svpino/multiplying-values-using-neural-networks-keras.ipynb

## multiplying-values-using-neural-networks-keras.ipynb
{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "multiplying-values-using-neural-networks-keras.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "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/svpino/a27f8039ce54c27b1c493ee866ee8d69/multiplying-values-using-neural-networks-keras.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z_qGVgfrAbJv",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "try:\n",
        "  %tensorflow_version 2.x\n",
        "except Exception:\n",
        "  pass\n",
        "\n",
        "import tensorflow as tf\n",
        "\n",
        "import numpy as np\n",
        "import logging\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "logger = tf.get_logger()\n",
        "logger.setLevel(logging.ERROR)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lIXH9TIHP4Fe",
        "colab_type": "code",
        "outputId": "5247a2a0-8cdd-44dc-caa2-f37ef81a11e3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 652
        }
      },
      "source": [
        "DATASET_TRAINING_SIZE = 100\n",
        "DATASET_TESTING_SIZE = 1000\n",
        "NUMBER_OF_ELEMENTS_TO_PRINT = 5\n",
        "\n",
        "# Let's first generate the training dataset. We are going to generate \n",
        "# a set of values ranging from 'low' to 'high'.\n",
        "X = np.random.randint(low=1, high=9, size=(DATASET_TRAINING_SIZE, 2))\n",
        "\n",
        "# We can determine the training labels by multiplying each pair generated\n",
        "# before.\n",
        "y = np.prod(X, axis=1).reshape(DATASET_TRAINING_SIZE, 1)\n",
        "\n",
        "# Since we are trying to approximate multiplication, we know there will \n",
        "# be a lot of variance in the results. Also, multipliying numbers can \n",
        "# really quickly spin out network out of control. We can minimize this \n",
        "# problem by normalizing the input values. In this case, we are using\n",
        "# log normalization.\n",
        "X = np.log(X)\n",
        "\n",
        "# Let's setup our network. \n",
        "model = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(units=4, input_shape=(2,)),\n",
        "  tf.keras.layers.Dense(units=4, activation=\"relu\"),\n",
        "  tf.keras.layers.Dense(units=1)\n",
        "])\n",
        "\n",
        "model.compile(loss='mean_squared_error', \n",
        "              optimizer=tf.keras.optimizers.Adam(0.01))\n",
        "\n",
        "# Let's start training our network using the generated training set.\n",
        "history = model.fit(X, y, epochs=250, batch_size=10, verbose=False)\n",
        "\n",
        "# At this point we already have our model fully trained. We can now \n",
        "# generate some testing data (using the same method we used to generate\n",
        "# our training data).\n",
        "X_test = np.random.randint(low=1, high=9, size=(DATASET_TESTING_SIZE, 2))\n",
        "y_test = np.prod(X_test, axis=1).reshape(DATASET_TESTING_SIZE, 1)\n",
        "\n",
        "# Before applying the log normalization to the training data, let's\n",
        "# print a few of the pairs.\n",
        "print(f\"X_test:\\n{X_test[:NUMBER_OF_ELEMENTS_TO_PRINT]}\")\n",
        "print(f\"y_test:\\n{y_test[:NUMBER_OF_ELEMENTS_TO_PRINT]}\")\n",
        "\n",
        "# We can now apply log normalization to the training data.\n",
        "X_test = np.log(X_test)\n",
        "\n",
        "# Let's run inference on the testing dataset.\n",
        "predictions = model.predict(X_test)\n",
        "print(f\"Predictions:\\n{predictions[:NUMBER_OF_ELEMENTS_TO_PRINT]}\")\n",
        "\n",
        "# To see how we did, we can compute the RMSE on the results of the\n",
        "# testing dataset\n",
        "rmse = np.sqrt(np.mean((predictions - y_test)**2))\n",
        "print(f\"\\nRMSE: {rmse}\")\n",
        "\n",
        "# Finally, we can plot the loss during training. \n",
        "plt.title(\"Loss\")\n",
        "plt.xlabel('Epoch')\n",
        "plt.ylabel(\"Loss\")\n",
        "plt.plot(history.history['loss'])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "X_test:\n",
            "[[4 3]\n",
            " [8 3]\n",
            " [5 8]\n",
            " [6 1]\n",
            " [3 8]]\n",
            "y_test:\n",
            "[[12]\n",
            " [24]\n",
            " [40]\n",
            " [ 6]\n",
            " [24]]\n",
            "Predictions:\n",
            "[[10.943055]\n",
            " [23.558733]\n",
            " [40.33994 ]\n",
            " [ 6.702338]\n",
            " [23.941874]]\n",
            "\n",
            "RMSE: 0.8370817671559032\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f99b16c1d30>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
