diff --git a/neural_nets_intro.ipynb b/neural_nets_intro.ipynb
index 093e83a9447f9315d7d43dbc6bcc91d4171eda82..85367a5d189a733acce7894243b8dba77e1d4a49 100644
--- a/neural_nets_intro.ipynb
+++ b/neural_nets_intro.ipynb
@@ -37,7 +37,7 @@
     "\n",
     "1997: Long-short term memory (LSTM) model\n",
     "\n",
-    "2014: GRU"
+    "2014: GRU, GAN ?"
    ]
   },
   {
@@ -64,17 +64,18 @@
     "$$\n",
     "f(weighted\\_sum) = \\left\\{\n",
     "        \\begin{array}{ll}\n",
-    "            0 & \\quad g < threshold \\\\\n",
-    "            1 & \\quad g \\geq threshold\n",
+    "            0 & \\quad weighted\\_sum < threshold \\\\\n",
+    "            1 & \\quad weighted\\_sum \\geq threshold\n",
     "        \\end{array}\n",
     "    \\right.\n",
     "$$\n",
-    "\n"
+    "\n",
+    "You can see that this is also a linear classifier as we introduced in script 02."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -84,7 +85,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -93,7 +94,7 @@
        "1"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -130,7 +131,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -147,7 +148,7 @@
    "source": [
     "# Calculating Boolean AND using a perceptron\n",
     "import matplotlib.pyplot as plt\n",
-    "threshold=1.5\n",
+    "threshold = 1.5\n",
     "w=[1,1]\n",
     "X=[[0,0],[1,0],[0,1],[1,1]]\n",
     "for i in X:\n",
@@ -156,14 +157,28 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this simple case we can rewrite our equation to $x_2 = ...... $ which describes a line in 2D:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f37f81bd400>"
+       "<Figure size 432x288 with 1 Axes>"
       ]
      },
      "metadata": {
@@ -208,7 +223,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -218,7 +233,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 63,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
@@ -233,9 +248,9 @@
     },
     {
      "data": {
-      "image/png": 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eCkYhWA73nf6/+g2glnPuMmApMC2nF3LOTXTO+ZxzvkqVKgUhmoSyEiVK8MQTT5CamkqNGjUYPXq0CkHEQ8EohO1A9t/4qwM7sw9wzh1wzh3z35wENAnCciVCNGjQgFWrVp2aLG/v3r1MmzZN5SBSxIJRCJ8AF5lZbTMrDnQBFmQfYGZVst1MBjKCsFyJIHFxcVSuXBmACRMm0KNHD66//nr+85//eJxMJHoEXAjOuRPAfcBisn7Qv+ac22Rmw80s2T/sATPbZGbrgQeAHoEuVyLXoEGDGDduHKtWreLSSy/l+eef5+TJk17HEol4Fqq75T6fz6WmpnodQzz0zTff0Lt3b9566y0GDRrEE0884XUkkZBnZmucc76CPFeT20nIuuCCC1i4cCEzZ87k2muvBWD37t1UrFhRk+WJFAJNXSEhzcy4/fbbqVy5Ms45UlJS8Pl8rFmzxutoIhFHhSBhw8x45JFH2L9/P82aNeORRx7hxx9/9DqWSMRQIUhYSU5OZtOmTdx5552MGjWKBg0aaLI8kSBRIUjYOffcc5k0aRJLly6ldu3aVK9e3etIIhFBhSBhq23btixevJjSpUtz9OhRrrnmGhYtWuR1LJGwpUKQiLB792727NnDDTfcwB133MH+/fu9jiQSdlQIEhHq1KnD2rVrGTp0KK+++ioJCQm89tprmv5CJB9UCBIxSpQowbBhw1i7di01a9ZkzJgxKgSRfFAhSMRJSkrio48+OjVZ3p49e5g6darKQeQsVAgSkeLi4jjvvPMAeOmll+jZsydt27Zly5YtHicTCV0qBIl4gwYNYsKECaSmppKUlMTo0aM1WZ5IDlQIEvFiYmK45557SE9Pp23btvTv359hw4Z5HUsk5GhyO4ka1atXZ8GCBbz22mtcffXVQNbfdq5YsSLFixf3OJ2I97SHIFHFzLj11ls577zzTk2W16RJEz755BOvo4l4ToUgUcvMGDBgAAcPHqRFixY8+OCDHD161OtYIp5RIUhUu+mmm9i0aRN33303f//737nsssv4/PPPvY4l4gkVgkS9cuXKMWHCBJYtW0bdunWpUaOG15FEPKFCEPFr06YNb7/99qnJ8tq0acMbb7zhdSyRIqNCEMnB7t27OXDgAMnJydx2223s27fP60gihU6FIJKDOnXqsGbNGh5//HFmz55N/fr1mTlzpqa/kIimQhDJRfHixRkyZAiffvopdevW5cUXX1QhSERTIYicRWJiIh9++CHz5s07NVne5MmTyczM9DqaSFCpEETyIDY2lkqVKgEwadIk7r77btq2bcvmzZs9TiYSPCoEkXx67LHHmDRpEmvXriUpKYlnn32WEydOeB1LJGAqBJF8MjPuuusu0tPTuf7663nooYcYOnSo17FEAqbJ7UQKqFq1asybN4/Zs2dz1VVXAVmT5VWoUIESJUp4nE4k/4Kyh2Bmvzezz81ss5k9msPjJcxslv/x1WZWKxjLldDTpw/ExYFZ1tc+fbxOVLjMjM6dO/9msrzVq1d7Ha1Aom37ya8FXAhmFgu8CLQHEoCuZpZw2rCewEHnXF3gH8DfAl2uhJ4+fWD8ePjlb8+cPJl1O1p+qJgZgwYN4tChQ7Rs2ZK//vWv/PDDD17HyrNo334CFuj7qs2sJTDMOdfOf3sAgHNuZLYxi/1jPjKzOGA3UMmdYeE+n8+lpqYGlE2KVlzcf3+YZBcbC9F0zvXw4cMMGDCAcePGUbt2bRYtWkS9evW8jnVW2n6RwczWOOd8BXluMA4ZVQO2Zbu93X9fjmOccyeAQ0DF01/IzHqZWaqZpWqqgPCT21+ljLa/Vvm73/2OF198kffee4/69etTs2ZNgJD/UJu2nwSjECyH+07/zs/LGJxzE51zPuec75f3fEv4iI3N3/2R7sorr2ThwoWUKlWKH374gauuuor58+d7HStX2n4SjELYDmSfL7g6sDO3Mf5DRuWAb4OwbAkhvXrl7/5osnfvXg4fPkyHDh249dZb2bNnj9eRfkPbT4JRCJ8AF5lZbTMrDnQBFpw2ZgHQ3X+9E/Dumc4fSHgaNw7uvfe/v1HGxmbdHjfO21yhoHbt2nzyySc8+eSTzJs3j4SEBP75z3+G1GEkbT8J+KQygJn9AXgOiAWmOudGmNlwINU5t8DMSgIzgEZk7Rl0cc59dabX1ElliVQZGRn07NmTmJgYVqxYQUyMPh8qwRPISeWgFEJhUCFIJDt58iQHDx4kPj6e3bt3M3/+fO6++26VgwTM63cZiUg+xcbGEh8fD8CUKVPo3bs3bdq04YsvvvA4mUQzFYKIxwYOHMjUqVPZuHEjDRo0YNSoUZosTzyhQhDxmJnxpz/9ifT0dNq3b88jjzyiyfLEE5rcTiREVKlShTlz5jBnzhxat24NwI4dO6hYsSIlS5b0OJ1EA+0hiISYjh07UqlSJZxzdOrUiUaNGrFy5UqvY0kUUCGIhCgzY9iwYRw9epQrrriCP//5zxw5csTrWBLBVAgiIaxdu3akpaXRt29fXnjhBS699FIyMjK8jiURSoUgEuLKli3LCy+8wIoVK0hKSqJWrVpA6E+WJ+FHhSASJq644greeOONU5PltW7dmjlz5ngdSyKICkEkDO3bt48ffviBlJQUOnXqxO7du72OJBFAhSAShmrVqsXHH3/MU089xZtvvklCQgIvv/yyDiNJQFQIImGqWLFiDBgwgHXr1pGQkMDUqVNVCBIQFYJImKtXrx4rVqxg3rx5xMTEsHv3bsaNG0dmZqbX0STMqBBEIkBMTAwVKlQAYOrUqfTt25crr7ySzz77zONkEk5UCCIRZsCAAUybNo309HQaNGjAU089xc8//+x1LAkDKgSRCGNmdOvWjYyMDJKTk3nssccYNmyY17EkDGhyO5EIVblyZV5//XXmzZtHq1atAE2WJ2emPQSRCNehQ4dfTZbXoEEDPvjgA69jSQhSIYhECTNj+PDhHD9+nNatW3Pffffx/fffex1LQogKQSSKXHfddWzcuJEHHniAcePGkZiYSHp6utexJESoEESizDnnnMOYMWP44IMPaNSoEbVr1wY0WZ6oEESi1uWXX878+fNPTZZ3+eWX8/rrr6sYopgKQUTYt28fP//8M7fccgspKSns2rXL60jiARWCiFCrVi1WrVrFqFGjeOuttzQ3UpRSIYgIAHFxcTz00EOsX7+eyy67jGnTpqkQoowKQUR+5eKLL2bZsmXMnTuXmJgYdu3axdixYzl58qTX0aSQqRBE5DeyT5b38ssvc//999O6dWv9PecIF1AhmFkFM1tiZl/6v5bPZdxJM1vnvywIZJkiUrQeffRRZsyYwRdffEHDhg158sknNVlehAp0D+FR4B3n3EXAO/7bOfnROdfQf0kOcJkiUoTMjP/5n/8hPT2dm2++mcGDBzNkyBCvY0khsEBOGpnZ50Ab59wuM6sCLHfOXZLDuCPOuXPy89o+n8+lpqYWOJuIFI4FCxbQsmVLKlWqxLZt24iPj6dUqVJexxI/M1vjnPMV5LmB7iFUds7tAvB/PS+XcSXNLNXMVplZhwCXKSIeSk5O/tVkeZdddhnvvfee17EkCM5aCGa21MzScrj8MR/LucDfWLcBz5nZhbksq5e/OFL37duXj5cXkaJmZowcOZLMzEzatGnDvffey+HDh72OJQEokkNGpz3nZeBN59zsM43TISOR8PDDDz8wZMgQnnvuOapWrcrixYtJSEjwOlbU8vKQ0QKgu/96d2D+6QPMrLyZlfBfjwdaAZpeUSRClClThr///e+sXLmSpk2bUqdOHUCT5YWjQAvhaeA6M/sSuM5/GzPzmdlk/5j6QKqZrQeWAU8751QIIhGmefPmzJkzh5IlS3LkyBFatGjBrFmzVAxhJKBCcM4dcM61dc5d5P/6rf/+VOfcXf7rK51zSc65Bv6vU4IRXERC14EDB3DO0aVLFzp06MDOnTu9jiR5oE8qi0jQ1axZk5UrV/Lss8/y73//m4SEBCZPnqy9hRCnQhCRQhEXF0f//v3ZuHEjDRs2ZMaMGSqEEKdCEJFCVbduXd59913mzZt3arK8MWPGaLK8EKRCEJFCFxMTQ/nyWVOdTZ8+nX79+nH55ZeTlpbmcTLJToUgIkXq4Ycf5pVXXuGrr76icePGPP744xw/ftzrWIIKQUSKmJnRpUsXMjIy6Ny5M8OGDWPo0KFexxIgzusAIhKd4uPj+de//sVtt91G8+bNAfjmm2+Ij4+ndOnSHqeLTtpDEBFP3XDDDcTHx+Oco3PnziQlJbFs2TKvY0UlFYKIhAQz4+mnn8bMuOaaa7jnnns4dOiQ17GiigpBRELG1VdfzYYNG3jwwQeZPHkyCQkJbNq0yetYUUOFICIhpXTp0jzzzDOsWrWKli1bcuGFWbPl60NthU+FICIhqWnTpsyePZuSJUvy/fff07RpU2bOnKliKEQqBBEJeQcPHiQuLo7bb7+dm266iW3btnkdKSKpEEQk5F1wwQV8+OGH/OMf/2DZsmUkJiby0ksvkZmZ6XW0iKJCEJGwEBsbS79+/di4cSPNmjXj1Vdf9TpSxFEhiEhYqVOnDkuWLGHu3LnExMSwc+dORo8ezYkTJ7yOFvZUCCISdsyMc889F4AZM2bQv39/WrZsyYYNGzxOFt5UCCIS1h5++GFmzZrF1q1badKkCUOHDuXYsWNexwpLKgQRCWtmxi233EJGRgZdu3Zl+PDhmiyvgDS5nYhEhIoVKzJ9+nS6du1Ks2bNANi6dSvx8fGUKVPG43ThQXsIIhJR2rdvT8WKFXHOccstt5CUlMTSpUu9jhUWVAgiEpHMjGeffZa4uDiuu+46evbsyXfffed1rJCmQhCRiNW6dWvWr1/Po48+yrRp00hISNCf7TwDFYKIRLRSpUoxcuRIVq9eTevWralbty6gyfJyokIQkajQpEkTZs2adWqyPJ/Px4wZM1QM2agQRCTqfPfdd5QoUYJu3bpxww038M0333gdKSSoEEQk6tSoUYP333+f559/nhUrVpCYmMj48eOjfrI8FYKIRKXY2Fjuv/9+0tLSaNmyJa+//jpm5nUsTwVUCGbW2cw2mVmmmfnOMO73Zva5mW02s0cDWaaISDDVqlWLxYsXM3fuXMyMHTt28Mwzz0TlZHmB7iGkAR2BFbkNMLNY4EWgPZAAdDWzhACXKyISNGZGuXLlAJg5cyYPP/wwzZs3Z926dR4nK1oBFYJzLsM59/lZhjUDNjvnvnLOHQdeBf4YyHJFRArLQw89xOzZs9mxYwc+n4/HHnuMn376yetYRcKC8ZYrM1sOPOicS83hsU7A751zd/lv3wE0d87dl8PYXkAv/81LydoDiVTxwH6vQxQirV94i+T1i+R1A7jEOVe2IE886+R2ZrYUOD+Hhx5zzs3PwzJyOkuTYws55yYCE/3LTXXO5XpeItxp/cKb1i98RfK6Qdb6FfS5Zy0E59y1BX1xv+1AjWy3qwM7A3xNEREJsqJ42+knwEVmVtvMigNdgAVFsFwREcmHQN92erOZbQdaAgvNbLH//qpmtgjAOXcCuA9YDGQArznnNuXh5ScGki0MaP3Cm9YvfEXyukEA6xeUk8oiIhL+9EllEREBVAgiIuIXMoUQ6dNgmFkFM1tiZl/6v5bPZdxJM1vnv4T8yfezbQ8zK2Fms/yPrzazWkWfsuDysH49zGxftm12lxc5C8LMpprZXjPL8fM+luV5/7pvMLPGRZ0xEHlYvzZmdijbthtS1BkLysxqmNkyM8vw/9z8cw5j8r/9nHMhcQHqA5cAywFfLmNigS1AHaA4sB5I8Dp7HtdvFPCo//qjwN9yGXfE66z5WKezbg+gDzDBf70LMMvr3EFevx7AWK+zFnD9rgQaA2m5PP4H4C2yPkvUAljtdeYgr18b4E2vcxZw3aoAjf3XywJf5PC9me/tFzJ7CC7yp8H4IzDNf30a0MHDLMGSl+2Rfb1nA20tfKaUDOfvt7Nyzq0Avj3DkD8C012WVcC5ZlalaNIFLg/rF7acc7ucc2v9178n6x2c1U4blu/tFzKFkEfVgG3Zbm/nt/8Ioaqyc24XZG1M4LxcxpU0s1QzW2VmoV4aedkep8a4rLcgHwIqFknH05kXAAACO0lEQVS6wOX1+y3Fv0s+28xq5PB4uArn/2951dLM1pvZW2aW6HWYgvAfhm0ErD7toXxvv7N+UjmYinIaDC+caf3y8TIXOOd2mlkd4F0z2+ic2xKchEGXl+0R0tvsLPKS/Q3gFefcMTPrTdbe0DWFnqxohPO2y4u1QE3n3BEz+wMwD7jI40z5YmbnAP8H9HPOHT794RyecsbtV6SF4CJ8GowzrZ+Z7TGzKs65Xf7dtr25vMZO/9ev/JMGNiLrOHYoysv2+GXMdjOLA8oRPrvxZ10/59yBbDcnAX8rglxFJaT/vwUq+w9Q59wiMxtnZvHOubCY+M7MipFVBv9yzs3JYUi+t1+4HTIK52kwFgDd/de7A7/ZIzKz8mZWwn89HmgFpBdZwvzLy/bIvt6dgHed/4xXGDjr+p12TDaZrGO5kWIB0M3/bpUWwKFfDntGAjM7/5fzWWbWjKyfhwfO/KzQ4M89Bchwzo3OZVj+t5/XZ8uznRG/maxGOwbsARb7768KLDrtzPkXZP3W/JjXufOxfhWBd4Av/V8r+O/3AZP91y8HNpL1bpaNQE+vc+dhvX6zPYDhQLL/ekngdWAz8DFQx+vMQV6/kcAm/zZbBtTzOnM+1u0VYBfws///Xk+gN9Db/7iR9cettvi/H3N891+oXvKwfvdl23argMu9zpyPdbuCrMM/G4B1/ssfAt1+mrpCRESA8DtkJCIihUSFICIigApBRET8VAgiIgKoEERExE+FICIigApBRET8/h/ojtcNQhRRCAAAAABJRU5ErkJggg==\n",
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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f37f8036a90>"
+       "<Figure size 432x288 with 1 Axes>"
       ]
      },
      "metadata": {
@@ -272,7 +287,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -315,14 +330,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f37f8297da0>"
+       "<Figure size 720x288 with 3 Axes>"
       ]
      },
      "metadata": {
@@ -335,26 +350,45 @@
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
     "\n",
-    "fig, ax = plt.subplots(1,3)\n",
-    "ax=ax.flatten()\n",
+    "plt.figure(figsize=(10, 4), constrained_layout=False)\n",
+    "plt.subplot(1, 3, 1)\n",
+    "\n",
+    "#fig, ax = plt.subplots(1,3)\n",
