+v666/Xyy+/rCNHjmjVqlW/aHEAAKB2qOdJcWVlpXbs2KFJkyY5x3x9fZWcnKyioiK3+xQVFSk7O9tlLCUlxRlGvvjiC5WUlCg5Odn5eEhIiBISElRUVKThw4dXm7OiokIVFRXOr0+cOCFJKi8v92Q5l8zxXcXFi66yS1nr6UoL+/a/eN+O099fhU4843sJx7vyzJX5/vslyst9Llpz+hrtm5/Ly4efy6urNv9cej7nD+s0xly82Hjg8OHDRpLZvHmzy3hOTo7p27ev233q169vli5d6jI2b94806JFC2OMMe+//76RZI4cOeJSk56eboYOHep2zunTpxtJbGxsbGxsbLVgO3To0EUziEdnWGwxadIkl7M2DodDX3/9tZo3by4fn8ufAC+H8vJytWnTRocOHVJwcLC326n1ON5XF8f76uJ4X30c8yvDGKNvv/1WrVq1umitR4ElNDRUfn5+Ki0tdRkvLS1VeHi4233Cw8MvWH/uv6WlpWrZsqVLTVxcnNs5AwICFBAQ4DLWpEkTT5biNcHBwXyzX0Uc76uL4311cbyvPo755RcSEnJJdR5ddOvv76/evXursLDQOeZwOFRYWKjExES3+yQmJrrUS9L69eud9e3atVN4eLhLTXl5uT744IPzzgkAAOoWj38llJ2drYyMDMXHx6tv377Kz8/XqVOnlJmZKUkaOXKkIiIilJubK0kaP368kpKSNGvWLKWmpmrZsmXavn27FixYIEny8fHRhAkT9Pjjj6tTp05q166dpk6dqlatWiktLe3yrRQAAFyzPA4sw4YN09GjRzVt2jSVlJQoLi5Oa9euVVhYmCTp4MGD8vX98cRNv379tHTpUk2ZMkWTJ09Wp06dtGrVKvXo0cNZ8+CDD+rUqVO69957dfz4cd14441au3atAgMDL8MS7RAQEKDp06dX+1UWrgyO99XF8b66ON5XH8fc+3yMuZT3EgEAAHgPnyUEAACsR2ABAADWI7AAAADrEVgAAID1CCwAAMB6BJarZN68eYqKilJgYKASEhK0detWb7dUK+Xm5qpPnz5q3LixWrRoobS0NH3yySfebqvOePLJJ533VsKVcfjwYd11111q3ry5goKCFBMTo+3bt3u7rVqpqqpKU6dOVbt27RQUFKQOHTpoxowZl/ZBfbjsCCxXwfLly5Wdna3p06eruLhYsbGxSklJUVlZmbdbq3XefvttjR07Vlu2bNH69et19uxZ3XbbbTp16pS3W6v1tm3bphdeeEHXX3+9t1uptb755hvdcMMNql+/vv75z3/q3//+t2bNmqWmTZt6u7Va6amnntL8+fM1d+5cffzxx3rqqaf09NNPa86cOd5urU7iPixXQUJCgvr06aO5c+dK+uHjDNq0aaNx48Zp4sSJXu6udjt69KhatGiht99+WzfddJO326m1Tp48qV69eun555/X448/rri4OOXn53u7rVpn4sSJev/99/Xuu+96u5U6YeDAgQoLC9OLL77oHLvjjjsUFBSkJUuWeLGzuokzLFdYZWWlduzYoeTkZOeYr6+vkpOTVVRU5MXO6oYTJ05Ikpo1a+blTmq3sWPHKjU11eX7HJff6tWrFR8fr/T0dLVo0UI9e/bUX//6V2+3VWv169dPhYWF2rdvnyRp9+7deu+99/Tb3/7Wy53VTR7fmh+eOXbsmKqqqpwfXXBOWFiY9u7d66Wu6gaHw6EJEybohhtucPkoCFxey5YtU3FxsbZt2+btVmq9zz//XPPnz1d2drYmT56sbdu26f7775e/v78yMjK83V6tM3HiRJWXl6tr167y8/NTVVWVZs6cqTvvvNPbrdVJBBbUWmPHjtWePXv03nvvebuVWuvQoUMaP3681q9fX6s++8tWDodD8fHxeuKJJyRJPXv21J49e1RQUEBguQL+53/+R3//+9+1dOlSde/eXbt27dKECRPUqlUrjrcXEFiusNDQUPn5+am0tNRlvLS0VOHh4V7qqvbLysrSG2+8oXfeeUetW7f2dju11o4dO1RWVqZevXo5x6qqqvTOO+9o7ty5qqiokJ+fnxc7rF1atmyp6Ohol7Fu3brp1Vdf9VJHtVtOTo4mTpyo4cOHS5JiYmJ04MAB5ebmEli8gGtYrjB/f3/17t1bhYWFzjGHw6HCwkIlJiZ6sbPayRijrKwsrVy5Uhs2bFC7du283VKtdsstt+ijjz7Srl27nFt8fLzuvPNO7dq1i7Bymd1www3V3qa/b98+RUZGeqmj2u306dPy9XV9mfTz85PD4fBSR3UbZ1iuguzsbGVkZCg+Pl59+/ZVfn6+Tp06pczMTG+3VuuMHTtWS5cu1euvv67GjRurpKREkhQSEqKgoCAvd1f7NG7cuNr1QQ0bNlTz5s25bugK+NOf/qR+/frpiSee0NChQ7V161YtWLBACxYs8HZrtdLvf/97zZw5U23btlX37t21c+dO5eXladSoUd5urW4yuCrmzJlj2rZta/z9/U3fvn3Nli1bvN1SrSTJ7bZo0SJvt1ZnJCUlmfHjx3u7jVrrH//4h+nRo4cJCAgwXbt2NQsWLPB2S7VWeXm5GT9+vGnbtq0JDAw07du3Nw8//LCpqKjwdmt1EvdhAQAA1uMaFgAAYD0CCwAAsB6BBQAAWI/AAgAArEdgAQAA1iOwAAAA6xFYAACA9QgsAADAegQWAABgPQILAACwHoEFAABY7/8BYB2oK2DDeikAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "temps = [0.1, 0.5, 1, 2, 5, 10, 100]\n",
        "for temp in temps:\n",
        "  sm = softmax(logits, temp)\n",
        "  plot(labels, sm, f\"Softmax, temperature: {temp}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Step 3: Interpretation\n",
        "\n",
        "1. the higher the temperature, the more uniform is the probability distribution, meaning it also increases the randomnes if you would draw a sample from that distribution\n",
        "2. the lower the temperature, the \"sharper\" the resulting distribution.\n",
        "3. High temperatures boost low probable events and damps high probable ones\n",
        "4. Low temperatures boost high probable events and damp low probable ones even more."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Hi6kNAntbiRq"
      },
      "outputs": [],
      "source": []
    }
  ],
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