diff --git a/notebooks/Block_2/Exercises Block 2 - Neural Networks.ipynb b/notebooks/Block_2/Exercises Block 2 - Neural Networks.ipynb
index 34838d4dba745894a5811d725b0aa268bb056ff3..848b5ae60deb427664171e5e2cdc2990a7b27df1 100644
--- a/notebooks/Block_2/Exercises Block 2 - Neural Networks.ipynb	
+++ b/notebooks/Block_2/Exercises Block 2 - Neural Networks.ipynb	
@@ -7,7 +7,7 @@
     "id": "YHI3vyhv5p85"
    },
    "source": [
-    "# Exercise 1 : Conversion from Celsius to Fahrenheit"
+    "# Exercise 1 : Conversion from Celsius to Fahrenheit (Simple Regression Analysis)"
    ]
   },
   {
@@ -26,7 +26,7 @@
     "\n",
     "\n",
     "Instead, we will give TensorFlow some sample Celsius values (0, 8, 15, 22, 38) and their corresponding Fahrenheit values (32, 46, 59, 72, 100).\n",
-    "Then, we will train a model that figures out the above formula through the training process."
+    "Then, we will train a model that figures out the above formula through the training process. This is a _simple regression analysis_ problem."
    ]
   },
   {
@@ -434,12 +434,12 @@
     "\n",
     "###  Datset\n",
     "\n",
-    "We investigate the data set of the challenger flight with broken O-rings (Y=1) vs start temperature."
+    "We investigate the data set of the challenger flight with broken O-rings (`Y=1`) versus start temperature."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -448,13 +448,13 @@
        "Text(0, 0.5, 'Broken O-rings')"
       ]
      },
-     "execution_count": 1,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -474,7 +474,7 @@
     "import numpy as np\n",
     "import pandas as pd\n",
     "import tempfile\n",
-    "data = np.asarray(pd.read_csv('./Daten/challenger.txt', sep=','), dtype='float32')\n",
+    "data = np.asarray(pd.read_csv('./challenger.txt', sep=','), dtype='float32')\n",
     "plt.plot(data[:,0], data[:,1], 'o')\n",
     "plt.axis([40, 85, -0.1, 1.2])\n",
     "plt.xlabel('Temperature [F]')\n",
@@ -483,11 +483,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 5,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[0. 1. 0. 0. 0. 0. 0. 0. 1. 1. 1. 0. 0. 1. 0. 0. 0. 0. 0. 0. 1. 0. 1.]\n"
+     ]
+    }
+   ],
    "source": [
-    "y_values = data[:,1]"
+    "y_values = data[:,1]\n",
+    "print(y_values)"
    ]
   },
   {
@@ -496,7 +505,7 @@
    "source": [
     "## Mathematical Notes\n",
     "\n",
-    "We are considering the likelihood $P(y_i=1|x_i)$ for the class $y_i=1$ given the $i-$th data point $x_i$ ($x_i$ could be a vector). This is given by:\n",
+    "We are considering the probability $P(y_i=1|x_i)$ for the class $y_i=1$ given the $i-$th data point $x_i$ ($x_i$ could be a vector). This is given by:\n",
     "\n",
     "$\n",
     "P(y_i=1 | x_i) = \\frac{e^{(b +  x_i w)}}{1 + e^{(b + x_i w)}} = [1 + e^{-(b + x_i w)}]^{-1}\n",
@@ -515,7 +524,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -536,10 +545,11 @@
     "# Initial Value for the weights\n",
     "w = -0.20\n",
     "b = 20.0\n",
-    "# Log-Likelihood \n",
+    "# predicted probabilities \n",
     "p_1 = 1 / (1 + np.exp(-x*w - b))\n",
-    "like = y * np.log(p_1) + (1-y) * np.log(1-p_1)\n",