+    "#ax=ax.flatten()\n",
     "\n",
     "pts=np.arange(-20,20, 0.1)\n",
     "\n",
     "# Sigmoid\n",
-    "ax[0].plot(pts, 1/(1+np.exp(-pts))) ;\n",
+    "plt.plot(pts, 1/(1+np.exp(-pts))) ;\n",
+    "\n",
     "\n",
+    "plt.subplot(1, 3, 2)\n",
     "# tanh\n",
-    "ax[1].plot(pts, np.tanh(pts*np.pi)) ;\n",
+    "plt.plot(pts, np.tanh(pts*np.pi)) ;\n",
     "\n",
     "# Rectified linear unit (ReLu)\n",
+    "plt.subplot(1, 3, 3)\n",
+    "\n",
     "pts_relu=[max(0,i) for i in pts];\n",
-    "ax[2].plot(pts, pts_relu) ;"
+    "plt.plot(pts, pts_relu) ;"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "Suggestion Uwe:\n",
+    "\n",
+    "1. more layers might improve power of single perctptron.\n",
+    "\n",
+    "2. regrettably math show that just \"stacking\" perceptrons only adds little improvements\n",
+    "\n",
+    "3. way around: look at nature how neuron works and introduce non linear activation functions.\n",
+    "\n",
+    "4. theoretical background: universal approximation theorem.\n",
+    "\n",
+    "\n",
+    "\n",
     "### Multi-layer preceptron neural network\n",
     "Universal function theorem\n",
     "\n",
@@ -370,6 +404,8 @@
     "\n",
     "### Google Playground\n",
     "\n",
+    "UWE: move up before discussing gradient stuff etc\n",
+    "\n",
     "https://playground.tensorflow.org/\n",
     "\n",
     "<img src=\"./images/neuralnets/google_playground.png\"/>"
@@ -462,6 +498,18 @@
     "## CNN examples"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "TODO: \n",
+    "\n",
+    "- does keras support scikit-learn api ? (.fit and .predict methods) ?\n",
+    "- if yes: we could use cross validation and hyper parameter optimzation for scikit-learn to evaluae / improve keras network.    \n",
+    "      \n",
+    "      "
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -486,7 +534,25 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.0"
+   "version": "3.7.2"
+  },
+  "latex_envs": {
+   "LaTeX_envs_menu_present": true,
+   "autoclose": false,
+   "autocomplete": true,
+   "bibliofile": "biblio.bib",
+   "cite_by": "apalike",
+   "current_citInitial": 1,
+   "eqLabelWithNumbers": true,
+   "eqNumInitial": 1,
+   "hotkeys": {
+    "equation": "Ctrl-E",
+    "itemize": "Ctrl-I"
+   },
+   "labels_anchors": false,
+   "latex_user_defs": false,
+   "report_style_numbering": false,
+   "user_envs_cfg": false
   }
  },
  "nbformat": 4,