Basics 03 - Activation Functions.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "id": "collected-undergraduate",
   "metadata": {},
   "source": [
    "# Layer Activation Functions\n",
    "* RELU (Rectified Linear Unit)\n",
    "* ELU (Exponential Linear Unit)\n",
    "* SELU (Scaled Exponential Linear Unit)\n",
    "* Sigmoid\n",
    "* Tanh\n",
    "* SoftPlus\n",
    "* SoftSign\n",
    "* SoftMax"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "figured-damage",
   "metadata": {},
   "source": [
    "### Different Ways to Call the Activation Function\n",
    "The below methods are equivalent when adding a new layer using Keras\n",
    "```python\n",
    "# method 1 - supply activation function as parameter\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "model = Sequential()\n",
    "model.add(Dense(64, activation='relu'))\n",
    "\n",
    "# method 2 - add activation as layer\n",
    "from tensorflow.keras import layers\n",
    "from tensorflow.keras import activations\n",
    "model.add(layers.Dense(64))\n",
    "model.add(layers.Activation(activations.relu))\n",
    "\n",
    "# method 3 - directly call class instances\n",
    "model.add(layers.Dense(64, activation=activations.relu))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "secret-sheffield",
   "metadata": {},
   "source": [
    "### Dependencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "still-october",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "pd.set_option('chained_assignment',None)\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "awful-interim",
   "metadata": {},
   "source": [
    "### Standardize the Curve Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "prescription-trinidad",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_curve(func, idx1=5, idx2=-5):\n",
    "    x1 = np.linspace(-10,10,100)\n",
    "    y1 = list(map(func, x1))\n",
    "\n",
    "    x2 = np.arange(-8,9,step=1)\n",
    "    y2 = list(map(func, x2))\n",
    "\n",
    "    plt.figure(figsize=(12,4))\n",
    "    plt.style.use('fivethirtyeight') # add this step to show grid\n",
    "    plt.style.use('grayscale')\n",
    "    _ = plt.plot(x1, y1, c='b', linewidth=2)\n",
    "    _ = plt.scatter(x2, y2, c='r', alpha=1, s=100)\n",
    "\n",
    "    plt.xticks(x2)\n",
    "    plt.yticks(y2[idx1:idx2])\n",
    "    plt.title(f\"{func.__name__} Activation Function\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "undefined-current",
   "metadata": {},
   "source": [
    "## ReLU (Rectified Linear Unit)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "hired-fifty",
   "metadata": {},
   "source": [
    "#### Mathematical Expression\n",
    "$$\\begin{equation*}\n",
    "a = f(x) = \\left\\{\n",
    "        \\begin{array}{ll}\n",
    "            0 & \\quad x \\leq 0 \\\\\n",
    "            x & \\quad x > 0\n",
    "        \\end{array}\n",
    "    \\right.\n",
    "\\end{equation*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bound-kernel",
   "metadata": {},
   "source": [
    "#### Visualization with Numpy Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cellular-wings",
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def relu(x):\n",
    "    return max(x,0)\n",
    "\n",
    "plot_curve(relu, 7, -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "compound-truck",
   "metadata": {},
   "source": [
    "#### Keras Implementation\n",
    "https://keras.io/api/layers/activations/#relu-function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "therapeutic-construction",
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "model = Sequential()\n",
    "model.add(Dense(64, activation='relu'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "steady-couple",
   "metadata": {},
   "source": [
    "#### PyTorch Implementation\n",
    "https://pytorch.org/docs/stable/generated/torch.nn.ReLU.html#torch.nn.ReLU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "dietary-google",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 0., 1.], dtype=torch.float64)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "a = nn.ReLU()\n",
    "t = torch.from_numpy(np.array([-1.0,0,1.0]))\n",
    "a(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "inner-state",
   "metadata": {},
   "source": [
    "#### TensorFlow Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "beautiful-warren",
   "metadata": {},
   "source": [
    "## ELU (Exponential Linear Unit)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acceptable-showcase",
   "metadata": {},
   "source": [
    "#### Mathematical Expression\n",
    "$$\\begin{equation*}\n",
    "a = f(x) = \\left\\{\n",
    "        \\begin{array}{ll}\n",
    "            \\alpha(e^{x}-1) & \\quad x \\leq 0 \\\\\n",
    "            x & \\quad x > 0\n",
    "        \\end{array}\n",
    "    \\right.\n",
    "\\end{equation*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "conceptual-slovakia",
   "metadata": {},
   "source": [
    "#### Visualization with Numpy Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ignored-welsh",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def selu(x):\n",
    "    alpha=1.67326324\n",
    "    if x > 0:\n",
    "        return x\n",
    "    return alpha * (np.exp(x) - 1)\n",
    "\n",
    "plot_curve(selu, 7,-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fuzzy-halloween",
   "metadata": {},
   "source": [
    "#### Keras Implementation\n",
    "https://keras.io/api/layers/activations/#elu-function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "equal-sustainability",
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "model = Sequential()\n",
    "model.add(Dense(64, activation='elu'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "civil-rating",
   "metadata": {},