-    "print(-np.mean(like))\n",
+    "# cross-entropy loss function\n",
+    "cross_entropy = y * np.log(p_1) + (1-y) * np.log(1-p_1)\n",
+    "print(-np.mean(cross_entropy))\n",
     "print(np.round(p_1,3))"
    ]
   },
@@ -563,7 +573,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -577,7 +587,7 @@
     },
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -598,9 +608,13 @@
     "y_pred = 1 / (1 + np.exp(-x_pred*w_val - b_val))\n",
     "plt.plot(x_pred, y_pred)\n",
     "\n",
+    "# predicted probabilities\n",
     "p_1 = 1 / (1 + np.exp(-x*w_val - b_val))\n",
-    "like = y * np.log(p_1) + (1-y) * np.log(1-p_1)\n",
-    "print(-np.mean(like))\n",
+    "\n",
+    "# cross-entropy loss function\n",
+    "cross_entropy = -np.mean(y * np.log(p_1) + (1-y) * np.log(1-p_1))\n",
+    "                         \n",
+    "print(cross_entropy)\n",
     "print(np.round(p_1,3))"
    ]
   },
@@ -608,7 +622,23 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## TODO : set up a Keras model"
+    "We can see that the value of the cross-entropy has decreased from 3.882916 to 0.9094435."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## TODO : determine the accuracy of this logistic regression model and the value of the cross-entropy function"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## TODO : set up a Keras model\n",
+    "\n",
+    "If there are two labels, we use `binary_crossentropy` as loss function. In this case, we use"
    ]
   },
   {
@@ -635,8 +665,6 @@
     }
    ],
    "source": [
-    "from keras.utils import to_categorical\n",
-    "y_binary = to_categorical(y)\n",
     "l0 = tf.keras.layers.Dense(<--- your code here ---->)\n",
     "model = tf.keras.Sequential([l0])\n",
     "model.compile(loss='binary_crossentropy', optimizer=tf.keras.optimizers.Adam(0.01))\n",
diff --git a/notebooks/Block_2/Solutions to Exercises - Block 2.ipynb b/notebooks/Block_2/Solutions to Exercises - Block 2.ipynb
index 6bbe5139f8f44eda4a56489aa50a4d44bc0157a2..e858721b511be9b97159c405339394230626ecc6 100644
--- a/notebooks/Block_2/Solutions to Exercises - Block 2.ipynb	
+++ b/notebooks/Block_2/Solutions to Exercises - Block 2.ipynb	
@@ -7,7 +7,7 @@
     "id": "YHI3vyhv5p85"
    },
    "source": [
-    "# Exercise 1 : Conversion from Celsius to Fahrenheit"
+    "# Exercise 1 : Conversion from Celsius to Fahrenheit (Simple Regression Analysis)"
    ]
   },
   {
@@ -25,8 +25,8 @@
     "Of course, it would be simple enough to create a conventional Python function that directly performs this calculation, but that wouldn't be machine learning.\n",
     "\n",
     "\n",
-    "Instead, we will give `TensorFlow` some sample Celsius values (0, 8, 15, 22, 38) and their corresponding Fahrenheit values (32, 46, 59, 72, 100).\n",
-    "Then, we will train a model that figures out the above formula through the training process."
+    "Instead, we will give TensorFlow some sample Celsius values (0, 8, 15, 22, 38) and their corresponding Fahrenheit values (32, 46, 59, 72, 100).\n",
+    "Then, we will train a model that figures out the above formula through the training process. This is a _simple regression analysis_ problem."
