nt-xent-loss/SoftMax and Sigmoid with temperature.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9fdd3830",
   "metadata": {},
   "source": [
    "# SoftMax and Sigmoid with temperature"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4922d532",
   "metadata": {},
   "source": [
    "## The effect of temperature on SoftMax\n",
    "\n",
    "We divide every value of the input distribution by a temperature $\\tau$.\n",
    "\n",
    "If $\\tau \\gt 1.0$ then we smooth out the distribution and the values get closer to each other, increasong the entropy of the distribution.\n",
    "\n",
    "If $\\tau \\lt 1.0$ then we make the distribution more uneven and the values are stretched out further apart. This reduces the entropy of the distribution, since there's a clear *high* value in the distribution that stands out relative to the others - i.e. its probability after the softmax is significantly higher than the rest of the values.\n",
    "\n",
    "## Links\n",
    "* https://stats.stackexchange.com/questions/527080/what-is-the-role-of-temperature-in-softmax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9a764b48",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "from torch.nn import functional as F\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c907f2da",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input Tensor: tensor([0.1081, 0.4376, 0.7697, 0.1929, 0.3626, 2.8451])\n",
      "\n",
      "Temperature: 0.1,  Tensor: tensor([ 1.0810,  4.3756,  7.6969,  1.9291,  3.6258, 28.4511])\n",
      "Temperature: 0.1, Softmax: tensor([1.2982e-12, 3.5007e-11, 9.6953e-10, 3.0316e-12, 1.6539e-11, 1.0000e+00])\n",
      "\n",
      "Temperature: 0.5,  Tensor: tensor([0.2162, 0.8751, 1.5394, 0.3858, 0.7252, 5.6902])\n",
      "Temperature: 0.5, Softmax: tensor([0.0040, 0.0078, 0.0151, 0.0048, 0.0067, 0.9615])\n",
      "\n",
      "Temperature: 1.0,  Tensor: tensor([0.1081, 0.4376, 0.7697, 0.1929, 0.3626, 2.8451])\n",
      "Temperature: 1.0, Softmax: tensor([0.0452, 0.0628, 0.0875, 0.0491, 0.0582, 0.6972])\n",
      "\n",
      "Temperature: 5.0,  Tensor: tensor([0.0216, 0.0875, 0.1539, 0.0386, 0.0725, 0.5690])\n",
      "Temperature: 5.0, Softmax: tensor([0.1427, 0.1524, 0.1629, 0.1451, 0.1502, 0.2467])\n",
      "\n",
      "Temperature: 10.0,  Tensor: tensor([0.0108, 0.0438, 0.0770, 0.0193, 0.0363, 0.2845])\n",
      "Temperature: 10.0, Softmax: tensor([0.1550, 0.1602, 0.1656, 0.1563, 0.1590, 0.2038])\n",
      "\n",
      "Temperature: 20.0,  Tensor: tensor([0.0054, 0.0219, 0.0385, 0.0096, 0.0181, 0.1423])\n",
      "Temperature: 20.0, Softmax: tensor([0.1609, 0.1636, 0.1663, 0.1616, 0.1630, 0.1845])\n"
     ]
    },
    {
