04_Redes_neuronales_densamente_conectadas.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "04_Redes_neuronales_densamente_conectadas.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0M4J-yXFSOTa",
        "colab_type": "text"
      },
      "source": [
        "# 04. Redes neuronales densamente conectadas\n",
        "[**Python Deep Learning** Introducción práctica con Keras y TensorFlow 2. Jordi Torres. Editorial Marcombo ISBN: 9788426728289 ](https://www.marcombo.com/python-deep-learning-9788426728289/)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ryl6ALGLSdUP",
        "colab_type": "text"
      },
      "source": [
        "## Inicializaciones"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s3KzA9ZUuLRB",
        "colab_type": "code",
        "outputId": "5e07b15d-84e7-4f5d-e2a0-652d3d5b0524",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "try:\n",
        "  # %tensorflow_version solo existe en Colab.\n",
        "  %tensorflow_version 2.x\n",
        "except Exception:\n",
        "  pass\n",
        "\n",
        "import tensorflow as tf\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "print(tf.__version__)"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "TensorFlow 2.x selected.\n",
            "2.1.0-rc1\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w2B0J5r5SzrT",
        "colab_type": "text"
      },
      "source": [
        "## 4.1 Caso de estudio: reconocimiento de dígitos"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "715hLvWqwPrJ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "4ebe1083-7586-427d-a9d1-4a12f5184391"
      },
      "source": [
        "mnist = tf.keras.datasets.mnist\n",
        "\n",
        "(x_train, y_train), (x_test, y_test) = mnist.load_data()"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "11493376/11490434 [==============================] - 0s 0us/step\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RGWzf-U5TBhm",
        "colab_type": "code",
        "outputId": "5e25eba7-da8a-484a-de89-86d8d48015b0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "plt.imshow(x_train[8], cmap=plt.cm.binary)\n",
        "print(y_train[8])"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjIsIGh0\ndHA6Ly9tYXRwbG90bGliLm9yZy8li6FKAAAL0klEQVR4nO3dXagc9R3G8eepMSgqGJslBo3GiiCh\n0ChLqPgWkfp2E/VCzIWkII0XCgpeVO2FXkqpbxdViDUYizUKvkWQVhsEEUHcSKrR2GokwcS8bBSj\ngpiov16cUY7x7OxmZ3Zn9ff9wLK789898zA5T2Z3Zvf8HREC8PP3i6YDABgPyg4kQdmBJCg7kARl\nB5KYNc6VzZ07NxYuXDjOVQKpbN26VXv37vVMY5XKbvsSSfdJOkzS3yLizrLHL1y4UJ1Op8oqAZRo\nt9s9x4Z+GW/7MEl/lXSppEWSltteNOzPAzBaVd6zL5H0fkR8EBH7Ja2VtKyeWADqVqXsJ0j6cNr9\n7cWyH7C90nbHdqfb7VZYHYAqRn40PiJWRUQ7ItqtVmvUqwPQQ5Wy75C0YNr9E4tlACZQlbK/Luk0\n26fYni3paknr6okFoG5Dn3qLiK9t3yDpX5o69bY6It6uLRmAWlU6zx4Rz0t6vqYsAEaIj8sCSVB2\nIAnKDiRB2YEkKDuQBGUHkqDsQBKUHUiCsgNJUHYgCcoOJEHZgSQoO5AEZQeSoOxAEpQdSIKyA0lQ\ndiAJyg4kQdmBJCg7kARlB5Kg7EASlB1IgrIDSVB2IAnKDiRB2YEkKDuQRKVZXDH5Dhw4UDr+6quv\nlo7feuutlZ6PyVGp7La3Svpc0jeSvo6Idh2hANSvjj37BRGxt4afA2CEeM8OJFG17