    ]
   },
   {
@@ -454,7 +454,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 8,
    "metadata": {
     "colab": {},
     "colab_type": "code",
@@ -466,19 +466,19 @@
      "output_type": "stream",
      "text": [
       "Finished training the model\n",
-      "[[211.74744]]\n",
-      "Model predicts that 100 degrees Celsius is: [[211.74744]] degrees Fahrenheit\n",
-      "These are the l0 variables: [array([[-0.07715903, -0.20700853,  0.09303203, -0.7815757 ]],\n",
-      "      dtype=float32), array([ 2.2330647, -3.0049088,  2.656292 , -3.0834572], dtype=float32)]\n",
-      "These are the l1 variables: [array([[ 0.37331566,  0.670332  , -0.6500106 , -0.16718145],\n",
-      "       [-0.13477354, -0.1432596 ,  0.85609394,  0.2517057 ],\n",
-      "       [ 1.290541  ,  0.86174154, -0.10719326,  0.621717  ],\n",
-      "       [ 0.2648061 , -0.6288689 ,  1.0755255 , -0.2527884 ]],\n",
-      "      dtype=float32), array([ 2.6429222,  2.9728847, -2.9935007,  2.8113384], dtype=float32)]\n",
-      "These are the l2 variables: [array([[ 0.8368167],\n",
-      "       [ 0.8074423],\n",
-      "       [-1.373887 ],\n",
-      "       [ 0.3907403]], dtype=float32), array([2.95269], dtype=float32)]\n"
+      "[[211.74745]]\n",
+      "Model predicts that 100 degrees Celsius is: [[211.74745]] degrees Fahrenheit\n",
+      "These are the l0 variables: [array([[-0.47996262,  0.25047022, -0.1492717 ,  0.11854655]],\n",
+      "      dtype=float32), array([-3.2115366,  3.1785958, -2.868187 ,  2.7906501], dtype=float32)]\n",
+      "These are the l1 variables: [array([[ 1.1949005 ,  0.80858207,  0.48969162,  0.57684636],\n",
+      "       [-0.31273484, -1.1010896 , -0.36613086,  0.34995782],\n",
+      "       [-0.07984556,  0.8192047 , -0.63080776, -0.01728256],\n",
+      "       [-0.8315819 ,  0.24608922,  0.9040395 ,  0.02908712]],\n",
+      "      dtype=float32), array([-3.1562395 , -3.0874147 ,  2.3403091 , -0.54884386], dtype=float32)]\n",
+      "These are the l2 variables: [array([[-1.1158108 ],\n",
+      "       [-1.3494587 ],\n",
+      "       [ 0.6974325 ],\n",
+      "       [-0.21758062]], dtype=float32), array([3.0711133], dtype=float32)]\n"
      ]
     }
    ],
@@ -523,12 +523,13 @@
     "\n",
     "###  Datset\n",
     "\n",
-    "We investigate the data set of the challenger flight with broken O-rings (Y=1) vs start temperature."
+    "We investigate the data set of the challenger flight with broken O-rings (`Y=1`\n",
+    ") vs start temperature."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 67,
    "metadata": {},
    "outputs": [
     {
@@ -537,7 +538,7 @@
        "Text(0, 0.5, 'Broken O-rings')"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 67,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -572,11 +573,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 68,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[0. 1. 0. 0. 0. 0. 0. 0. 1. 1. 1. 0. 0. 1. 0. 0. 0. 0. 0. 0. 1. 0. 1.]\n"
+     ]
+    }
+   ],
    "source": [
-    "y_values = data[:,1]"
+    "y_values = data[:,1]\n",
+    "print(y_values)"
    ]
   },
   {
@@ -604,7 +614,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 69,
    "metadata": {},
    "outputs": [
     {
@@ -625,10 +635,11 @@
     "# Initial Value for the weights\n",
     "w = -0.20\n",
     "b = 20.0\n",
-    "# Log-Likelihood \n",
+    "# predicted probabilities \n",
     "p_1 = 1 / (1 + np.exp(-x*w - b))\n",
-    "like = y * np.log(p_1) + (1-y) * np.log(1-p_1)\n",
-    "print(-np.mean(like))\n",
+    "# cross-entropy loss function\n",
+    "cross_entropy = -np.mean(y * np.log(p_1) + (1-y) * np.log(1-p_1))\n",
+    "print(cross_entropy)\n",
     "print(np.round(p_1,3))"
    ]
   },
@@ -652,7 +663,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 70,
    "metadata": {},
    "outputs": [
     {
@@ -687,9 +698,13 @@
     "y_pred = 1 / (1 + np.exp(-x_pred*w_val - b_val))\n",
     "plt.plot(x_pred, y_pred)\n",
     "\n",
+    "# predicted probabilities\n",
     "p_1 = 1 / (1 + np.exp(-x*w_val - b_val))\n",
-    "like = y * np.log(p_1) + (1-y) * np.log(1-p_1)\n",
-    "print(-np.mean(like))\n",
+    "\n",
+    "# cross-entropy loss function\n",
+    "cross_entropy = -np.mean(y * np.log(p_1) + (1-y) * np.log(1-p_1))\n",
+    "                         \n",
+    "print(cross_entropy)\n",
     "print(np.round(p_1,3))"
    ]
   },
