Lucs1590/plot_activation_functions.ipynb

## plot_activation_functions.ipynb
{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Imports"
      ],
      "metadata": {
        "id": "y4Ahp_BsTY-Q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import math\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "O3F6FnGLTUfO"
      },
      "execution_count": 39,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Math Methods"
      ],
      "metadata": {
        "id": "rTfLDXwITeoq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def sigmoid(x):\n",
        "  \"\"\"It transforms an input value into a range between 0 and 1.\"\"\"\n",
        "  return 1 / (1 + math.exp(-x))"
      ],
      "metadata": {
        "id": "U6zIevaiTW5F"
      },
      "execution_count": 40,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def tanh(x):\n",
        "  \"\"\"It is an extension of the sigmoid function and also maps the input to a range between -1 and 1.\"\"\"\n",
        "  return (math.exp(x) - math.exp(-x)) / (math.exp(x) + math.exp(-x))"
      ],
      "metadata": {
        "id": "uOOaGvePThTi"
      },
      "execution_count": 41,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def relu(x):\n",
        "  \"\"\"It applies a simple thresholding operation to the input values, transforming negative values to zero and leaving positive values unchanged.\"\"\"\n",
        "  return max(0,x)"
      ],
      "metadata": {
        "id": "tmV-ggQ6U-sl"
      },
      "execution_count": 42,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def leaky_relu(x, alpha=0.1):\n",
        "  \"\"\" Variation of ReLU, however, unlike ReLU, the Leaky ReLU allows a small non-zero gradient for negative inputs\"\"\"\n",
        "  return max(x, alpha * x)"
      ],
      "metadata": {
        "id": "_FwI3VVgVh3S"
      },
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def softmax(x):\n",
        "  \"\"\"It takes a vector of real numbers as input and outputs a probability distribution over multiple classes.\"\"\"\n",
        "  e_x = np.exp(x - np.max(x))\n",
        "  return e_x / np.sum(e_x, axis=0)"
      ],
      "metadata": {
        "id": "YGtt1XyEYqot"
      },
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Plot Methods"
      ],
      "metadata": {
        "id": "VZuBfJ3IT7_Q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_sigmoid():\n",
        "    # Generate 100 equally spaced values from -10 to 10\n",
        "    x = np.linspace(-10, 10, 100)\n",
        "    # Compute the sigmoid function values\n",
        "    y = 1 / (1 + np.exp(-x))\n",
        "\n",
        "    plt.plot(x, y)\n",
        "    plt.xlabel('Input')\n",
        "    plt.ylabel('Output')\n",
        "    plt.title('Sigmoidal Activation Function')\n",
        "    plt.grid(True)\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "azWd8Bz-T9kb"
      },
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_tanh():\n",
        "    # Generate values for x\n",
        "    x = np.linspace(-10, 10, 100)\n",
        "\n",
        "    # Compute tanh values for corresponding x\n",
        "    tanh = np.tanh(x)\n",
        "\n",
        "    # Plot the tanh function\n",
        "    plt.plot(x, tanh)\n",
        "    plt.xlabel('Input')\n",
        "    plt.ylabel('Output')\n",
        "    plt.title('Tanh Activation Function')\n",
        "    plt.grid(True)\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "Zn8a4Mt6UcDg"
      },
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_relu():\n",
        "    # Generate values for x\n",
        "    x = np.linspace(-10, 10, 100)\n",
        "\n",
        "    # Compute ReLU values for corresponding x\n",
        "    relu = np.maximum(0, x)\n",
        "\n",
        "    # Plot the ReLU function\n",
        "    plt.plot(x, relu)\n",
        "    plt.xlabel('Input')\n",
        "    plt.ylabel('Output')\n",
        "    plt.title('ReLU Activation Function')\n",
        "    plt.grid(True)\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "bNXP3nMmVRTF"
      },
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_leaky_relu():\n",
        "    # Generate values for x\n",
        "    x = np.linspace(-10, 10, 100)\n",
        "\n",
        "    # Define the leaky ReLU function\n",
        "    def leaky_relu(x, alpha=0.1):\n",
        "        return np.where(x >= 0, x, alpha * x)\n",
        "\n",
        "    # Compute leaky ReLU values for corresponding x\n",
        "    leaky_relu_values = leaky_relu(x)\n",
        "\n",
        "    # Plot the leaky ReLU function\n",
        "    plt.plot(x, leaky_relu_values)\n",