CHpBdsbbK+c\n6QG2V9ru2O50u92KqwMwrKplPycizpR0qaTrbZ938AMiYlVEtCOi3Wq1Kq4OwLAqlT0idhTXeyQ9\nLWlJHaEA1G/osts+yvYx392WdJGkTXUFA1CvKkfj50l62vZ3P+cfEfHPWlKhNvv27SsdX7p0aen4\n8ccfXzq+a9euSs/H+Axd9oj4QNJvaswCYIQ49QYkQdmBJCg7kARlB5Kg7EASfMUVpfqdWuPU208H\ne3YgCcoOJEHZgSQoO5AEZQeSoOxAEpQdSIKyA0lQdiAJyg4kQdmBJCg7kARlB5Kg7EASlB1Igu+z\no5Ivv/yy6QgYEHt2IAnKDiRB2YEkKDuQBGUHkqDsQBKUHUiC8+yoZMOGDaXjZ5111piSoJ++e3bb\nq23vsb1p2rLjbL9o+73ies5oYwKoapCX8Q9LuuSgZbdIWh8Rp0laX9wHMMH6lj0iXpb0yUGLl0la\nU9xeI+nymnMBqNmwB+jmRcTO4vYuSfN6PdD2Stsd251utzvk6gBUVflofESEpCgZXxUR7Yhot1qt\nqqsDMKRhy77b9nxJKq731BcJwCgMW/Z1klYUt1dIeraeOABGpe95dtuPSVoqaa7t7ZJul3SnpCds\nXytpm6SrRhkSw5s1q/yf+Nhjjy0d//TTT0vHt2zZcsiZ0Iy+ZY+I5T2GLqw5C4AR4uOyQBKUHUiC\nsgNJUHYgCcoOJMFXXH/m+p1aO/fcc0vHn3vuuTrjoEHs2YEkKDuQBGUHkqDsQBKUHUiCsgNJUHYg\nCcoOJEHZgSQoO5AEZQeSoOxAEpQdSIKyA0lQdiAJvs+OSj7++OOmI2BA7NmBJCg7kARlB5Kg7EAS\nlB1IgrIDSVB2IAnOs6OSdevWNR0BA+q7Z7e92vYe25umLbvD9g7bG4vLZaONCaCqQV7GPyzpkhmW\n3xMRi4vL8/XGAlC3vmWPiJclfTKGLABGqMoBuhtsv1m8zJ/T60G2V9ru2O50u90KqwNQxbBlf0DS\nqZIWS9op6a5eD4yIVRHRjoh2q9UacnUAqhqq7BGxOyK+iYhvJT0oaUm9sQDUbaiy254/7e4Vkjb1\neiyAydD3PLvtxyQtlTTX9nZJt0taanuxpJC0VdJ1I8yIEbrgggtKx5mf/eejb9kjYvkMix8aQRYA\nI8THZYEkKDuQBGUHkqDsQBKUHUiCr7gmd9JJJ1V6/v79+0vHt23b1nPs5JNPrrRuHBr27EASlB1I\ngrIDSVB2IAnKDiRB2YEkKDuQBOfZk5s1q9qvQESUjn/11VeVfj7qw54dSIKyA0lQdiAJyg4kQdmB\nJCg7kARlB5LgPHtyy5YtKx0//fTTS8fffffd0vF7772359j9999f+lzUiz07kARlB5Kg7EASlB1I\ngrIDSVB2IAnKDiTBeXaUuvjii0vHP/roo9Lxu+++u844qKDvnt32Atsv2X7H9tu2byyWH2f7Rdvv\nFddzRh8XwLAGeRn/taSbI2KRpN9Kut72Ikm3SFofEadJWl/cBzCh+pY9InZGxBvF7c8lbZZ0gqRl\nktYUD1sj6fJRhQRQ3SEdoLO9UNIZkl6TNC8idhZDuyTN6/GclbY7tjvdbrdCVABVDFx220dLelLS\nTRHx2fSxmPqrgzP+5cGIWBUR7Yhot1qtSmEBDG+gsts+XFNFfzQinioW77Y9vxifL2nPaCICqEPf\nU2+2LekhSZsjYvp5lHWSVki6s7h+diQJMdGmfj16mz179piSoJ9BzrOfLekaSW/Z3lgsu01TJX/C\n9rWStkm6ajQRAdShb9kj4hVJvf77vrDeOABGhY/LAklQdiAJyg4kQdmBJCg7kARfcUUl+/btKx1/\n5plneo5deeWVdcdBCfbsQBKUHUiCsgNJUHYgCcoOJEHZgSQoO5AE59lR6vHHHy8dP+KII0rHFy1a\nVGccVMCeHUiCsgNJUHYgCcoOJEHZgSQoO5AEZQeS4Dw7Sp1//vml45s3by4dP/LII+uMgwrYswNJ\nUHYgCcoOJEHZgSQoO5AEZQeSoOxAEoPMz75A0iOS5kkKSasi4j7bd0j6g6Ru8dDbIuL5UQVFM9au\nXdt0BNRkkA/VfC3p5oh4w/YxkjbYfrEYuyci/jK6eADqMsj87Dsl7Sxuf257s6QTRh0MQL0O6T27\n7YWSzpD0WrHoBttv2l5te06P56y03bHd6Xa7Mz0EwBgMXHbbR0t6UtJNEfGZpAcknSppsab2/HfN\n9LyIWBUR7Yhot1qtGiIDGMZAZbd9uKaK/mhEPCVJEbE7Ir6JiG8lPShpyehiAqiqb9ltW9JDkjZH\nxN3Tls+f9rArJG2qPx6AugxyNP5sSddIesv2xmLZbZKW216sqdNxWyVdN5KEAGoxyNH4VyR5hiHO\nqQM/IXyCDkiCsgNJUHYgCcoOJEHZgSQoO5AEZQeSoOxAEpQdSIKyA0lQdiAJyg4kQdmBJCg7kIQj\nYnwrs7uStk1bNFfS3rEFODSTmm1Sc0lkG1ad2U6OiBn//ttYy/6jldudiGg3FqDEpGab1FwS2YY1\nrmy8jAeSoOxAEk2XfVXD6y8zqdkmNZdEtmGNJVuj79kBjE/Te3YAY0LZgSQaKbvtS2z/1/b7tm9p\nIkMvtrfafsv2RtudhrOstr3H9qZpy46z/aLt94rrGefYayjbHbZ3FNtuo+3LGsq2wPZLtt+x/bbt\nG4vljW67klxj2W5jf89u+zBJ/5P0O0nbJb0uaXlEvDPWID3Y3iqpHRGNfwDD9nmSvpD0SET8ulj2\nZ0mfRMSdxX+UcyLijxOS7Q5JXzQ9jXcxW9H86dOMS7pc0u/V4LYryXWVxrDdmtizL5H0fkR8EBH7\nJa2VtKyBHBMvIl6W9MlBi5dJWlPcXqOpX5ax65FtIkTEzoh4o7j9uaTvphlvdNuV5BqLJsp+gqQP\np93frsma7z0kvWB