@@ -697,53 +712,92 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## TODO : set up a Keras model"
+    "We can see that the value of the cross-entropy has decreased from 3.882916 to 0.9094435."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## TODO : determine the accuracy of this logistic regression model"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 71,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Accuracy:  0.8695652173913043\n"
+     ]
+    }
+   ],
+   "source": [
+    "y_pred = np.round(p_1, decimals=0).astype('int')\n",
+    "accuracy = np.mean(y==y_pred)\n",
+    "print(\"Accuracy: \", accuracy)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## TODO : set up a Keras model\n",
+    "\n",
+    "If there are two labels, we use `binary_crossentropy` as loss function. In this case, we use `softmax` as output layer."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 72,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "<keras.callbacks.History at 0x7fd95118a410>"
+       "<keras.callbacks.History at 0x7ff9ec4cf890>"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 72,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "from tensorflow.keras.utils import to_categorical\n",
-    "y_binary = to_categorical(y)\n",
-    "\n",
     "l0 = tf.keras.layers.Dense(units=1, activation = tf.nn.sigmoid, input_shape=[1])\n",
     "model = tf.keras.Sequential([l0])\n",
-    "model.compile(loss='binary_crossentropy', optimizer=tf.keras.optimizers.Adam(0.01))\n",
+    "model.compile(loss='binary_crossentropy', optimizer=tf.keras.optimizers.Adam(0.01), metrics=['accuracy'])\n",
     "model.fit(x, y, epochs=10000, verbose=False)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 73,
    "metadata": {},
    "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "WARNING:tensorflow:5 out of the last 9 calls to <function Model.make_predict_function.<locals>.predict_function at 0x7ff9ec4d09e0> triggered tf.function retracing. Tracing is expensive and the excessive number of tracings could be due to (1) creating @tf.function repeatedly in a loop, (2) passing tensors with different shapes, (3) passing Python objects instead of tensors. For (1), please define your @tf.function outside of the loop. For (2), @tf.function has experimental_relax_shapes=True option that relaxes argument shapes that can avoid unnecessary retracing. For (3), please refer to https://www.tensorflow.org/guide/function#controlling_retracing and https://www.tensorflow.org/api_docs/python/tf/function for  more details.\n"
+     ]
+    },
     {
      "data": {
       "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x7fd950f0bc90>]"
+       "[<matplotlib.lines.Line2D at 0x7ff9ec50e710>]"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 73,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -765,14 +819,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 74,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[array([[-0.23204683]], dtype=float32), array([15.034954], dtype=float32)]\n"
+      "[array([[-0.23215847]], dtype=float32), array([15.042496], dtype=float32)]\n"
      ]
     }
    ],
@@ -782,21 +836,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 75,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.4416347\n",
-      "[[0.43  0.23  0.274 0.322 0.375 0.158 0.13  0.23  0.859 0.603 0.23  0.045\n",
-      "  0.375 0.939 0.375 0.086 0.23  0.023 0.069 0.036 0.086 0.069 0.829]]\n"
+      "Cross-entropy:  0.4416346\n",
+      "Accuracy:  0.8695652173913043\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -817,10 +870,31 @@
     "y_pred = 1 / (1 + np.exp(-x_pred*w_val - b_val))\n",
     "plt.plot(x_pred, y_pred)\n",
     "\n",
+    "# predicted probabilities\n",
     "p_1 = 1 / (1 + np.exp(-x*w_val - b_val))\n",
-    "like = y * np.log(p_1) + (1-y) * np.log(1-p_1)\n",
-    "print(-np.mean(like))\n",
-    "print(np.round(p_1,3))"
+    "\n",
+    "# cross-entropy loss function\n",
+    "cross_entropy = -np.mean(y * np.log(p_1) + (1-y) * np.log(1-p_1))\n",
+    "print(\"Cross-entropy: \", cross_entropy)\n",
+    "y_pred = np.round(p_1, decimals=0).astype('int')\n",
+    "accuracy = np.mean(y==y_pred)\n",
+    "print(\"Accuracy: \", accuracy)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "model.evaluate(x, y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The value of the cross-entropy loss function could be decreased from "
    ]
   },
   {