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KPQXdo1lERKEA5LJakioiAgoFABpzWXoL6imIiCgUgMa6iJ4BhYKIiEIBaMwrFEREQKEA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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}
	{
	"nbformat": 4,
	"nbformat_minor": 0,
	"metadata": {
	"colab": {
	"name": "multiplying-values-using-neural-networks-keras.ipynb",
	"provenance": [],
	"collapsed_sections": [],
	"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/svpino/a27f8039ce54c27b1c493ee866ee8d69/multiplying-values-using-neural-networks-keras.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "z_qGVgfrAbJv",
	"colab_type": "code",
	"colab": {}
	},
	"source": [
	"try:\n",
	" %tensorflow_version 2.x\n",
	"except Exception:\n",
	" pass\n",
	"\n",
	"import tensorflow as tf\n",
	"\n",
	"import numpy as np\n",
	"import logging\n",
	"import matplotlib.pyplot as plt\n",
	"\n",
	"logger = tf.get_logger()\n",
	"logger.setLevel(logging.ERROR)"
	],
	"execution_count": 0,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "lIXH9TIHP4Fe",
	"colab_type": "code",
	"outputId": "5247a2a0-8cdd-44dc-caa2-f37ef81a11e3",
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 652
	}
	},
	"source": [
	"DATASET_TRAINING_SIZE = 100\n",
	"DATASET_TESTING_SIZE = 1000\n",
	"NUMBER_OF_ELEMENTS_TO_PRINT = 5\n",
	"\n",
	"# Let's first generate the training dataset. We are going to generate \n",
	"# a set of values ranging from 'low' to 'high'.\n",
	"X = np.random.randint(low=1, high=9, size=(DATASET_TRAINING_SIZE, 2))\n",
	"\n",
	"# We can determine the training labels by multiplying each pair generated\n",
	"# before.\n",
	"y = np.prod(X, axis=1).reshape(DATASET_TRAINING_SIZE, 1)\n",
	"\n",
	"# Since we are trying to approximate multiplication, we know there will \n",
	"# be a lot of variance in the results. Also, multipliying numbers can \n",
	"# really quickly spin out network out of control. We can minimize this \n",
	"# problem by normalizing the input values. In this case, we are using\n",
	"# log normalization.\n",
	"X = np.log(X)\n",
	"\n",
	"# Let's setup our network. \n",
	"model = tf.keras.Sequential([\n",
	" tf.keras.layers.Dense(units=4, input_shape=(2,)),\n",
	" tf.keras.layers.Dense(units=4, activation=\"relu\"),\n",
	" tf.keras.layers.Dense(units=1)\n",
	"])\n",
	"\n",
	"model.compile(loss='mean_squared_error', \n",
	" optimizer=tf.keras.optimizers.Adam(0.01))\n",
	"\n",
	"# Let's start training our network using the generated training set.\n",
	"history = model.fit(X, y, epochs=250, batch_size=10, verbose=False)\n",
	"\n",
	"# At this point we already have our model fully trained. We can now \n",
	"# generate some testing data (using the same method we used to generate\n",
	"# our training data).\n",
	"X_test = np.random.randint(low=1, high=9, size=(DATASET_TESTING_SIZE, 2))\n",
	"y_test = np.prod(X_test, axis=1).reshape(DATASET_TESTING_SIZE, 1)\n",
	"\n",
	"# Before applying the log normalization to the training data, let's\n",
	"# print a few of the pairs.\n",
	"print(f\"X_test:\\n{X_test[:NUMBER_OF_ELEMENTS_TO_PRINT]}\")\n",
	"print(f\"y_test:\\n{y_test[:NUMBER_OF_ELEMENTS_TO_PRINT]}\")\n",
	"\n",
	"# We can now apply log normalization to the training data.\n",
	"X_test = np.log(X_test)\n",
	"\n",
	"# Let's run inference on the testing dataset.\n",
	"predictions = model.predict(X_test)\n",
	"print(f\"Predictions:\\n{predictions[:NUMBER_OF_ELEMENTS_TO_PRINT]}\")\n",
	"\n",
	"# To see how we did, we can compute the RMSE on the results of the\n",
	"# testing dataset\n",
	"rmse = np.sqrt(np.mean((predictions - y_test)**2))\n",
	"print(f\"\\nRMSE: {rmse}\")\n",
	"\n",
	"# Finally, we can plot the loss during training. \n",
	"plt.title(\"Loss\")\n",
	"plt.xlabel('Epoch')\n",
	"plt.ylabel(\"Loss\")\n",
	"plt.plot(history.history['loss'])"
	],
	"execution_count": 0,
	"outputs": [
	{
	"output_type": "stream",
	"text": [
	"X_test:\n",
	"[[4 3]\n",
	" [8 3]\n",
	" [5 8]\n",
	" [6 1]\n",
	" [3 8]]\n",
	"y_test:\n",
	"[[12]\n",
	" [24]\n",
	" [40]\n",
	" [ 6]\n",
	" [24]]\n",
	"Predictions:\n",
	"[[10.943055]\n",
	" [23.558733]\n",
	" [40.33994 ]\n",
	" [ 6.702338]\n",
	" [23.941874]]\n",
	"\n",
	"RMSE: 0.8370817671559032\n"
	],
	"name": "stdout"
	},
	{
	"output_type": "execute_result",
	"data": {
	"text/plain": [
	"[<matplotlib.lines.Line2D at 0x7f99b16c1d30>]"
	]
	},
	"metadata": {
	"tags": []
	},
	"execution_count": 4
	},
	{
	"output_type": "display_data",
	"data": {
	"image/png": 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KPQXdo1lERKEA5LJakioiAgoFABpzWXoL6imIiCgUgMa6iJ4BhYKIiEIBaMwrFEREQKEA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\nAElFTkSuQmCC\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {
	"tags": []
	}
	}
	]
	}
	]
	}