7g+2VTYeZwbyI2Fnc3iVpXpNhZtB3Gu9xOmia8YnZdsNMf14VB+h+7JyIOFPS\npZKuL16uTqSYeg82SedOB5rGe1xmmGb8e01uu2GnP6+qibLvkLRg2v0Ti2UTISJ2FNd7JD2tyZuK\nevd3M+gW13sazvO9SZrGe6ZpxjUB267J6c+bKPvrkk6zfYrt2ZKulrSugRw/Yvuo4sCJbB8l6SJN\n3lTU6yStKG6vkPRsg1l+YFKm8e41zbga3naNT38eEWO/SLpMU0fkt0j6UxMZeuT6laT/FJe3m84m\n6TFNvaw7oKljG9dK+qWk9ZLek/RvScdNULa/S3pL0puaKtb8hrKdo6mX6G9K2lhcLmt625XkGst2\n4+OyQBIcoAOSoOxAEpQdSIKyA0lQdiAJyg4kQdmBJP4PCKah1KhMT5gAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OOVttVw2TMuU",
        "colab_type": "code",
        "outputId": "64d1edfa-5004-4ac1-ed22-5e727e096a6d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 501
        }
      },
      "source": [
        "np.set_printoptions(precision=2, suppress=True, linewidth=120)\n",
        "print(np.matrix(x_train[8]))"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   5  63 197   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0  20 254 230  24   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0  20 254 254  48   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0  20 254 255  48   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0  20 254 254  57   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0  20 254 254 108   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0  16 239 254 143   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0 178 254 143   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0 178 254 143   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0 178 254 162   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0 178 254 240   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0 113 254 240   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0  83 254 245  31   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0  79 254 246  38   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0 214 254 150   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0 144 241   8   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0 144 240   2   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0 144 254  82   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0 230 247  40   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0 168 209  31   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]\n",
            " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lqciPxRNU99j",
        "colab_type": "text"
      },
      "source": [
        "## 4.4 Función de activación softmax"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eY_9fDfkVExh",
        "colab_type": "text"
      },
      "source": [
        "Modelo con una capa softmax para visualizar los modelos aprendidos"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wpaiBuKeTNGr",
        "colab_type": "code",
        "outputId": "db2b0d59-96e9-4cc9-d10e-fe31f6490202",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 259
        }
      },
      "source": [
        "x_train = x_train.reshape((60000, 784))\n",
        "x_test = x_test.reshape((10000, 784))\n",