     "data": {
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885WZmanLL788mEsDAAAICvIjAADQUlhMEP/kdvjwYR0+fFihoUe+BHDZsmVav369Tj/9dGVnZ8tqtQZraSdkt9sVGRmpqqoqRUREBHs5AADIYgn2CoLHn9lMoM/5TTk/coe/49mSjwPJu2OB2Hk3nvh5N574eT6W2Hk3nvj5Z153z/dBLUo1ZRSlAACNTUtOqppTUaq5oyjlX/xi6zl+sfUO8fMOx67neO15J9hFqVD/bP74Kioq3OrXrVs3P68EAACgcSA/AgAALU1QilIJCQmOfx+9UMvyq/KkMUYWi0W1tbUBXxsAAEAwkB8BAICWJihFKYvFolNPPVXXX3+9Lr30Usc9EwAAAFoq8iMAANDSBCXb+fbbb/XCCy9owYIFevbZZ3Xttddq/Pjx6tOnTzCWAwAAEHTkRwAAoKVpFYyNxsTE6K677tLmzZv18ssv64cfflBKSoqGDRumuXPn6vDhw8FYFgAAQNCQHwEAgJYmKEWpXzvzzDM1b948bdmyRW3btlV2drb27dsX7GUBAAAEDfkRAABoCYJelCopKdGECRPUs2dPHThwQLNmzdLJJ58c7GUBAAAEDfkRAABoCYJyTymbzaaFCxdq/vz5+uGHH3TNNdeopKREffv2DcZyAAAAgo78CAAAtDRBKUrFx8era9euGjdunH7729+qdevWqq2t1caNG536DRgwIBjLAwAACDjyIwAA0NJYjDEm0Btt1ep/nxq0WCySpGOXYbFYVFtbG9B1NYTdbldkZKSqqqoUERER7OUAAKD/f0ptkfyZzQTqnN8c8iN3+DueLfk4kLw7Foidd+OJn3fjiZ/nY4mdd+OJn3/mdfd8H5QrpbZt2xaMzQIAADRa5EcAAKClCdrH9ySpoqJCcXFxjr8G/lpFRUWglwUAABA05EcAAKClCeq37yUkJGj37t0u7Xv37lVCQkIQVgQAABBc5EcAAKClCGpRyhhT518BDxw4oPDw8CCsCAAAILjIjwAAQEsRlI/v5ebmSjpys8577rlHbdu2dTxXW1ur999/X4MGDQrG0gAAAIKC/AgAALQ0QSlKlZWVSTryl8BNmzbJarU6nrNarRo4cKBuv/32YCwNAAAgKMiPAABASxPwotTMmTNVWFioNm3a6IYbbtBTTz3l169XBgAAaOzIjwAAQEtkMcaYQG4wNDRU3333nbp06aKQkBDZbDZ16dIlkEvwCbvdrsjISFVVVZE0AgAahTpuQ9Ri+DObCcQ5v7nkR+7wdzxb8nEgeXcsEDvvxhM/78YTP8/HEjvvxhM//8zr7vk+4FdKde3aVcuXL9dFF10kY4y+/fZb/fzzz3X27datW4BXBwAAEHjkRwAAoCUK+JVSc+bM0Z///GcdOnSo3j5Hv3WmtrY2gCtrGK6UAgA0Ni35L31N/Uqp5pIfuYMrpfyLqy08x9UW3iF+3uHY9RyvPe8E+0qpgBelJGn//v365ptvNGDAAL3zzjvq1KlTnf0GDhwY4JW5j6IUAKCxaclJVVMvSknNIz9yB0Up/+IXW8/xi613iJ93OHY9x2vPO8EuSgXl2/fat2+vfv36af78+Ro+fLjCwsKCsQwAAIBGg/wIAAC0NEEpSh01btw4SVJpaak2b94si8WiPn36aMiQIcFcFgAAQNCQHwEAgJYiqEWpXbt2acyYMVqzZo1OPvlkGWNUVVWlc845R0uWLFFUVFQwlwcAABBw5EcAAKClaBXMjf/5z3+W3W7XZ599pv/+97/64Ycf9Omnn8put+u2224L5tIAAACCgvwIAAC0FEG50flRkZGReuedd3TGGWc4tX/wwQfKyMjQvn37grMwN3CjcwBAY9OSb9TZHG50flRTzo/cwY3O/YubJXuOmyV7h/h5h2PXc7z2vBPsG50H9Uqpw4cPq3Xr1i7trVu31uHDh4OwIgAAgOAiPwIAAC1FUItS5557riZOnKjvvvvO0bZz505NmjRJ5513XhBXBgAAEBzkRwAAoKUIalHqmWee0f79+9W9e3f16NFDp59+urp37679+/fr6aefDubSAAAAgoL8CAAAtBRB/fa9uLg4ffzxxyoqKtIXX3whY4z69u3r0V8BCwoK9Oijj8pms6lv376aMWOG0tPT6+y7fv163XXXXfriiy908OBBxcfH66abbtKkSZO83SUAAACv+DI/AgAAaMyCcqXU+++/rzfffNPx8/nnn6+IiAg98cQTuvrqq3XjjTequrra7fmWLl2qnJwc5eXlqaysTOnp6Ro1apQqKirq7N+uXTvdeuutWrdunTZv3qy7775bd999t+bMmeP1vgEAAHjC1/kRAABAYxeUotS0adO0ceNGx8+bNm3SH//4R51//vmaPHmy/vnPfyo/P9/t+Z544gmNHz9eEyZMUJ8+fTRjxgzFxcVp9uzZdfYfPHiwrr76avXt21fdu3fXtddeqwsuuEDFxcX1bqO6ulp2u93pAQAA4Cu+zo8AAAAau6AUpcrLy50uQV+yZImGDh2quXPnKjc3VzNnztSyZcvcmqumpkalpaXKyMhwas/IyFBJSYlbc5SVlamkpERnn312vX3y8/MVGRnpeMTFxbk1NwAAgDt8mR8BAAA0BUEpSv3www+Kjo52/Lx27VpdeOGFjp/POOMM7dixw6259uzZo9raWqf5JCk6OlqVlZXHHXvqqacqLCxMycnJuuWWWzRhwoR6+06ZMkVVVVWOh7vrAwAAcIcv8yMAAICmIChFqejoaG3btk3SkSudPv74Y6Wmpjqe379/v1q3bt2gOS0Wi9PPxhiXtmMVFxfro48+0rPPPqsZM2Zo8eLF9fYNCwtTRESE0wMAAMBX/JEfAQAANGZB+fa9Cy+8UJMnT9YjjzyiV199VW3btnX6pryNGzeqR48ebs3VuXNnhYSEuFwVtWvXLperp46VkJAgSerfv7++//57TZs2TVdffXUD9wYAAMB7vsyPAAAAmoKgXCn1wAMPKCQkRGeffbbmzp2ruXPnymq1Op5//vnnXe4RVR+r1aqkpCQVFRU5tRcVFSktLc3tNRlj+EYbAAAQNL7MjwAAAJqCoFwpFRUVpeLiYlVVVemkk05SSEiI0/MvvfSSTjrpJLfny83NVVZWlpKTk5Wamqo5c+aooqJC2dnZko7cD2rnzp1auHChJGnWrFnq1q2bevfuLUlav369HnvsMf35z3/20R4CAAA0jK/zIwAAgMYuKFdKHRUZGemScElSx44dnf4yeCKZmZmaMWOGpk+frkGDBmndunUqLCxUfHy8JMlms6miosLR//Dhw5oyZYoGDRqk5ORkPf3003r44Yc1ffp073cKAADAC77KjySpoKBACQkJCg8PV1JSkoqLi+vta7PZNHbsWPXq1UutWrVSTk5Onf2WL1+uxMREhYWFKTExUa+88kqD1gQAAHCUxRhjgr2IpshutysyMlJVVVXc9BwA0Cic4Ps9mjV/ZjNN9Zy/dOlSZWVlqaCgQMOHD9dzzz2nv/3tb/r888/VrVs3l/7bt2/Xk08+qaSkJD355JM6++yzNWPGDKc+GzZsUHp6uu6//35dfvnleuWVV3Tvvfdq/fr1SklJcWtd/o5nSz4OJO+OBWLn3Xji59144uf5WGLn3Xji55953T3fU5TyUFNNUAEAzVdLTqooSrlKSUnRkCFDNHv2bEdbnz59NHr0aOXn5x937IgRIzRo0CCXolRmZqbsdrvefPNNR9uFF16oDh061PstxtXV1U737bTb7YqLi6Mo5Sf8Yus5frH1DvHzDseu53jteSfYRamgfnwPAAAAvldTU6PS0lKXG6NnZGSopKTE43k3bNjgMucFF1xw3Dnz8/MVGRnpeMTFxXm8fQAA0LxQlAIAAGhm9uzZo9raWkVHRzu1R0dHq7Ky0uN5KysrGzznlClTVFVV5Xjs2LHD4+0DAIDmJSjfvgcAAAD/sxzzmQRjjEubv+cMCwtTWFiYV9sEAADNE1dKAQAANDOdO3dWSEiIyxVMu3btcrnSqSFiYmJ8PicAAGi5KEoBAAA0M1arVUlJSSoqKnJqLyoqUlpamsfzpqamusy5atUqr+YEAAAtFx/fAwAAaIZyc3OVlZWl5ORkpaamas6cOaqoqFB2drakI/d62rlzpxYuXOgYU15eLkk6cOCAdu/erfLyclmtViUmJkqSJk6cqLPOOkuPPPKILrvsMr322mt65513tH79+oDvHwAAaPooSgEAADRDmZmZ2rt3r6ZPny6bzaZ+/fqpsLBQ8fHxkiSbzaaKigqnMYMHD3b8u7S0VIsWLVJ8fLy2b98uSUpLS9OSJUt0991365577lGPHj20dOlSpaSkBGy/AABA82ExxphgL6IpstvtioyMVFVVlSIiIoK9HAAA5OX9q5s0f2YznPN9y9/xbMnHgeTdsUDsvBtP/LwbT/w8H0vsvBtP/Pwzr7vne+4pBQAAAAAAgICjKAUAAAAAAICAoygFAAAAAACAgKMoBQAAAAAAgICjKAUAAAAAAICAoygFAAAAAACAgKMoBQAAAAAAgICjKAUAAAAAAICAoygFAAAAAACAgKMoBQAAAAAAgICjKAUAAAAAAICAoygFAAAAAACAgKMoBQAAAAAAgICjKAUAAAAAAICAoygFAAAAAACAgKMoBQAAAAAAgICjKAUAAAAAAICAoygFAAAAAACAgKMoBQAAAAAAgICjKAUAAAAAAICAoygFAAAAAACAgKMoBQAAAAAAgICjKAUAAAAAAICAoygFAAAAAACAgKMoBQAAAAAAgICjKAUAAAAAAICAoygFAAAAAACAgKMoBQAAAAAAgICjKAUAAAAAAICAoygFAAAAAACAgKMoBQAAAAAAgIBrNkWpgoICJSQkKDw8XElJSSouLq6374oVK3T++ecrKipKERERSk1N1dtvvx3A1QIAAAAAALRszaIotXTpUuXk5CgvL09lZWVKT0/XqFGjVFFRUWf/devW6fzzz1dhYaFKS0t1zjnn6NJLL1VZWVm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      "text/plain": [
       "<Figure size 1200x1380 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "torch.manual_seed(21)\n",
    "x = torch.randn(6).abs()\n",
    "\n",
    "temperatures = [0.1, 0.5, 1.0, 5.0, 10.0, 20.0]\n",
    "\n",
    "def softmax_with_temperature(x, temperatures):\n",