   "source": [
    "#### PyTorch Implementation\n",
    "https://pytorch.org/docs/stable/generated/torch.nn.ELU.html#torch.nn.ELU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "alpha-petersburg",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-0.6321,  0.0000,  1.0000], dtype=torch.float64)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "a = nn.ELU()\n",
    "t = torch.from_numpy(np.array([-1.0,0,1.0]))\n",
    "a(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adequate-magic",
   "metadata": {},
   "source": [
    "#### TensorFlow Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "devoted-visibility",
   "metadata": {},
   "source": [
    "## SELU (Scaled Exponential Linear Unit)\n",
    "where alpha and scale are pre-defined constants (alpha=1.67326324 and scale=1.05070098).\n",
    "\n",
    "Basically, the SELU activation function multiplies scale (> 1) with the output of the tf.keras.activations.elu function to ensure a slope larger than one for positive inputs.\n",
    "\n",
    "The values of alpha and scale are chosen so that the mean and variance of the inputs are preserved between two consecutive layers as long as the weights are initialized correctly (see tf.keras.initializers.LecunNormal initializer) and the number of input units is \"large enough\" (see reference paper for more information)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "utility-addition",
   "metadata": {},
   "source": [
    "#### Mathematical Expression\n",
    "$$\\begin{equation*}\n",
    "a = f(x) = \\left\\{\n",
    "        \\begin{array}{ll}\n",
    "            s\\cdot\\alpha(e^{x}-1) & \\quad x \\leq 0 \\\\\n",
    "            s\\cdot x & \\quad x > 0\n",
    "        \\end{array}\n",
    "    \\right.\n",
    "\\end{equation*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "offshore-knight",
   "metadata": {},
   "source": [
    "#### Visualization with Numpy Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "significant-teach",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def selu(x):\n",
    "    alpha=1.67326324\n",
    "    scale=1.05070098\n",
    "    if x > 0:\n",
    "        return scale * x\n",
    "    return scale * alpha * (np.exp(x) - 1)\n",
    "\n",
    "plot_curve(selu, 7,-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "pretty-bubble",
   "metadata": {},
   "source": [
    "#### Keras Implementation\n",
    "https://keras.io/api/layers/activations/#selu-function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "polish-stockholm",
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "model = Sequential()\n",
    "model.add(Dense(64, activation='selu'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "guilty-omaha",
   "metadata": {},
   "source": [
    "#### PyTorch Implementation\n",
    "https://pytorch.org/docs/stable/generated/torch.nn.SELU.html#torch.nn.SELU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "binary-ballet",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-1.1113,  0.0000,  1.0507], dtype=torch.float64)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "a = nn.SELU()\n",
    "t = torch.from_numpy(np.array([-1.0,0,1.0]))\n",
    "a(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "empty-roads",
   "metadata": {},
   "source": [
    "#### TensorFlow Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "generic-imaging",
   "metadata": {},
   "source": [
    "## Sigmoid\n",
    "The Sigmoid function is that it maps anything on the real numbers line from to the open interval (0, 1) which can be interpreted as probability. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "confirmed-theorem",
   "metadata": {},
   "source": [
    "#### Mathematical Expression\n",
    "$$\\sigma(x)=\\frac{1}{1+e^{-x}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "parliamentary-harvest",
   "metadata": {},
   "source": [
    "#### Visualizaiton with Numpy Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "photographic-arrest",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sigmoid(x):\n",
    "    return 1 / (1+np.exp(-x))\n",
    "\n",
    "plot_curve(sigmoid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "illegal-marine",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999546021312976"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "refined-riding",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.5397868702434395e-05"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid(-10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dirty-access",
   "metadata": {},
   "source": [
    "#### Properties of the Sigmoid Function\n",
    "* the output at 0 is always 0.5\n",
    "* the output is always bounded within (0,1)\n",
    "* as the input value deviates from 0, the output changes slower and slower\n",
    "* sigmoid(10) ~ 0.9995 and sigmoid(-10) ~ 0.0005\n",
    "* output values of multiplicative inverses are always probabilitic complements"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "antique-continuity",
   "metadata": {},
   "source": [
    "$$\\sigma(x) = 1 - \\sigma(-x)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "talented-photographer",
   "metadata": {},
   "source": [
    "#### Keras Implementation\n",
    "https://keras.io/api/layers/activations/#sigmoid-function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "sustainable-damage",
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "model = Sequential()\n",
    "model.add(Dense(64, activation='sigmoid'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "mounted-confidence",
   "metadata": {},
   "source": [
    "#### PyTorch Implementation\n",
