Sigmoid_like Function

sigmoid_like-function.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Sigmoid_like Function",
      "provenance": [],
      "authorship_tag": "ABX9TyPqPErJWyG2IZo0FlCDXofj",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/SiuMath/679e8bb4bce13d5f2383a27eca649575/sigmoid_like-function.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dhq5PkFU1u2-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        },
        "outputId": "102ed6c9-47ea-4761-f838-e87bd19200c6"
      },
      "source": [
        "!pip install -q git+https://www.github.com/google/neural-tangents\n"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "  Building wheel for neural-tangents (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Building wheel for frozendict (setup.py) ... \u001b[?25l\u001b[?25hdone\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XL56mNug1vVj",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "19b34000-cd31-4b93-9e27-91893c007934"
      },
      "source": [
        "import jax.numpy as np \n",
        "from jax.nn import sigmoid \n",
        "from jax.api import jit, grad  \n",
        "from jax.scipy.special import erf\n",
        "\n",
        "\n",
        "from IPython.display import set_matplotlib_formats\n",
        "set_matplotlib_formats('png', 'svg')\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns \n",
        "\n",
        "sns.set_style(style='white')\n",
        "\n",
        "from jax.config import config as jax_config\n",
        "jax_config.update('jax_enable_x64', True)"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1muVa_TN10uH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def format_plot(x='', y='', title='',  grid=True):  \n",
        "  ax = plt.gca()\n",
        "    \n",
        "  plt.grid(grid)\n",
        "  plt.xlabel(x, fontsize=20)\n",
        "  plt.ylabel(y, fontsize=20)\n",
        "  plt.title(title, fontsize=20)\n",
        "  \n",
        "def finalize_plot(shape=(1, 1)):\n",
        "  plt.gcf().set_size_inches(\n",
        "    shape[0] * 1.5 * plt.gcf().get_size_inches()[1], \n",
        "    shape[1] * 1.5 * plt.gcf().get_size_inches()[1])\n",
        "  plt.tight_layout()"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vkMs5KSs13Jf",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 352
        },
        "outputId": "e776ae2a-becc-43fc-9f3e-b80d09053a43"
      },
      "source": [
        "def sigmoid_like(x, c=2.):\n",
        "  return (1. + erf(x / c)) / 2. \n",
        "\n",
        "ts = np.linspace(-5, 5, 1000)\n",
        "\n",
        "plt.plot(ts, sigmoid(ts), label='Sigmoid')\n",
        "\n",
        "for c in [2., 2.4]:\n",
        "  plt.plot(ts, sigmoid_like(ts, c), label=f'Sigmoid_like({c})')\n",
        "\n",
        "plt.legend(fontsize=14)\n",
        "format_plot()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VvR9jh_V16h7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 412
        },
        "outputId": "c3a2a82d-c191-43c8-e2a9-67267a56c3e0"
      },
      "source": [
        "ts = np.linspace(-5, 5, 1000)\n",
        "cs = np.linspace(2.39, 2.41, 50)\n",
        "\n",
        "@jit \n",
        "def loss(c):\n",
        "  return np.sum((sigmoid(ts) - sigmoid_like(ts, c))**2)\n",
        "\n",
        "plt.plot(cs, [loss(c) for c in cs])\n",
        "format_plot('$c$', 'Squared Loss', 'Squared loss Sigmoid / Sigmoid_like($c$)')"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
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          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3b5pLUTC2Crg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 218
        },
        "outputId": "e56eabcc-bbd9-4b73-8c58-1c0d1bfd2e7a"
      },
      "source": [
        "grad_loss = jit(grad(loss))\n",
        "hessian_loss = jit(grad(grad_loss))\n",
        "\n",
        "def newton_method(x):\n",
        "  return x - grad_loss(x) / hessian_loss(x)\n",
        "\n",
        "c = 1.\n",
        "print('\\t c \\t\\t Squared Loss \\n')\n",
        "for _ in range(10):  \n",
        "  c = newton_method(c)\n",
        "  print(c, '\\t', loss(c))\n",
        "  "
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\t c \t\t Squared Loss \n",
            "\n",
            "1.9533568223550044 \t 0.9165731820490621\n",
            "2.3451486376472293 \t 0.06300501719089713\n",
            "2.4010735847027127 \t 0.050175909250883104\n",
            "2.4020560568337066 \t 0.05017212569435061\n",
            "2.4020563531719525 \t 0.05017212569400667\n",
            "2.4020563531719796 \t 0.050172125694006676\n",
            "2.4020563531719796 \t 0.050172125694006676\n",
            "2.4020563531719796 \t 0.050172125694006676\n",
            "2.4020563531719796 \t 0.050172125694006676\n",
            "2.4020563531719796 \t 0.050172125694006676\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-zHAqPuM2HB_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}