        "    plt.xlabel('Input')\n",
        "    plt.ylabel('Output')\n",
        "    plt.title('Leaky ReLU Activation Function')\n",
        "    plt.grid(True)\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "O-ZV__JbVZ5S"
      },
      "execution_count": 48,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_softmax():\n",
        "    class_labels = [\"Class A\", \"Class B\", \"Class C\"]\n",
        "    probabilities = np.array([0.2, 0.3, 0.5])\n",
        "    plt.bar(class_labels, probabilities)\n",
        "    plt.xlabel(\"Classes\")\n",
        "    plt.ylabel(\"Probability\")\n",
        "    plt.title(\"Softmax Activation Function\")\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "6QYX1UGNY8Zb"
      },
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Usage"
      ],
      "metadata": {
        "id": "P7JN8hTRZhp9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "default_values = [10, -1, 5]"
      ],
      "metadata": {
        "id": "P54gbLQeZgn_"
      },
      "execution_count": 50,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Sigmoid"
      ],
      "metadata": {
        "id": "nNnFldl8Z7xw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "for value in default_values:\n",
        "    print(f'{value} = {sigmoid(value)}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MP_sE_gzZ6oh",
        "outputId": "634609be-9324-48eb-f4f7-7e3234150ea5"
      },
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "10 = 0.9999546021312976\n",
            "-1 = 0.2689414213699951\n",
            "5 = 0.9933071490757153\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plot_sigmoid()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "26-XP3iBaeUm",
        "outputId": "a0dddfc1-d9cb-4831-c5ba-5fe8598d6140"
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Tanh"
      ],
      "metadata": {
        "id": "UKHcCyB2aikQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "for value in default_values:\n",
        "    print(f'{value} = {tanh(value)}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TgXlKtIWahry",
        "outputId": "780b9930-1fd6-49cb-9472-53dd9a105efe"
      },
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "10 = 0.9999999958776926\n",
            "-1 = -0.7615941559557649\n",
            "5 = 0.999909204262595\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plot_tanh()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "AboWUtAQiihR",
        "outputId": "96678a5c-0420-4d03-e9a5-230564ae362d"
      },
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## ReLU"
      ],
      "metadata": {
        "id": "t6kLSSwMaolI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "for value in default_values:\n",
        "    print(f'{value} = {relu(value)}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F0uEsg9marKY",
        "outputId": "ebb25273-7bff-479a-f4a4-e139f751385d"
      },
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "10 = 10\n",
            "-1 = 0\n",
            "5 = 5\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plot_relu()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "eb0ifeLcjBXM",
        "outputId": "738c3e88-01bc-460c-c5ff-de2886a95a22"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Leaky ReLU"
      ],
      "metadata": {
        "id": "YBU-7vpkarqe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "for value in default_values:\n",
        "    print(f'{value} = {leaky_relu(value)}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3-oba81EiapV",
        "outputId": "6f7aa664-f7db-4b8a-d8ef-ca6c0ae38c79"
      },
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "10 = 10\n",
            "-1 = -0.1\n",
            "5 = 5\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plot_leaky_relu()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "5d4Svf8vjTg3",
        "outputId": "955258bf-a36d-4c19-adaf-a65232b4bf8f"
      },
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Softmax"
      ],
      "metadata": {
        "id": "lhDxNncZibbY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.array([1, 2, 3])\n",
        "result = softmax(x)\n",
        "print(result)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7-GVrUHEiewe",
        "outputId": "61279b78-9689-4c76-de69-2367ee7b3873"
      },
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.09003057 0.24472847 0.66524096]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plot_softmax()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "peeCD8IxjlEX",
        "outputId": "e1f1bfef-9386-400a-e753-1bf76a009dd9"
      },
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}