    "https://pytorch.org/docs/stable/generated/torch.nn.Sigmoid.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "current-intensity",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.2689, 0.5000, 0.7311], dtype=torch.float64)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "a = nn.Sigmoid()\n",
    "t = torch.from_numpy(np.array([-1.0,0,1.0]))\n",
    "a(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adopted-covering",
   "metadata": {},
   "source": [
    "#### TensorFlow Implementation\n",
    "* tf.sigmoid\n",
    "* tf.math.sigmoid https://www.tensorflow.org/api_docs/python/tf/math/sigmoid\n",
    "* tf.keras.activations.sigmoid https://www.tensorflow.org/api_docs/python/tf/keras/activations/sigmoid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "reduced-commercial",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(1,), dtype=float32, numpy=array([0.26894143], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(3,), dtype=float32, numpy=array([0.26894143, 0.5       , 0.7310586 ], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(1,), dtype=float32, numpy=array([0.26894143], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(3,), dtype=float32, numpy=array([0.26894143, 0.5       , 0.7310586 ], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(1,), dtype=float32, numpy=array([0.26894143], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(3,), dtype=float32, numpy=array([0.26894143, 0.5       , 0.7310586 ], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "t1 = tf.constant([-1.0], dtype=tf.float32)\n",
    "t2 = tf.constant([-1.0, 0, 1.0], dtype=tf.float32)\n",
    "\n",
    "display(tf.sigmoid(t1))\n",
    "display(tf.sigmoid(t2))\n",
    "display(tf.math.sigmoid(t1))\n",
    "display(tf.math.sigmoid(t2))\n",
    "display(tf.keras.activations.sigmoid(t1))\n",
    "display(tf.keras.activations.sigmoid(t2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "colored-unknown",
   "metadata": {},
   "source": [
    "#### TensorFlow Probability API\n",
    "https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Sigmoid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "divided-spectrum",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(3,), dtype=float32, numpy=array([0.26894143, 0.5       , 0.7310586 ], dtype=float32)>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# needs separate install\n",
    "import tensorflow_probability as tfp\n",
    "a = tfp.bijectors.Sigmoid()\n",
    "a(t2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "demonstrated-gazette",
   "metadata": {},
   "source": [
    "## Tanh"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "related-huntington",
   "metadata": {},
   "source": [
    "#### Mathematical Expression\n",
    "$$tanh(x) = \\frac{\\sinh(x)}{\\cosh(x)} = \\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "retired-firmware",
   "metadata": {},
   "source": [
    "#### Visualizaiton with Numpy Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "accompanied-islam",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4/vnn+fbbbxk6dKjpdyo8PJzTp09TtWpV06hzIiIPQ0WNiBQqDg4OTJkyha+++oo9e/YQEhKCwWDAy8uLatWq0aJFC6ZOncry5csJDQ3F3t6eOnXqMHPmTK5cuWJTRc2BAwe4fPkyVatWpW7dundd18/Pj927dxMYGEiXLl2ws7Nj4sSJNG/enMDAQH744QeSkpLw8PCgdu3aZh/sK1WqxKRJk1i9ejVbtmwxne3p2LFjjvpCdO3alb1792YacjqjatWqMXPmTJYsWcKePXtITU2lWrVqTJ48GRcXlyyLmgEDBhAXF0dYWBirVq0iNTWVRo0a3bWocXR05H//+x/r1q1jx44d+Pv7Y29vj4+PD0OGDDGdybEFb7zxBh4eHuzYsYOAgAA8PT3p0KEDgwYNyrWLfTo6OvLxxx+zadMmtm3bxvbt20lLS8PT05MWLVrQtGlT07rNmjVj1KhRbNq0CX9/f9PADXcragBGjBhBjRo12LBhAzt27CA5OZmyZcsyYMAA+vfvn+WFN0VE7pddaGiowdohREREREREHpT61IiIiIiISL6mokZERERERPI1FTUiIiIiIpKvqagREREREZF8rVCOfpbdFbdFRERERMS2ZTUips7UiIiIiIhIvqaiRkRERERE8rVC2fwsI4NBl+mxNXZ2djbxviiHbeYA28miHMqRH3KA7WRRDuXIDznAtrKIUVYXbs5IZ2pERERERCRfU1EjIiIiIiL5mooaERERERHJ11TUiIiISN5JTYU1a8DPj50Afn6wdi2kpSmHcthODlvLIvfNLjQ0tND1gsp4nRp1ArM9ttI5TzlsMwfYThblUI78kAOsmOX6dejeHY4cgYSE28udnKBRIwgIAG9v5VAO6+awtSySpYwDBWR1nRoVNTbyD0dus5UPAsphmznAdrIoh3LkhxxgpSxpadCmDezdm/06LVvCTz+BfR42HFEO5chPWSRb9ypqCv2QziIiIgVSaiqsXw/Llt1uSjN0KPTubZkPZuvXG7/1vpsjRzBs8Cele2+SkzGbUlKMh5B+e+d8WppxymreYDBOaWlg+PEn0g6Ww4AfadhjwC7zdLAYTNiHoUUr4Pb26fMZb7Nblt06pvn94XCwHlATA9kMTXvQEV47CM2aZflwrtSl+w/AgQZA7ezXOeAIY7LPkStsJYetZbFBDg4wcKC1U9xbnp2p8ff3Z/Xq1URERODj48OoUaNo2LBhtutv2LABf39/rl69SpkyZXjhhRfo3Lmz2TqxsbEsXryYXbt2cevWLby8vBg+fLjZmZd0K1asYNGiRfTs2ZPXXnvN7DGdqbFttvLtpnLYZg6wnSzKoRw2myMPmtIkJkJUFPz1l/ltVBRER0NMDMTGZphC9hJzPZY4ipNIMRJwIpFimeZTcMzVQxeR3OXsDHFx1k5hpTM1ISEhzJ07l7Fjx9KgQQM2btzIhAkTWLZsGWXKlMm0/saNG/nqq68YN24cderU4eTJk8yYMYOSJUvSpk0bAFJSUhg3bhyurq689957eHl5cePGDRwdM/8xPHHiBIGBgVStWjUvDk9ERMR2paUZC5qsmtIkJBiXd+9u1pQmKgp+/904Xb4MV64Yp6tXb99GRd1vkJY5XtPBARwdzaciRYyTg4NxyjifPtnbG6eM8/b2YGeX4TZ8L3aREdhhwJ60rM7TGCev0vB4O9I/N9nZYTaf8Ta7ZdmtA2C3fRtcu3r7PtkUvGXLQqfOWT+Wxf7uW3CwWY5slS0Lnbs85M7yQQ5by2KDiha1doKcyZOiZs2aNXTp0oVu3boBMGbMGPbt20dAQAAjRozItP727dvp1q0bHTp0AKB8+fKcPHmSlStXmoqaLVu2EB0dzezZs02FTNmyZTM9V0xMDB999BHjx4/n66+/zovDExERsV3ZNPsyAOfwYT/N+e1APU63v8DpxMqcPg0REfd+2iJFwN3dOJUqZT5fqhS4uECJEhmmmVMoceAHihOHEwk4kfDPuZlEs/kiT3XGPmhTLr8IGfhNhs2b771eCz9Y2y4Pc3yesxxN/eDr7Iuah88xJ+c5luXhB3hbyWFrWeSB5XpRk5yczKlTp3juuefMljdr1ozjx49nuU1SUhJF7ygDixUrxsmTJ0lJSaFIkSKEhYVRv359Zs+eTVhYGK6urjzxxBMMGDCAIkVuH8ann37K448/zqOPPqqiRkRECp+lSyEhgQg82E9z9tHCNN3gnyZnKcAPtzcpXhyqVzdOFSsav5AuV8588vC4z644RevAwKnmzd/u5OQELw59kKPMuaFDISTk3jmGDVOOwpjD1rLIA8v1oiY6Opq0tDTc3d3Nlru7u3Pw4MEst2nevDlbtmzhX//6F7Vq1eLUqVMEBQWRkpJCdHQ0np6eXL58mYMHD9KhQwemTZvG1atX+fzzz4mPj+eVV14BIDAwkEuXLvGf//wnx3ntHvo8ruQFW3lflMOcreQA28miHOaUw5xlc9gBLehHT47wCb9SN9MapblBC/bRgGMk8zszOQ2cJi7uCkePwtGjuZvmJ6DVXdbZk5BAm2eeya4hlnIoR57nsLUs8uBsYvSzQYMGERkZyahRozAYDHh4eNC5c2dWrVpl+odgMBhwd3dn3LhxODg4UKtWLW7dusW8efN4+eWXuXDhAosWLWL27NlmZ27uxRY6k4o5dfJVjnuxlSzKoRzWzpGYCKGh4O8PGzca+76s+ucxJ+JpygHTeZqW7MWHc7fH3fLz49PAH7J+4txyjwELWgUEkGYD10NRjkKew9aySJbu9SVRro/p6Obmhr29PVF39CiMiorKdPYmXbFixZgwYQLBwcGsWrWKVatWUbZsWYoXL06pUqUA8PDw4JFHHsHBwcG0XeXKlUlISCA6OpoTJ04QHR3N0KFD6dChAx06dODIkSNs3LiRDh06kJSUlNuHKiIiYhWHD8OgQeDlBV27woIFxoKmcmUY0/U0IY6duYUru/kXM3mTfqymSsaCxlJNaby9jQMSfPMN+PkRAsahpVesMC631IdE5VCO/JRFHkieDOn8yiuvUK1aNcaNG2daNnDgQB5//PEsBwrIymuvvUbp0qV59913AVi4cCE7d+7k22+/xf6fRr1BQUHMnTuXzZs3Exsby40bN8ye4+OPP6ZChQoMGDAAHx8fU4WnIZ1tW2H6llU5HoytZFEO5bBkDoMBtm+HTz6BHTtuL2/UCHr2NE6NGoGdwXYvJFhQ3xvlKFg5wLayiJFVhnTu27cv06ZNo06dOtSvX5+AgABu3rzJ008/DcDUqVMBmDRpEgAXLlzg119/pW7duvz999+sWbOGc+fOMXHiRNNz9ujRA39/f+bOnUvPnj25evUqy5Yto0ePHtjZ2eHi4oKLi4tZDicnJ1xdXalSpUpeHKaIiEieS0qC1athxozbfV5cXGDECHj1VahW7Y4N7OyN16G513VqdGV0ESlA8qSoad++Pbdu3WL58uVERkbi4+PD9OnTTUMwX79+3Wz9tLQ01qxZw4ULFyhSpAiNGzdmzpw5ZkM2e3t788knnzBv3jxGjBiBh4cHXbt2ZWB+uMSpiIjIfUpNhfnzYdo0uHTJuKxsWXjtNRg50jiccrbSm9Js2ABLlxISFER7Pz9jk7OePVXQiEiBkyfNz2ydmp/ZNls55asctpkDbCeLcihHXuU4edJYf/z8s/F+3bowbhw8/zwUK2bZLLlJOZQjP+QA28oiRlZpfiYiIiL3LyXF2Mzs/feNI5uVKwdz5kCvXjq5IiJyNypqREREbMCxY8ZrAB44YLw/bBh8+in8MwioiIjchb73ERERsaKkJJg8GZo2NRY0lSrB1q2weLEKGhGRnNKZGhERESuJjDReCmPPHuP9V16B6dPB1dW6uURE8hsVNSIiIlZw+TJ06gS//AIVK8LXX0OGcWxEROQ+qKgRERGxsDNnoGNH+OMPqFPHeFHNChWsnUpEJP9SnxoRERELOnYM2rY1FjTNm8OuXSpoREQelooaERERC9mzB9q1g6tXjU3Ndu6E0qWtnUpEJP9TUSMiImIB27dDhw4QFQU9esDmzVCypLVTiYgUDCpqRERE8tjGjcZRzuLiYPBgWLsWnJysnUpEpOBQUSMiIpJbUlNhzRrw82MngJ8fx2du4/nnDSQnw2uvwZIlUETD9IiI5Ko8+7Pq7+/P6tWriYiIwMfHh1GjRtGwYcMs150+fTpbt27NtNzJyYktW7aY7icnJ7N8+XK2b99OREQE7u7uPPvsszzzzDMABAYGsm3bNv744w8MBgM1atRg2LBhNGjQIG8OUkREJN3169C9Oxw5AgkJtAdubf6RZ7bMIs5gx8C+8cya5YydnbWDiogUPHlS1ISEhDB37lzGjh1LgwYN2LhxIxMmTGDZsmWUKVMm0/qjRo3ipZdeMls2evToTEXQlClTuHHjBm+++SaPPPIIkZGRJCUlmR4/fPgwvr6+jB49mmLFirF27VrGjx/PwoULeeSRR/LiUEVERCAtzVjQ7N1rWmQAhrKUU4aaNOQI8/8Yg50hFOzUSEJEJLflSVGzZs0aunTpQrdu3QAYM2YM+/btIyAggBEjRmRa38XFxez+sWPHuHz5MhMnTjQt279/PwcPHmTFihW4ubkBULZsWbPt3nnnHbP7r7/+Ort372bfvn0qakREJO+sX288Q5PBDMaxnmdw4y/W8QzFj18Cf3/o3ds6GUVECrBc/7ooOTmZU6dO0axZM7PlzZo14/jx4zl6jqCgIHx8fKhfv75p2e7du6lVqxbfffcdffv2ZcCAAcyePZv4+Pi7ZklKSqKkhpcREZG8tHQpJCSY7n5PO95mOgD/xyCqc8b4+JIl1kooIlKg5fqZmujoaNLS0nB3dzdb7u7uzsGDB++5fUxMDN9//z3Dhw83W37lyhWOHTuGo6MjH3zwATExMcyZM4eIiAg++OCDLJ9ryZIlODs706ZNm2z3Z6fGzTbJVt4X5TBnKznAdrIoh7nCmmMn0P6f+UuU5zlWk4YDE5lKdzaZ1gsJCqKDlV6jwvreZEc5zClHZraURe7N5sZf2b59O2lpaXTq1MlsucFgwM7OjnfeecfUXG3MmDGMHz+eyMhIPDw8zNZfu3YtmzZtYsaMGZQoUSLb/RkMhtw/CHkodnZ2NvG+KIdt5gDbyaIcymHi5webN5OEI8/yHdcpQwd2MIV3zVZr7+eHITDQstko5O+NcijHA7ClLGJ0ryIz15ufubm5YW9vT1RUlNnyqKioTGdvshIUFMTjjz+Oq6ur2XIPDw9Kly5t1v+mcuXKAFy/ft1s3bVr17JkyRKmT59OnTp1HvRQREREcmboUHBy4i0+4Sce4xEusJL+OJB2ex0nJxg2zHoZRUQKsFwvahwdHalZsybh4eFmyw8cOGDWRyYrv/76K2fOnDENMJBR/fr1iYiIMOtDc+HCBQCzEdW+++47lixZwrRp0zSUs4iIWEbv3qx55HVm8xqOJLGGvnhx03ydRo2gZ0+rxBMRKejyZFzJvn37snXrVoKCgvjzzz+ZM2cON2/e5OmnnwZg6tSpTJ06NdN2gYGBPPLIIzRu3DjTY08++SSurq58/PHH/PHHHxw7doy5c+fSrl070xmgVatWsXDhQt566y0qVqxIZGQkkZGRxMTE5MVhioiIAHArxp7R0VMAmFlkAq24PbQzTk7QsiUEBIC9hnMWEckLedKnpn379ty6dYvly5cTGRmJj48P06dPNw3BfGdzMYC4uDhCQkIYNGhQls/p7OzMjBkzmDNnDq+88golS5bkscceM7u+jb+/PykpKUyePNls286dO/P222/n4hGKiIjc9uGHcO2GA61bG3j1jbaw7DQhQUG09/MzNjnr2VMFjYhIHrILDQ0tdL2gfH19TfPqBGZ7bKVznnLYZg6wnSzKoRwAp05B/fqQkgL79kH6FQ1s5fUA28miHMqRH3KAbWURo4wDBYSGhmZ6XF8biYiIPIQ33oDkZONYAXdcok1ERCxERY2IiMgD2rIFgoLA1RWy6CoqIiIWoqJGRETkASQlwdixxvn//hcyDMQpIiIWpqJGRETkAcyZY+xPU6sWjB5t7TQiIoWbihoREZH7dO0apA+0OWsWFC1q3TwiIoWdihoREZH7NGkS3LoFfn7Qtau104iIiIoaERGR+xAeDkuXgqOj8SyNiIhYn4oaERGRHDIYYMwY4+3YsVCjhrUTiYgIqKgRERHJsZUr4eefjSOdvfOOtdOIiEg6FTUiIiI5kJYGH31knP/oI+O1aURExDaoqBEREcmBLVvgxAmoUAEGDrR2GhERyUhFjYiISA7MmGG8fe01DeEsImJrVNSIiIjcQ3g4fP89lCwJL71k7TQiInInFTUiIiL38MknxtuRI8HNzbpZREQkMxU1IiIid3H2LKxdC0WKGJueiYiI7VFRIyIicheffWYc+ax/f3jkEWunERGRrKioERERyUZEBCxebJwfN866WUREJHsqakRERLLx5ZcQFwedO0PDhtZOIyIi2VFRIyIikoWEBJgzxzj/1lvWzSIiInenokZERCQLy5fD9evw6KPQvr2104iIyN2oqBEREblDWhp8+qlxftw4sLOzbh4REbk7FTUiIiJ32LQJfvsNKlWCvn2tnUZERO5FRY2IiMgd0i+2+frr4Oho3SwiInJvKmpEREQy2LMHwsKgVCkYPtzaaUREJCdU1IiIiGQwf77xduRIcHGxbhYREckZFTUiIiL/+PtvWLPGOK+zNCIi+YeKGhERkX+sWWO82Oa//gXVq1s7jYiI5JSKGhERkX8sXWq8HTrUujlEROT+qKgREREBTp+G3buheHHo08faaURE5H6oqBEREQGWLTPe9u0LJUtaNYqIiNwnFTUiIlLopabC//2fcV5Nz0RE8h8VNSIiUujt3AkXL0LVqvD449ZOIyIi90tFjYiIFHrpAwQMGQJ2dlaNIiIiD0BFjYiIFGpRUbBhg7GYGTzY2mlERORBqKgREZFCbdUqSEyEDh2gUiVrpxERkQehokZERAo1XZtGRCT/U1EjIiKF1i+/wP794OoKvXpZO42IiDwoFTUiIlJopV+bpl8/cHa2ahQREXkIKmpERKRQSk6G5cuN82p6JiKSv6moERGRQik4GK5dg9q1oWVLa6cREZGHoaJGREQKpYwDBOjaNCIi+ZuKGhERKXRu3IBNm8DBAQYOtHYaERF5WCpqRESk0Fm9GlJSoHNnKFfO2mlERORhqagREZFC57vvjLcvvGDdHCIikjtU1IiISKFy6RLs3g3FisHTT1s7jYiI5AYVNSIiUqisWwcGAzz1FJQsae00IiKSG1TUiIhIoZLe9OzZZ62bQ0REco+KGhERKTQuXoSwMHBygm7drJ1GRERyi4oaEREpNNasMd76+YGLi3WziIhI7lFRIyIihUZ607PnnrNuDhERyV0qakREpFD480/YsweKFzcOEiAiIgWHihoRESkU1q413nbrBiVKWDeLiIjkLhU1IiJSKGjUMxGRgktFjYiIFHjnzsG+fcYzNF27WjuNiIjkNhU1IiJS4KWPevb008Y+NSIiUrCoqBERkQJv9WrjrZqeiYgUTCpqRESkQDtzBg4cMF6XRk3PREQKJhU1IiJSoKU3PevRA5ycrJtFRETyhooaEREp0DTqmYhIwaeiRkRECqzTp+HQIXB1hU6drJ1GRETyiooaEREpsNT0TESkcFBRIyIiBZZGPRMRKRxU1IiISIH0229w9Ci4uUHHjtZOIyIieUlFjYiIFEjr1hlve/SAYsWsm0VERPKWihoRESmQ0ouaZ56xbg4REcl7KmpERKTA+eMPOHjQeMFNjXomIlLwqagREZECZ/16462fn0Y9ExEpDFTUiIhIgaOmZyIihYuKGhERKWDK8fPPxjM0XbtaO4uIiFhCkbx6Yn9/f1avXk1ERAQ+Pj6MGjWKhg0bZrv+4cOHmTdvHufOnaN06dL069eP7t2739dzJiUlMX/+fHbu3ElSUhJNmjRh7NixeHl55dVhioiILUhNNbY5W7aM0fRiDtC5wSVcipdD39+JiBR8efKXPiQkhLlz5/LCCy+wcOFC6tevz4QJE7h27VqW61+5coWJEydSv359Fi5cyPPPP8/s2bP54Ycf7us5v/jiC3bt2sW7777L559/TmxsLBMnTiQ1NTUvDlNERGzB9evw2GMwaBBs3sxxjG3Onjn8LrRpY3xcREQKtDwpatasWUOXLl3o1q0blStXZsyYMXh6ehIQEJDl+gEBAXh6ejJmzBgqV65Mt27d6Ny5M999912OnzMmJobNmzczcuRImjVrRs2aNZk0aRJnz57lwIEDeXGYIiJibWlp0L077N0LCQncoDQ/0A5Hkng6eb1xeffuxvVERKTAyvWiJjk5mVOnTtGsWTOz5c2aNeP48eNZbnPixIlM6zdv3pzffvuNlJSUHD3nqVOnSElJoXnz5qbHvb29qVSpEr/88ktuHJqIiNia9evhyBHT3QC6k4YDHdhJKaKNC48cAX9/6+QTERGLyPWiJjo6mrS0NNzd3c2Wu7u7ExUVleU2kZGRWa6fmppKdHR0jp4zMjISe3t73NzczNbx8PAgMjLyYQ9LRERs0dKlkJBgurvun6ZnvVl/e52EBFiyxNLJRETEgvJsoID8ws7OztoRJAu28r4ohzlbyQG2k0U5zFk6x06g/T/zf+HGDp7EnlR64m+2XkhQEB2s8BrZyvsCtpNFOcwphzlbyQG2lUXuLdeLGjc3N+zt7TOdlYmKisp0piWdh4dHlus7ODjg5uaGwWC453N6eHiQlpZGdHQ0pUqVMq0TGRlJgwYNss1rMBju5/DEAuzs7GzifVEO28wBtpNFOWwgh58fbN4MQCDdSKYoTxCKFzfNVmvv54chMNCi0WzlfQHbyaIcypEfcoBtZRGjexWZud78zNHRkZo1axIeHm62/MCBA9SvXz/LberWrZupM394eDi1atWiSJEiOXrOmjVrUqRIEbN1bty4wfnz56lXr15uHJqIiNiaoUONF6QB1tMbgGdYZ76OkxMMG2bpZCIiYkF5MvpZ37592bp1K0FBQfz555/MmTOHmzdv8vTTTwMwdepUpk6dalq/e/fu3Lx5k7lz5/Lnn38SFBTE1q1befbZZ3P8nC4uLjz11FMsWLCAAwcOcPr0aaZOnUrVqlVp2rRpXhymiIhYW+/e0KgRsRQnmC4A9GKD+TqNGkHPnpbPJiIiFpMnfWrat2/PrVu3WL58OZGRkfj4+DB9+nTKli0LwPU7rhlQrlw5pk2bxrx580zDO48ePZp27drl+DkBXn31VRwcHJg8eTKJiYk0adKEiRMn4uDgkBeHKSIi1mZvDwEBbHlsFvG/F6cVP1OBy8bHnJyMBU1AgHE9EREpsOxCQ0MLXYNBX19f07zaS9oeW2nHqhy2mQNsJ4ty2E6O/v0MrFptxye1F9Pk5HDa+/kZm5z17Gm1gsZW3hewnSzKoRz5IQfYVhYxytinJjQ0NNPjhX70MxERyd8SEiAwyPjP7pnNL1K16nCLDwogIiLWpfPxIiKSr+3YATEx8OijUKWKtdOIiIg1qKgREZF8bd0/g5317m3dHCIiYj0qakREJN9KToaNG43zzzxj3SwiImI9KmpERCTfCg2FqCioU8c4iYhI4aSiRkRE8q3vvjPeZrismYiIFEIqakREJF9KTob1643zfftaN4uIiFiXihoREcmXdu40Nj2rV884iYhI4aWiRkRE8qXVq423anomIiIqakREJN9JSoING4zzKmpERERFjYiI5Dvbt0N0NDRsCLVrWzuNiIhYm4oaERHJdzTqmYiIZKSiRkRE8pXERPD3N85r1DMREQEVNSIiks9s2wa3bkHjxlCzprXTiIiILVBRIyIi+YqanomIyJ1U1IiISL6RkAAbNxrnVdSIiEg6FTUiIpJvBAfD339D06ZQrZq104iIiK1QUSMiIvmGmp6JiEhWVNSIiEi+EB8PAQHGeY16JiIiGamoERGRfGHLFoiNhebNoUoVa6cRERFboqJGRETyBTU9ExGR7KioERERmxcXB5s2GefV9ExERO6kokZERGxeUJCxsGnVCipXtnYaERGxNSpqRETE5qnpmYiI3I2KGhERsWl//208UwPQp491s4iIiG1SUSMiIjZtzRrjcM7/+hdUrGjtNCIiYotU1IiIiE1butR4O3SodXOIiIjtUlEjIiI26/Rp2L0bSpTQqGciIpI9FTUiImKzli0z3vbtCy4uVo0iIiI2TEWNiIjYpNRU+Ppr47yanomIyN2oqBEREZu0YwdcugTVqhkHCRAREcmOihoREbFJ6QMEDBkCdnZWjSIiIjZORY2IiNicqCjw9zcWM4MGWTuNiIjYOhU1IiJic1auhMRE6NABKlWydhoREbF1KmpERMTm6No0IiJyP1TUiIiITTl+HMLDwc0NevWydhoREckPVNSIiIhNSb82Tb9+4Oxs1SgiIpJPqKgRERGbkZwMy5cb59X0TEREckpFjYiI2IwtW+D6dahTB1q0sHYaERHJL1TUiIiIzcg4QICuTSMiIjmlokZERGzC9esQGAgODjBwoLXTiIhIfqKiRkREbMKKFZCSAl27Qtmy1k4jIiL5iYoaERGxOoNB16YREZEHp6JGRESsLiQEjh0Db2/o1s3aaUREJL9RUSMiIlY3Y4bxdvRoKFrUullERCT/UVEjIiJWdewYBAdD8eLwyivWTiMiIvmRihoREbGq9LM0w4aBp6d1s4iISP6kokZERKzm4kX49luwt4c33rB2GhERya9U1IiIiNXMnm0cxrlPH6hSxdppREQkv1JRIyIiVnHrFixYYJwfN866WUREJH9TUSMiIlbx1VfGwqZdO2je3NppREQkP1NRIyIiFpeUBJ99Zpx/6y2rRhERkQJARY2IiFjc6tVw6RLUqQNdu1o7jYiI5HcqakRExKIMBvjkE+P8uHHGkc9EREQehv6ViIiIRW3bZrzgZrly8MIL1k4jIiIFgYoaERGxqPSLbY4ZA8WKWTeLiIgUDCpqRETEYg4dgh07oEQJGDnS2mlERKSgUFEjIiIWk96XZsQIcHe3bhYRESk4VNSIiIhFhIfDqlXg6Ahjx1o7jYiIFCQqakREJM8ZDMY+NAYDvPYaVK5s7UQiIlKQqKgREZE89+238PPPUKYMvPuutdOIiEhBo6JGRETyVEwMjB9vnJ82DVxdrZtHREQKHhU1IiKSp6ZNg8uXoXlzGDzY2mlERKQgUlEjIiJ55uxZ+PRT4/zs2WCv/zoiIpIH9O9FRETyzJtvQmIiDBwIrVpZO42IiBRUKmpERCRP7NgB/v7GC21On27tNCIiUpCpqBERkVyXnGwcuhngnXegfHnr5hERkYJNRY2IiOS6L7+EEyegWjV4/XVrpxERkYJORY2IiOSqGzfgvfeM8zNnQrFi1s0jIiIFn4oaERF5cKmpsGYN+PmxE8DPjwnP/cFff0GnTvD001bOJyIihUKR3H7CpKQk5s+fz86dO0lKSqJJkyaMHTsWLy+vbLfp168f165dy7S8ZcuWTM/QuzQiIoKvvvqKvXv3EhcXR/ny5Rk7diyNGzcmJSWFxYsXs2/fPi5fvkzx4sVp3LgxL730EmXKlMntwxQRkevXoXt3OHIEEhJoD/zfZk+WUoWidkl89u7f2Nl5WjuliIgUArle1HzxxReEhYXx7rvv4urqyrx585g4cSILFizAwcEhy23mz59PWlqa6X5ERAQjR47kiSeeMC2LiYlh9OjR1K9fn2nTplGqVCkuX76Mu7s7AAkJCZw+fZoXXniB6tWrExsby5dffsmECRNYvHhxtvsWEZEHkJZmLGj27jUtOkJDRrIAgLmGV6kz7hj89JMuTiMiInkuV4uamJgYNm/ezPjx42nWrBkAkyZNol+/fhw4cIAWLVpkuV2pUqXM7m/evJnixYvj6+trWrZy5Uo8PDyYNGmSaVm5cuVM8y4uLsyYMcPsed544w2GDh3Kn3/+SdWqVR/28EREJN369cYzNP/4CzeeYR0JODOUJQxnERxxMo7p3Lu39XKKiEihkKtfn506dYqUlBSaN29uWubt7U2lSpX45ZdfcvQcBoOBzZs307FjR4pl6F0aFhZGnTp1+OCDD+jVqxfDhw9nw4YNGAyGbJ8rLi4OgJIlSz7gEYmISJaWLoWEBADSsGMQ/8cZqvMoB/mCV7ED4+NLllg1poiIFA65eqYmMjISe3t73NzczJZ7eHgQGRmZo+cIDw/nypUr+Pn5mS2/fPkyGzdupG/fvjz//PP8/vvvzJ49G4BevXplep7k5GTmzZtHmzZt7tqfx87OLke5xLJs5X1RDnO2kgNsJ0thzbETaP/P/HTeZhPdKUUUa+mDMwmm9UKCguhghdeosL4vd2MrWZTDnHKYs5UcYFtZ5N5yVNQsXryYb7755q7rzJo1K1cCBQUFUbt2bapXr2623GAwUKtWLUaMGAFAjRo1uHjxIv7+/pmKmtTUVD766CNiYmL46KOP7rq/u53pEeuws7OzifdFOWwzB9hOlkKdw88PNm9mBx14lykAfMMAqvKH2Wrt/fwwBAZaNFqhfl+yYStZlEM58kMOsK0sYnSvIjNHRU2fPn3o2LHjXdfx9vbmxIkTpKWlER0dbdZPJjIykgYNGtxzP1FRUYSFhfFa+mWoM/D09KRy5cpmyypXrsz69evNlqWmpjJlyhTOnj3LZ599lumskYiI5IKhQ7mw8xT9E1eShgPvMhk/Npuv4+QEw4ZZJ5+IiBQqOSpq3NzcclQc1KxZkyJFihAeHs6TTz4JwI0bNzh//jz16tW75/bBwcE4OjrSoUOHTI/Vq1ePCxcumC27ePGi2XDNKSkpTJ48mXPnzjFr1iw8PDzuuU8REbl/iX696VOkDjcTvejEVt7jg8wrNWoEPXtaPJuIiBQ+uTpQgIuLC0899RQLFizgwIEDnD59mqlTp1K1alWaNm1qWm/QoEFs2LDBbNv0AQLat2+Ps7Nzpufu27cvJ06c4JtvvuHSpUt8//33rF+/nh49egDGMzTvv/8+v/76K++88w52dnZERkYSGRlJYmJibh6miEihlpwMw4bbsy+2HpWKXuHbYsNw4Paw/Dg5QcuWEBCg4ZxFRMQicv06Na+++ioODg5MnjyZxMREmjRpwsSJE82uE3PhwgWio6PNtjt8+DAXL140G7I5o9q1azNlyhQWLVrE//3f/1GmTBmGDh1Kz3++Bbxx4wZhYWEAjBw50mzbCRMm0KVLl1w8ShGRwikhAZ57zlivlCgB60LK4HlhNixdSkhQEO39/IxNznr2VEEjIiIWYxcaGlroekFlvP6NOoHZHlvpnKcctpkDbCdLYctx6xb06AHffw/u7rBli/GEjKVz3ItyZGYrWZRDOfJDDrCtLGKUcaCA0NDQTI/n+pkaEREpeG7ehK5dITwcypWDbdugfn1rpxIRETFSUSMiInd18SJ07AgnT0LVqrBjB1SpYu1UIiIit6nBs4iIZOv0aXjsMWNB06AB7N6tgkZERGyPihoREcnSzz9D27Zw/jy0amXsS1OunLVTiYiIZKaiRkREzMTFwbhxxoLm+nVj07Pt20GX/hIREVulokZEREx27TJeM/PTT433x4+HTZvAxcW6uURERO5GAwWIiAgxMfD22/DFF8b79evDkiXQvLl1c4mIiOSEztSIiBRyO3YYi5gvvoAiReC//zUO3ayCRkRE8gudqRERKYQMBggNhRkzjBfRBHj0UVi61Nj8TEREJD9RUSMiUoikpMDatfDJJ3DwoHGZszP85z/G/jOOjtbNJyIi8iDU/ExEJD9KTYU1a8DPj50Afn7GaiUtLcvVY2Lg88+henXo399Y0Hh5weTJcOGCsahRQSMiIvlVrp+pSUpKYv78+ezcuZOkpCSaNGnC2LFj8fLyynabuLg4lixZwu7du4mKiqJGjRqMGjWK2rVrm6134cIFFi5cyMGDB0lJSaFSpUr85z//oXLlymbrGQwG3n77bfbt28f7779Pu3btcvswRUSs5/p16N4djhyBhATaA2zeDCEhxvZkAQHg7U1sLGzbBv7+sHEjREcbN69ZE958EwYONJ6lERERye9yvaj54osvCAsL491338XV1ZV58+YxceJEFixYgIODQ5bbfPLJJ5w9e5a3334bLy8vtm/fzrhx41i6dKmpGLpy5QqjR4+mU6dOzJw5ExcXF86fP49zFv+Rv/vuO+zs7HL70ERErC8tzVjQ7N2b+bGEBG7sPUNg6wX413uHbdvtSEi4/XCbNvDWW8bN7XWeXkRECpBc/bcWExPD5s2bGTlyJM2aNaNmzZpMmjSJs2fPcuDAgSy3SUxMZNeuXYwYMYLGjRtToUIFhgwZQvny5QkICDCtt2jRIpo1a8a///1vatasSfny5WnVqhXe3t5mz3fy5EnWrVvHhAkTcvPQRESM7rPZV65bv954hgYwAOepyFqeYTwf05YfKctVhp19l4BNxoKmZUuYNg1OnICwMOjZUwWNiIgUPLn6r+3UqVOkpKTQPMM4oN7e3lSqVIlffvkly21SU1NJS0ujaNGiZsuLFSvGsWPHAEhLS+Pnn3/Gx8eH8ePH07NnT15++WVCQkLMtomLi+PDDz/kzTffxN3dPTcPTfKatT8oKodt57CVLNevw2OPwaBBsHnz7WZfAwcaT4Ncv55nu05JgbNnIfh/R5ma8Do98Kc8l6nMefqylk8YTxhtcSCVLmxhfv25XLoEe/YYrz9Tp06eRRMREbG6XG1+FhkZib29PW5ubmbLPTw8iIyMzHKb4sWLU69ePb755huqVKmCh4cHISEhnDhxggoVKgDw119/ER8fz4oVKxg6dCgvvfQSBw8e5KOPPsLZ2ZnWrVsDMHPmTFq0aEHLli1znFnN1KzPCwgAGgHOYPqgGL95M0eA7sAN5Si0OWwlix3wE9AqqwcTEmDvXvaUKUMbjGdQ7p89xiMt989UBagO1PhnqgIUBSabbeVOJC3YZ5oeZxeu/E3IcahQYfQDJXkYtvI3VTkys5UsymFOOczZSg6wrSxybzkqahYvXsw333xz13VmzZr1wCEmTpzI//73P5599lns7e2pWbMm7du359SpU4DxTA1AmzZtePbZZwGoXr06v/32G/7+/rRu3Zpt27Zx5swZFixYcF/7Nhge7OOH5JK0NOM33Fn0D3DG+AHyesuW8NNPedtmRjlsM4ctZVm71nhGJmMnlTs0L1acvxatJLZDd2JiIDYW/v4boqLgr7+Mtxnnb9yAq1fhyhXjSZ57nXSqUAFqxB+lYWQoLdhHS/ZSjTNk9W+3vZ8fhsDAhzni+2ZnZ2cTf1OVIzNbyaIcypEfcoBtZRGjexWZOSpq+vTpQ8eOHe+6jre3NydOnCAtLY3o6GhKlSpleiwyMpIGDRpku22FChX4/PPPiY+PJy4uDk9PTz744APKlSsHgJubGw4ODvj4+JhtV7lyZVMTtIMHD/Lnn3/StWtXs3UmT55M3bp1mTNnTk4O1eLOn4fDh62dworCfoaDjwDe2a9zsCj8Zy/8c0ZOOcxzPOjf3Ltu99MeOFgJKJt5u/SP0AeLYnh7H7S6fe4i43Peaz4ntwYDGPaGYzhYDwO1MGCXaUrDHsOBoqS9fARD40dJS+OuU2qqcUpJyTyfkmKckpMzT0k/VyExYTOJFCMBJxIpZpqPx5lYSpCY6AQD7/3aZ6d0aShbFsqVg0qVoEaN21O1alC8OLD2FAx8+67FFU5OMGzYgwcRERHJZ3JU1Li5uWVqUpaVmjVrUqRIEcLDw3nyyScBuHHjBufPn6devXr33N7Z2RlnZ2f+/vtv9u/fz8iRIwFwdHSkdu3aXLhwwWz9ixcvUras8UPXiy++yHPPPWf2+LBhw3j55Zd57LHHcnKYVrFjB7z4orVTWNNj/0x3kQxMVw7L5mjzz3SPHJ/kdQ6AFv9Md5ECLMzrHE3vuYYdaRR3SKSEpzMuLlCiBLi4gLv77alUqdu3pUsbC5hy5cDbG+7oWpi13r2NwzZnNfpZukaNjCMCiIiIFBK52qfGxcWFp556igULFuDu7m4a0rlq1ao0bXr7A8GgQYPo1asXvXr1AmDfvn0YDAYqVarEpUuXmD9/PpUqVTI769KvXz8++OADGjRoQJMmTTh06BAhISFMmTIFAC8vryyvhePt7U358uVz8zBzVcWK8PTT1k5hRT+FQUTEvdfzLG1sgqQcWeZ40Ga/2W63ezdE3Mx+u/ReI6W9sPtX22yf817zObm127Edu+tXszhHY8CetNu35cth36M79vbG7eztwcHBeHvn5OAARYoYb++cd3TMZvrwPZzCf6QYiTiR8M95GuO8EwmUIBZn4rHr4gd52ezL3t54HZoM16kxcXIyFjQBARriTERECpVcv07Nq6++ioODA5MnTyYxMZEmTZowceJEs2vUXLhwgej0q8ABsbGxLFq0iBs3blCyZEkef/xxXnzxRYoUuR2vbdu2vPnmm6xYsYK5c+fyyCOPMHHiRNMgAflVx47GqdDym2ocPepeWvlBQB5+UFSOO3JMy1mOln6wPo/7bfh9lrMsj/rBvO55lyO5AQz8n200+/L2NvYh2rABli4lJCiI9n5+xn1rzGYRESmE7EJDQwtdLyhfX1/TvDqBWVkOOl/j5AQrVhib3ShH4cphS1nuMmCBiaUGT7iDrXRoVQ7bzAG2k0U5lCM/5ADbyiJGGQcKCA0NzfS4vs4T6+rd29hc5m4s0T9AOWwzhy1lSW/21bKlsYjKyMnJuFzNvkRERKxC/33Fumzlg6Jy2GYOW8uS3uzrm2/Az48QMF4EdMUK43Lvu4xaJyIiInlGRY1Yn618UFQO28xha1ns7eGZZyAwkA5gHBSgd2+doREREbEi9alRe0mbYyvtWJXDNnOA7WRRDuXIDznAdrIoh3LkhxxgW1nESH1qRERERESkQFNRIyIiIiIi+VquX6cmv8l4Kktsh628L8phzlZygO1kUQ5zymHOVnKA7WRRDnPKYc5WcoBtZZF705kaERERERHJ11TUiIiIiIhIvlYom59lNWKCiIiIiIjkTzpTIyIiIiIi+ZqKGhERERERydcKZfMzyR8iIyOZP38+4eHhxMXFUaFCBfr160fHjh0tluHq1av0798/y8dGjhxJv379LJYF4Ndff2Xx4sX88ssv2NnZUbVqVT766CPc3NwsmmPs2LEcOXLEbJmvry///e9/LZojncFg4O2332bfvn28//77tGvXzqL7nzFjBocOHeLmzZs4OztTr149XnrpJSpXrmyxDLdu3WLZsmWEh4dz7do13NzcaN26NcOGDbP4z8emTZsICQnh9OnTxMbGsnLlSsqWLWuRffv7+7N69WoiIiLw8fFh1KhRNGzY0CL7TnfkyBG+++47Tp06xc2bN5kwYQJdunSxaIYVK1bw448/cuHCBRwdHalbty4jRoygSpUqFs2xYcMGAgMDuXr1KgA+Pj4MGDCA1q1bWzTHnVasWMGiRYvo2bMnr732mkX3vWzZMr7++muzZe7u7qxfv96iOQAiIiL46quv2Lt3L3FxcZQvX56xY8fSuHFji2Xo168f165dy7S8ZcuWTJ8+3WI5UlNT+frrr9m+fTsRERF4enry5JNPMmTIEBwcHCyWQx6cihqxWdOmTePWrVt8+OGHlCpVit27dzNt2jS8vb1p1KiRRTJ4eXmxbt06s2U//vgjn3/+ucU/OJ84cYLx48fTr18/Xn31VYoUKcIff/xhtT+2Xbp0YcSIEab7RYsWtUoOgO+++86qQ2/WrFmTTp064e3tza1bt/j6668ZN24cK1eupEgRy/yZjYiI4ObNm4wcORIfHx9u3LjBZ599xocffsgnn3xikQzpEhMTadasGY899hhffPGFxfYbEhLC3LlzGTt2LA0aNGDjxo1MmDCBZcuWUaZMGYvliI+Px8fHh06dOjFt2jSL7Tejw4cP06NHD2rXro3BYGDp0qW8+eabLFu2DFdXV4vl8PLy4qWXXuKRRx4hLS2NrVu38u6777JgwQKqVatmsRwZnThxgsDAQKpWrWqV/QNUrFiRzz77zHTf3t7yDWdiYmIYPXo09evXZ9q0aZQqVYrLly/j7u5u0Rzz588nLS3NdD8iIoKRI0fyxBNPWDTHypUr8ff35+2336Zq1aqcOXOG6dOn4+joyKBBgyyaRR6MihqxWcePH2fMmDHUrVsXgGeffZb169dz8uRJixU1Dg4OeHh4mC378ccfadq0KeXKlbNIhnTz5s2jZ8+eDBgwwLSsYsWKFs2QkZOTU6bXxhpOnjzJunXrWLBgAb1797ZKhu7du5vmy5Yty7Bhwxg+fDiXL1+mUqVKFslQpUoVJk+ebLpfoUIFXn75ZSZNmkRsbCwlSpSwSA6APn36APDbb79ZbJ8Aa9asoUuXLnTr1g2AMWPGsG/fPgICAswK8LzWqlUrWrVqBWDRb5ozurOQnTRpEt26deP48eO0adPGYjnatm1rdn/48OEEBATwyy+/WKWoiYmJ4aOPPmL8+PGZzpZYUlb/Wyxt5cqVeHh4MGnSJNMyS/9fAyhVqpTZ/c2bN1O8eHF8fX0tmuOXX36hdevWpt+PsmXL0qZNG3799VeL5pAHpz41YrMaNGjA999/T3R0NGlpaezevZu//vqLpk2bWi3T5cuXOXjwoOlDk6VERUXxyy+/4OnpyejRo+nVqxdjxozhwIEDFs2RUUhICD169GDIkCF8+eWXxMXFWTxDXFwcH374IW+++abFv13MTnx8PMHBwZQpU8ZiTa6yExcXh6OjI05OTlbNYQnJycmcOnWKZs2amS1v1qwZx48ft1Iq2xEXF0daWholS5a0WobU1FRCQkKIj4+nfv36Vsnw6aef8vjjj/Poo49aZf/prly5Qp8+fejfvz+TJ0/m8uXLFs8QFhZGnTp1+OCDD+jVqxfDhw9nw4YNGAwGi2dJZzAY2Lx5Mx07dqRYsWIW3XeDBg04fPgw58+fB+DcuXMcOnSIli1bWjSHPDidqRGb9d577zFlyhR69uyJg4MDjo6OvPPOO1SvXt1qmYKCgihVqhSPPfaYRfd75coVwNgWe+TIkdSoUYPvv/+e8ePHs2DBAou/Jh06dKBMmTKULl2ac+fOsXDhQs6ePWvxZk4zZ86kRYsWNvFPx9/fnwULFpCQkEDFihX59NNPrdokLyYmhiVLluDn51co2oOnf/lxZ3Hr7u7OwYMHrZTKdsyZM4fq1aubznxb0tmzZ3n11VdJSkrC2dmZyZMnW6XpV2BgIJcuXeI///mPxfedUZ06dZgwYQKVKlXir7/+Yvny5YwaNYqlS5datP/b5cuX2bhxI3379uX555/n999/Z/bs2QD06tXLYjkyCg8P58qVK/j5+Vl83/379ycuLo4hQ4Zgb29PamoqAwYMoGfPnhbPIg9GRY1Y1OLFi/nmm2/uus6sWbNo3LgxixcvJjo6mhkzZuDm5kZYWBjTp0/ns88+e+gP8feTI11qairBwcF06tQp1/pJ5DRH+v66devGU089BUCNGjU4fPgwmzZt4vXXX7dYlsaNG/P000+bllWtWpVy5crx73//m1OnTlGzZk2L5Lh+/TpnzpxhwYIFD7W/h82R/jPy5JNP0qxZMyIiIvjuu+94//33mTNnzkOfJXmQn9X4+HgmTZpE6dKlefnllx9q/w+TQ2zDF198wfHjx5k9e7ZVCtyKFSuyaNEiYmJi2LVrl+nvuCUHLTh//jyLFi1i9uzZFuvnlp07v4SpW7cuzz//PFu3buXZZ5+1WA6DwUCtWrVMTTNr1KjBxYsX8ff3t1pRExQURO3ata3y5WVoaCjbtm3jnXfewcfHh99//525c+dStmxZqxRZcv9U1IhF9enT556jl3l7e3Pp0iU2bNjAwoULTX/cqlevztGjR9mwYQNvvfWWRXJk9NNPPxEZGZmrf9xymiMqKgowjhyUUeXKlbMcNSYvs2SlVq1a2Nvbc/HixYcuanKaIzg4mD///JOuXbuaPTZ58mTq1q3LnDlzLJIjnYuLCy4uLjzyyCPUrVuX7t27s2vXLjp16mTRHPHx8bz99tuAcbCN3Dpb9DA/H5bg5uaGvb296XclXVRUlM00TbSGL774gpCQEGbNmkX58uWtksHR0ZEKFSoAxr8VJ0+eZM2aNYwfP95iGU6cOEF0dDRDhw41LUtLS+Po0aMEBASwZcsWq51ZdXZ2xsfHh0uXLll0v56enplGaKxcubJVRmED4+9qWFiYxUejSzd//nyeffZZ2rdvDxi/sLt27Rrffvutipp8QkWNWJSbm1uOTq8nJiYCZPpW0d7e3myUlLzOkVFQUBCNGjXK1c75Oc1RtmxZSpcuzYULF8yWX7x4Mde+7XyQ1yTd2bNnSUtLw9PT02I5XnzxRZ577jmzZcOGDePll1/OleaBD/N6GAwGDAYDycnJFs0RFxfHhAkTMBgM/O9//8PZ2fmh9/8gOazB0dGRmjVrEh4ebjZq0oEDB3j88cetF8yK5syZQ2hoKLNmzbLYgBU5kVu/G/ejbdu21KpVy2zZxx9/TIUKFRgwYACOjo4WzZNRUlIS58+ft/hZznr16mX5P8WSIwVmFBwcjKOjIx06dLDK/hMTE7P8zGHNPkZyf1TUiE2qVKkSFSpU4LPPPuPll1/G1dWVsLAwDhw4wIcffmjxPNeuXWP//v2mb8Atzc7Ojueee45ly5ZRtWpVatSoQWhoKCdOnGDMmDEWzXLp0iV27NhBq1atcHNz49y5c3z55ZfUqFHDop1/vby88PLyyrTc29vbot9IX7p0iV27dtGkSRNKlSrFjRs3WLlyJY6Ojha9FkdcXBxvvfUWsbGxfPjhhyQkJJCQkABAyZIlLfqhLTIyksjISNMHpnPnzhETE4O3t3eeDifct29fpk2bRp06dahfvz4BAQHcvHnTrLmkJcTHx5u+dTcYDFy7do3ff/+dkiVLWuwD42effcb27duZMmUKJUuWJDIyEjCeFcjNYvdevvrqK1q1aoW3tzdxcXHs3LmTw4cPW3yo6/QzqRk5OTnh6upq8Wv3fPnll7Ru3ZoyZcoQFRXF8uXLSUhIoHPnzhbN0bdvX0aNGsU333yDr68vp0+fZv369bz44osWzQG3Bwho3769RX8+M2rdujXffvstZcuWpUqVKpw+fZo1a9Y89Nl2sRy70NBQlaBiky5evMhXX33F8ePHiY+Pp3z58vTt29fiF7EDWLp0KRs2bGDt2rVW7fydPo7+rVu38PHxYfjw4RYfDe769et89NFHnDt3jvj4eLy8vGjVqhWDBw+26PUvsuLr62vxi29ev36dTz/9lFOnThETE4O7uzsNGzZk0KBBFv12/PDhw9n2rbJ0X5esLi4IWOQilP7+/qxatYrIyEh8fHx49dVXLTYEfLrs3ovOnTtb7IuR7IbDHTx4MEOGDLFIBjAOaX348GEiIyMpUaIEVatW5bnnnqNFixYWy5CdsWPHUqVKFYs3d5o8eTJHjx4lOjqaUqVKUadOHYYNG5apebEl/PzzzyxatIgLFy5QpkwZevbsSe/evS1+3a9Dhw7xxhtvMG/ePOrUqWPRfaeLi4tjyZIl7N69m6ioKDw9PfH19WXw4MFW/b8vOaeiRkRERERE8jVdp0ZERERERPI1FTUiIiIiIpKvqagREREREZF8TUWNiIiIiIjkaypqREREREQkX1NRIyIiIiIi+ZqKGhERERERyddU1IiIiIiISL6mokZERERERPK1/weODsSJh14hVwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def tanh(x):\n",
    "    return np.tanh(x)\n",
    "\n",
    "plot_curve(tanh, 6, -6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "wooden-hayes",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999092042625951"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tanh(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "robust-maryland",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.9999092042625951"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tanh(-5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "welsh-transportation",
   "metadata": {},
   "source": [
    "#### Properties of the Tanh Function\n",
    "* The Tanh function maps the real axis to (-1,1)\n",
    "* The output values are symetrically about the origin\n",
    "* The output value approaches 1 and -1 quickly at small input deviation from zero"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "analyzed-worry",
   "metadata": {},
   "source": [
    "#### Keras Implementation\n",
    "https://keras.io/api/layers/activations/#tanh-function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "chicken-nicholas",
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "model = Sequential()\n",
    "model.add(Dense(64, activation='tanh'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reflected-marijuana",
   "metadata": {},
   "source": [
    "#### PyTorch Implementation\n",
    "https://pytorch.org/docs/stable/generated/torch.nn.Tanh.html#torch.nn.Tanh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "handled-termination",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-0.7616,  0.0000,  0.7616], dtype=torch.float64)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "a = nn.Tanh()\n",
    "t = torch.from_numpy(np.array([-1.0,0,1.0]))\n",
    "a(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "exotic-carolina",
   "metadata": {},
   "source": [
    "#### TensorFlow Implementation\n",
    "* tf.tanh\n",
    "* tf.math.tanh https://www.tensorflow.org/api_docs/python/tf/math/tanh\n",
    "* tf.keras.activations.tanh https://www.tensorflow.org/api_docs/python/tf/keras/activations/tanh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "preliminary-reasoning",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(1,), dtype=float32, numpy=array([-0.99990916], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(3,), dtype=float32, numpy=array([-0.99990916,  0.        ,  0.99990916], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(1,), dtype=float32, numpy=array([-0.99990916], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(3,), dtype=float32, numpy=array([-0.99990916,  0.        ,  0.99990916], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(1,), dtype=float32, numpy=array([-0.99990916], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(3,), dtype=float32, numpy=array([-0.99990916,  0.        ,  0.99990916], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "t1 = tf.constant([-5], dtype=tf.float32)\n",
    "t2 = tf.constant([-5, 0, 5], dtype=tf.float32)\n",
    "\n",
    "display(tf.tanh(t1))\n",
    "display(tf.tanh(t2))\n",
    "display(tf.math.tanh(t1))\n",
    "display(tf.math.tanh(t2))\n",
    "display(tf.keras.activations.tanh(t1))\n",
    "display(tf.keras.activations.tanh(t2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "czech-exclusive",
   "metadata": {},
   "source": [
    "## SoftPlus"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "third-ethnic",
   "metadata": {},
   "source": [
    "#### Mathematical Expression\n",
    "$$a = f(x) = \\log{(e^{x}) + 1)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "comprehensive-range",
   "metadata": {},
   "source": [
    "#### Visualizaiton with Numpy Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "naval-preserve",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def softplus(x):\n",
    "    return np.log(np.exp(x) + 1)\n",
    "\n",
    "plot_curve(softplus, 8, -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "final-pearl",
   "metadata": {},
   "source": [
    "#### Keras Implementation\n",
    "https://keras.io/api/layers/activations/#softplus-function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "white-wagner",