        "x_train, x_test = x_train / 255.0, x_test / 255.0\n",
        "\n",
        "model = tf.keras.models.Sequential([\n",
        "  tf.keras.layers.Dense(10, activation='softmax', name=\"FC1\", input_shape=(784,))\n",
        "])\n",
        "model.summary()\n",
        "\n",
        "model.compile(optimizer='adam',\n",
        "              loss='sparse_categorical_crossentropy',\n",
        "              metrics=['accuracy'])\n",
        "\n",
        "model.fit(x_train, y_train, epochs=1)\n",
        "\n",
        "model.evaluate(x_test,  y_test, verbose=2)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"sequential\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "FC1 (Dense)                  (None, 10)                7850      \n",
            "=================================================================\n",
            "Total params: 7,850\n",
            "Trainable params: 7,850\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n",
            "Train on 60000 samples\n",
            "60000/60000 [==============================] - 6s 98us/sample - loss: 0.4711 - accuracy: 0.8768\n",
            "10000/10000 - 1s - loss: 0.3086 - accuracy: 0.9162\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.3085567438960075, 0.9162]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Nhi-XHXoVqpn",
        "colab_type": "text"
      },
      "source": [
        "Figura 4.14 Modelo aprendido correspondiente al número 0"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2L96kEYlVSdQ",
        "colab_type": "code",
        "outputId": "90a74549-adeb-49ff-c41b-693508130ee1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "w = model.get_weights()\n",
        "w = np.asarray(w[0])\n",
        "plt.figure()\n",
        "plt.imshow(w[:,0].reshape([28,28]), cmap=plt.get_cmap('seismic_r'))"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f7a0eb5d240>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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EEI0LbZcVIhFkdiESQWYXIhFkdiESQWYXIhHM3XN2sqKijLdpE06f3RkZm3xpARkgvJuU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\nXYhEkNmFSASZXYhE+F8vQkYMOD324gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JF1cc6xoWtGE",
        "colab_type": "text"
      },
      "source": [
        "Figura 4.5 Matriz de parámetros correspondiente al modelo de la categoría cero"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z0EhD5-QVSgA",
        "colab_type": "code",
        "outputId": "a4b81181-c72f-4c28-de1b-f51b67123cc5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        }
      },
      "source": [
        "np.set_printoptions(precision=0, suppress = True, linewidth=220)\n",
        "print(np.matrix (255*(w[:,0].reshape([28,28]))))"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[  13.   19.   18.   17.  -21.  -12.   10.  -11.  -16.   20.    3.   22.   15.   -8.  -15.   -7.    1.   14.   -6.  -20.  -13.   17.   -6.   18.  -15.  -12.   12.    1.]\n",