    "    print(f\"Input Tensor: {x}\")\n",
    "    nrows = (len(temperatures) + 1) // 2\n",
    "    ncols = 2\n",
    "    fig = plt.figure(figsize=(ncols * 6, nrows * 4.6))\n",
    "\n",
    "    for i, t in enumerate(temperatures):\n",
    "        _x = x / t\n",
    "        print(f\"\\nTemperature: {t},  Tensor: {_x}\")\n",
    "        print(f\"Temperature: {t}, Softmax: {F.softmax(_x, dim=0)}\")\n",
    "        \n",
    "        plt.subplot(nrows, ncols, i + 1)\n",
    "        # plt.plot(_x, F.softmax(_x, dim=0))\n",
    "        xstr = list(map(lambda x: f\"{x:.4f}\", _x.tolist()))\n",
    "        plt.bar(xstr, F.softmax(_x, dim=0), color ='blue')\n",
    "        plt.title(f\"Temperature: {t}\")\n",
    "        plt.xlabel(\"Logits(x)\")\n",
    "        plt.ylabel(\"SoftMax(x)\")\n",
    "    # end for\n",
    "    \n",
    "    fig.tight_layout()\n",
    "    plt.show()\n",
    "# end def\n",
    "\n",
    "softmax_with_temperature(x, temperatures)\n",
    "\n",
    "# print(x)\n",
    "# print(F.softmax(x, dim=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67161799",
   "metadata": {},
   "source": [
    "# The effect of temperature on Sigmoid\n",
    "\n",
    "From the graphs below we can see that as the temperature $\\tau$ takes lower values, the Sigmoid function returns values closer and closer to 0.0 and 1.0 since we're artifically stretching out the values away from 0.0. When the temperature $\\tau$ takes greater values, we compress the values, and hence, the Sigmoid function returns values closer and closer to 0.0.\n",
    "\n",
    "tl;dr As the temperature $\\tau$ takes on smaller values, more of our input distribution is mapped to values closer to 0.0 and 1.0 by the Sigmoid function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "708bcbb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x920 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_with_temperatures(x, temperatures):\n",
    "    nrows = (len(temperatures) + 1) // 2\n",
    "    ncols = 2\n",
    "    fig = plt.figure(figsize=(ncols * 6, nrows * 4.6))\n",
    "    for i, t in enumerate(temperatures):\n",
    "        plt.subplot(nrows, ncols, i + 1)\n",
    "        _x = x / t\n",
    "        plt.plot(_x, _x.sigmoid())\n",
    "        plt.title(f\"Temperature: {t}\")\n",
    "        plt.xlabel(\"Logits(x)\")\n",
    "        plt.ylabel(\"Sigmoid(x)\")\n",
    "    # end for\n",
    "    fig.tight_layout()\n",
    "    plt.show()\n",
    "# end def\n",
    "\n",
    "x = torch.tensor(list(range(-800, 800))) / 100.0\n",
    "plot_with_temperatures(x, [0.1, 0.5, 1.0, 2.0])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}