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "model = Sequential()\n",
    "model.add(Dense(64, activation='softplus'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "featured-funds",
   "metadata": {},
   "source": [
    "#### PyTorch Implementation\n",
    "https://pytorch.org/docs/stable/generated/torch.nn.Softplus.html#torch.nn.Softplus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "continent-surgery",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.3133, 0.6931, 1.3133], dtype=torch.float64)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "a = nn.Softplus()\n",
    "t = torch.from_numpy(np.array([-1.0,0,1.0]))\n",
    "a(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tested-illustration",
   "metadata": {},
   "source": [
    "#### TensorFlow Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "generic-alarm",
   "metadata": {},
   "source": [
    "## SoftSign"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "missing-visibility",
   "metadata": {},
   "source": [
    "#### Mathematical Expression\n",
    "$$a = f(x) = \\frac{x}{|x|+1}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "impressive-layer",
   "metadata": {},
   "source": [
    "#### Visualizaiton with Numpy Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "illegal-mission",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def softsign(x):\n",
    "    return x / (np.abs(x) + 1)\n",
    "\n",
    "plot_curve(softsign)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "large-delicious",
   "metadata": {},
   "source": [
    "#### Keras Implementation\n",
    "https://keras.io/api/layers/activations/#softsign-function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "indie-panama",
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "model = Sequential()\n",
    "model.add(Dense(64, activation='softsign'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "turned-citation",
   "metadata": {},
   "source": [
    "#### PyTorch Implementation\n",
    "https://pytorch.org/docs/stable/generated/torch.nn.Softsign.html#torch.nn.Softsign"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "fleet-turning",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-0.5000,  0.0000,  0.5000], dtype=torch.float64)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "a = nn.Softsign()\n",
    "t = torch.from_numpy(np.array([-1.0,0,1.0]))\n",
    "a(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sustainable-hepatitis",
   "metadata": {},
   "source": [
    "#### TensorFlow Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "northern-bradford",
   "metadata": {},
   "source": [
    "## SoftMax"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "focal-trick",
   "metadata": {},
   "source": [
    "#### Mathematical Expression\n",
    "$$f(x_i) = \\frac{e^{x_i}}{\\sum_{k=1}^{N}e^k}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "opposed-failing",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'SoftMax Activation Function')"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def softmax(x):\n",
    "    return np.exp(x) / sum(np.exp(x))\n",
    "\n",
    "x1 = np.linspace(-10,10,100)\n",
    "y1 = softmax(x1)\n",
    "\n",
    "x2 = np.arange(-8,9,step=1)\n",
    "y2 = softmax(x2)\n",
    "\n",
    "plt.figure(figsize=(12,4))\n",
    "plt.style.use('grayscale')\n",
    "_ = plt.bar(x1, y1, color='b')\n",
    "_ = plt.bar(x2, y2, color='r')\n",
    "\n",
    "plt.xticks(x2)\n",
    "plt.yticks(y2[-4:])\n",
    "plt.title(\"SoftMax Activation Function\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "hungry-narrow",
   "metadata": {},
   "source": [
    "#### Properties of the SoftMax Function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ordinary-operator",
   "metadata": {},
   "source": [
    "#### Keras Implementation\n",
    "https://keras.io/api/layers/activations/#softmax-function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "vietnamese-pacific",
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "model = Sequential()\n",
    "model.add(Dense(64, activation='softmax'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "diverse-pricing",
   "metadata": {},
   "source": [
    "#### PyTorch Implementation\n",
    "https://pytorch.org/docs/stable/generated/torch.nn.Softmax.html#torch.nn.Softmax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "conventional-projector",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.0900, 0.2447, 0.6652], dtype=torch.float64)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "a = nn.Softmax(dim=-1)   # NOTE that axis dimension is required, supply -1 if using array\n",
    "t = torch.from_numpy(np.array([-1.0,0,1.0]))\n",
    "a(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "stupid-shift",
   "metadata": {},
   "source": [
    "#### TensorFlow Implementation\n",
    "* tf.nn.softmax https://www.tensorflow.org/api_docs/python/tf/nn/softmax\n",
    "* tf.keras.activations.softmax https://www.tensorflow.org/api_docs/python/tf/keras/activations/softmax\n",
    "* tf.keras.layers.Softmax https://www.tensorflow.org/api_docs/python/tf/keras/layers/Softmax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "supported-wheel",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(1,), dtype=float32, numpy=array([1.], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(3,), dtype=float32, numpy=array([0.09003057, 0.24472848, 0.66524094], dtype=float32)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "t1 = tf.constant([-1.0], dtype=tf.float32)\n",
    "t2 = tf.constant([-1.0, 0, 1.0], dtype=tf.float32)\n",
    "\n",
    "display(tf.nn.softmax(t1))\n",
    "display(tf.nn.softmax(t2))"
   ]
  }
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