            " [  10.   -8.    8.   19.   11.   15.    2.   12.   16.   -2.  -20.  -21.    4.    9.   -7.   -2.  -33.  -18.  -17.  -46.  -37.  -28.  -30.  -18.   -5.    6.   21.    7.]\n",
            " [   9.    4.   -6.    3.   14.  -34.  -11.  -30.  -32.  -37.  -39.  -53.  -18.  -18.  -37.  -37.  -67.  -79.  -41.  -60.  -24.  -53.  -23.   -1.   -2.  -13.  -19.    8.]\n",
            " [   5.   18.   -0.   17.  -28.  -28.  -32.  -21.  -15.  -24.  -52.  -20.  -15.  -13.  -51.  -46.  -51.  -22.  -52.  -36.  -63.  -41.  -38.  -29.   -5.  -23.    1.   -8.]\n",
            " [ -16.   15.    6.  -21.  -47.  -53.  -43.  -45.  -26.  -19.   -2.  -13.  -25.   -5.  -12.  -10.   16.  -25.   -9.   -5.   -2.  -34.  -32.  -18.  -33.  -26.  -12.  -25.]\n",
            " [  12.   -6.   12.    3.  -36.  -74.  -24.  -24.  -22.  -38.  -22.  -31.   14.   19.   22.   19.   19.   18.    9.   20.    8.   -2.   -1.  -43.  -38.  -81.  -31.   -2.]\n",
            " [   0.   13.   -5.  -33.  -26.  -17.  -19.  -25.  -25.  -10.  -15.  -20.  -11.    3.   16.   10.   44.   45.   21.   27.    7.   22.   -6.  -26.  -60.  -72.  -31.  -25.]\n",
            " [  -4.   -7.  -10.  -42.  -29.  -39.  -34.  -46.  -28.  -38.   -1.    5.  -18.   24.   15.   29.   32.   46.   36.   18.    5.   -7.   20.    9.  -41.  -79.  -66.    7.]\n",
            " [   8.    9.  -17.  -37.  -53.  -46.  -25.  -13.  -39.  -20.    4.   -0.  -13.   -6.   18.    4.   39.   57.   28.   43.   31.    3.   14.   -3.  -42.  -89.  -57.  -28.]\n",
            " [ -18.   -5.   -2.  -22.  -51.  -29.  -16.  -29.  -13.  -14.  -27.   -8.   -9.   32.    9.   -0.   16.   19.   26.   21.    7.    2.   11.   33.  -18.  -61.  -74.   -1.]\n",
            " [  -4.  -25.  -20.   -7.  -42.  -11.  -34.  -14.    0.    4.   -3.    1.   21.   31.   15.  -19.  -20.    0.   43.   30.   23.   20.   44.   34.   23.  -80.  -64.  -27.]\n",
            " [  11.   13.  -10.  -38.  -60.   -3.  -24.   10.  -30.  -11.    3.   10.   -3.  -33.  -65.  -76.  -66.  -44.    7.   25.   33.   48.   25.   36.   28.  -53.  -57.  -27.]\n",
            " [  -0.  -13.  -30.  -52.  -46.  -20.   -7.  -10.  -15.   -6.   28.   -5.   12.  -44.  -75.  -87.  -97.  -54.  -38.  -15.   -4.   26.   41.   59.   30.  -26.  -43.  -22.]\n",
            " [ -20.   15.    4.  -24.   -6.    1.   36.   14.   11.   -5.   27.   -1.   -9.  -56. -106. -109.  -81.  -69.  -12.   13.   -4.   36.   50.   69.   40.   11.  -13.   -2.]\n",
            " [ -24.  -21.    4.  -51.  -28.    1.   35.    9.   29.   15.   25.    4.  -44. -107. -120. -122.  -96.  -57.  -44.  -14.   -8.   31.   45.   49.   33.   -5.  -27.  -17.]\n",
            " [  -8.  -28.  -29.  -39.  -17.    8.   25.   36.   44.   36.   44.  -13.  -58.  -87.  -89. -116.  -94.  -37.    3.    3.   30.    7.   34.   21.   31.   -9.  -40.  -37.]\n",
            " [ -16.  -25.  -39.  -67.    8.   31.   24.   21.   23.   42.   35.  -21.  -71.  -88. -118.  -99.  -38.  -40.   -7.   -8.   15.   18.    8.   37.   -9.  -16.  -30.   -6.]\n",
            " [  16.  -10.  -42.  -44.  -25.   34.   17.   42.   19.   23.   47.  -38.  -60. -107.  -90.  -71.  -51.  -13.   -1.   16.  -15.   26.   20.    8.    8.   -8.   -8.   10.]\n",
            " [ -13.    8.  -33.  -49.  -25.    0.   11.   22.   37.   43.   41.   -9.  -33.  -86.  -59.  -30.  -15.    7.   17.  -21.  -16.   19.   20.  -16.   -0.  -13.  -29.  -22.]\n",
            " [  -7.    3.  -22.  -40.   -7.   14.    8.   23.   13.   16.   42.   11.  -21.  -31.  -26.  -22.  -11.  -19.    2.   -4.   -8.    6.    5.   -1.    1.  -28.  -57.  -34.]\n",
            " [  -5.   -3.  -21.  -61.  -21.    1.  -15.    5.   19.   44.   37.   30.   -1.   -0.    5.    3.    1.    9.   -3.   -3.  -21.  -18.  -25.   -5.  -17.  -25.   -3.  -14.]\n",
            " [ -17.    8.    5.  -17.  -39.  -12.   24.   15.   -7.   30.   13.   52.   19.   16.   13.   -3.   -7.  -13.  -25.  -29.   -4.  -13.  -11.  -44.   -5.  -11.  -21.   12.]\n",
            " [ -16.  -19.  -21.  -15.  -32.   -6.   -1.   23.   -1.   35.   35.   28.   21.   24.   20.   13.  -14.   -7.   -7.    1.  -30.   -5.  -39.  -38.  -11.   11.   20.    2.]\n",
            " [  -0.   -6.    2.  -24.  -60.  -42.  -29.   17.  -10.   36.   49.   33.   37.   39.   16.   28.   12.   -4.  -44.  -38.  -35.  -31.  -35.  -44.   -2.  -42.   -7.  -11.]\n",
            " [  -9.   -0.   -4.  -15.  -24.  -19.  -29.  -18.  -40.  -17.  -12.  -15.   -6.   -3.  -17.  -36.  -46.  -24.  -44.  -54.  -73.  -56.  -33.  -17.  -18.   -7.    9.   12.]\n",
            " [  13.   -2.   16.   -4.  -24.  -48.  -43.  -72.  -67.  -74.  -76.  -76.  -70.  -74.  -95. -101.  -93.  -69.  -68.  -76.  -51.  -49.  -21.  -35.   -6.  -17.   -9.  -17.]\n",
            " [  -1.    5.   21.   16.  -12.   -8.   -6.  -37.  -19.  -61.  -70.  -52.  -41.  -78.  -36.  -38.  -41.  -60.  -54.  -17.  -45.  -31.  -32.  -29.  -18.   12.   -0.  -20.]\n",
            " [   4.   -8.   -1.   14.  -21.   -4.  -22.   -5.  -39.    1.  -14.  -18.   -7.  -22.   -9.  -12.   -4.   -9.  -22.  -23.  -12.  -31.   -4.  -10.  -21.  -19.   10.  -11.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vDEEuEtgW9qV",
        "colab_type": "text"
      },
      "source": [
        "Figura 4.16 Modelo aprendido correspondiente al número 3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "227dP4lWVSji",
        "colab_type": "code",
        "outputId": "a7bd822d-72ed-4bd0-fa95-965c4f706a8b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "w = model.get_weights()\n",
        "w = np.asarray(w[0])\n",
        "plt.figure()\n",
        "plt.imshow(w[:,3].reshape([28,28]), cmap=plt.get_cmap('seismic_r'))"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f7a003039b0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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IRJDZhUiEnJa4VlUB06eH9YqKSJ4I4b7GXbvy1FpFBd9zLEW1eHFYO7/LGzz4uee4/pvf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\nD+YAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}